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Sample records for wmap observations bayesian

  1. WMAP haze: Directly observing dark matter?

    International Nuclear Information System (INIS)

    Forbes, Michael McNeil; Zhitnitsky, Ariel R.

    2008-01-01

    In this paper, we show that dark matter in the form of dense matter/antimatter nuggets could provide a natural and unified explanation for several distinct bands of diffuse radiation from the core of the Galaxy spanning over 13 orders of magnitude in frequency. We fix all of the phenomenological properties of this model by matching to x-ray observations in the keV band, and then calculate the unambiguously predicted thermal emission in the microwave band, at frequencies smaller by 11 orders of magnitude. Remarkably, the intensity and spectrum of the emitted thermal radiation are consistent with - and could entirely explain - the so-called 'WMAP haze': a diffuse microwave excess observed from the core of our Galaxy by the Wilkinson Microwave Anisotropy Probe (WMAP). This provides another strong constraint of our proposal, and a remarkable nontrivial validation. If correct, our proposal identifies the nature of the dark matter, explains baryogenesis, and provides a means to directly probe the matter distribution in our Galaxy by analyzing several different types of diffuse emissions.

  2. BAYESIAN ANALYSIS OF WHITE NOISE LEVELS IN THE FIVE-YEAR WMAP DATA

    International Nuclear Information System (INIS)

    Groeneboom, N. E.; Eriksen, H. K.; Gorski, K.; Huey, G.; Jewell, J.; Wandelt, B.

    2009-01-01

    We develop a new Bayesian method for estimating white noise levels in CMB sky maps, and apply this algorithm to the five-year Wilkinson Microwave Anisotropy Probe (WMAP) data. We assume that the amplitude of the noise rms is scaled by a constant value, α, relative to a pre-specified noise level. We then derive the corresponding conditional density, P(α | s, C l , d), which is subsequently integrated into a general CMB Gibbs sampler. We first verify our code by analyzing simulated data sets, and then apply the framework to the WMAP data. For the foreground-reduced five-year WMAP sky maps and the nominal noise levels initially provided in the five-year data release, we find that the posterior means typically range between α = 1.005 ± 0.001 and α = 1.010 ± 0.001 depending on differencing assembly, indicating that the noise level of these maps are biased low by 0.5%-1.0%. The same problem is not observed for the uncorrected WMAP sky maps. After the preprint version of this letter appeared on astro-ph., the WMAP team has corrected the values presented on their web page, noting that the initially provided values were in fact estimates from the three-year data release, not from the five-year estimates. However, internally in their five-year analysis the correct noise values were used, and no cosmological results are therefore compromised by this error. Thus, our method has already been demonstrated in practice to be both useful and accurate.

  3. Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Planets and Celestial Calibration Sources

    Science.gov (United States)

    Weiland, J. L.; Odegard, N.; Hill, R. S.; Wollack, E.; Hinshaw, G.; Greason, M. R.; Jarosik, N.; Page, L.; Bennett, C. L.; Dunkley, J.; Gold, B.; Halpern, M.; Kogut, A.; Komatsu, E.; Larson, D.; Limon, M.; Meyer, S. S.; Nolta, M. R.; Smith, K. M.; Spergel, D. N.; Tucker, G. S.; Wright, E. L.

    2011-02-01

    We present WMAP seven-year observations of bright sources which are often used as calibrators at microwave frequencies. Ten objects are studied in five frequency bands (23-94 GHz): the outer planets (Mars, Jupiter, Saturn, Uranus, and Neptune) and five fixed celestial sources (Cas A, Tau A, Cyg A, 3C274, and 3C58). The seven-year analysis of Jupiter provides temperatures which are within 1σ of the previously published WMAP five-year values, with slightly tighter constraints on variability with orbital phase (0.2% ± 0.4%), and limits (but no detections) on linear polarization. Observed temperatures for both Mars and Saturn vary significantly with viewing geometry. Scaling factors are provided which, when multiplied by the Wright Mars thermal model predictions at 350 μm, reproduce WMAP seasonally averaged observations of Mars within ~2%. An empirical model is described which fits brightness variations of Saturn due to geometrical effects and can be used to predict the WMAP observations to within 3%. Seven-year mean temperatures for Uranus and Neptune are also tabulated. Uncertainties in Uranus temperatures are 3%-4% in the 41, 61, and 94 GHz bands; the smallest uncertainty for Neptune is 8% for the 94 GHz band. Intriguingly, the spectrum of Uranus appears to show a dip at ~30 GHz of unidentified origin, although the feature is not of high statistical significance. Flux densities for the five selected fixed celestial sources are derived from the seven-year WMAP sky maps and are tabulated for Stokes I, Q, and U, along with polarization fraction and position angle. Fractional uncertainties for the Stokes I fluxes are typically 1% to 3%. Source variability over the seven-year baseline is also estimated. Significant secular decrease is seen for Cas A and Tau A: our results are consistent with a frequency-independent decrease of about 0.53% per year for Cas A and 0.22% per year for Tau A. We present WMAP polarization data with uncertainties of a few percent for Tau A

  4. SEVEN-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP ) OBSERVATIONS: PLANETS AND CELESTIAL CALIBRATION SOURCES

    International Nuclear Information System (INIS)

    Weiland, J. L.; Odegard, N.; Hill, R. S.; Greason, M. R.; Wollack, E.; Hinshaw, G.; Kogut, A.; Jarosik, N.; Page, L.; Bennett, C. L.; Gold, B.; Larson, D.; Dunkley, J.; Halpern, M.; Komatsu, E.; Limon, M.; Meyer, S. S.; Nolta, M. R.; Smith, K. M.; Spergel, D. N.

    2011-01-01

    We present WMAP seven-year observations of bright sources which are often used as calibrators at microwave frequencies. Ten objects are studied in five frequency bands (23-94 GHz): the outer planets (Mars, Jupiter, Saturn, Uranus, and Neptune) and five fixed celestial sources (Cas A, Tau A, Cyg A, 3C274, and 3C58). The seven-year analysis of Jupiter provides temperatures which are within 1σ of the previously published WMAP five-year values, with slightly tighter constraints on variability with orbital phase (0.2% ± 0.4%), and limits (but no detections) on linear polarization. Observed temperatures for both Mars and Saturn vary significantly with viewing geometry. Scaling factors are provided which, when multiplied by the Wright Mars thermal model predictions at 350 μm, reproduce WMAP seasonally averaged observations of Mars within ∼2%. An empirical model is described which fits brightness variations of Saturn due to geometrical effects and can be used to predict the WMAP observations to within 3%. Seven-year mean temperatures for Uranus and Neptune are also tabulated. Uncertainties in Uranus temperatures are 3%-4% in the 41, 61, and 94 GHz bands; the smallest uncertainty for Neptune is 8% for the 94 GHz band. Intriguingly, the spectrum of Uranus appears to show a dip at ∼30 GHz of unidentified origin, although the feature is not of high statistical significance. Flux densities for the five selected fixed celestial sources are derived from the seven-year WMAP sky maps and are tabulated for Stokes I, Q, and U, along with polarization fraction and position angle. Fractional uncertainties for the Stokes I fluxes are typically 1% to 3%. Source variability over the seven-year baseline is also estimated. Significant secular decrease is seen for Cas A and Tau A: our results are consistent with a frequency-independent decrease of about 0.53% per year for Cas A and 0.22% per year for Tau A. We present WMAP polarization data with uncertainties of a few percent for Tau

  5. First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Beam Profiles and Window Functions

    Science.gov (United States)

    Page, L.; Barnes, C.; Hinshaw, G.; Spergel, D. N.; Weiland, J. L.; Wollack, E.; Bennett, C. L.; Halpern, M.; Jarosik, N.; Kogut, A.; Limon, M.; Meyer, S. S.; Tucker, G. S.; Wright, E. L.

    2003-09-01

    Knowledge of the beam profiles is of critical importance for interpreting data from cosmic microwave background experiments. In this paper, we present the characterization of the in-flight optical response of the WMAP satellite. The main-beam intensities have been mapped to the satellite in the same observing mode as for CMB observations. The beam patterns closely follow the prelaunch expectations. The full width at half-maximum is a function of frequency and ranges from 0.82d at 23 GHz to 0.21d at 94 GHz; however, the beams are not Gaussian. We present (a) the beam patterns for all 10 differential radiometers, showing that the patterns are substantially independent of polarization in all but the 23 GHz channel; (b) the effective symmetrized beam patterns that result from WMAP's compound spin observing pattern; (c) the effective window functions for all radiometers and the formalism for propagating the window function uncertainty; and (d) the conversion factor from point-source flux to antenna temperature. A summary of the systematic uncertainties, which currently dominate our knowledge of the beams, is also presented. The constancy of Jupiter's temperature within a frequency band is an essential check of the optical system. The tests enable us to report a calibration of Jupiter to 1%-3% accuracy relative to the CMB dipole. WMAP is the result of a partnership between Princeton University and the NASA Goddard Space Flight Center. Scientific guidance is provided by the WMAP Science Team.

  6. NINE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) OBSERVATIONS: FINAL MAPS AND RESULTS

    Energy Technology Data Exchange (ETDEWEB)

    Bennett, C. L.; Larson, D.; Weiland, J. L. [Department of Physics and Astronomy, The Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218-2686 (United States); Jarosik, N.; Page, L. [Department of Physics, Jadwin Hall, Princeton University, Princeton, NJ 08544-0708 (United States); Hinshaw, G.; Halpern, M. [Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1 (Canada); Odegard, N.; Hill, R. S. [ADNET Systems, Inc., 7515 Mission Drive, Suite A100, Lanham, MD 20706 (United States); Smith, K. M. [Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 (Canada); Gold, B. [School of Physics and Astronomy, University of Minnesota, 116 Church Street S.E., Minneapolis, MN 55455 (United States); Komatsu, E. [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild Str. 1, D-85741 Garching (Germany); Nolta, M. R. [Canadian Institute for Theoretical Astrophysics, 60 St. George Street, University of Toronto, Toronto, ON M5S 3H8 (Canada); Spergel, D. N. [Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544-1001 (United States); Wollack, E.; Kogut, A. [Code 665, NASA/Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Dunkley, J. [Oxford Astrophysics, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH (United Kingdom); Limon, M. [Columbia Astrophysics Laboratory, 550 West 120th Street, Mail Code 5247, New York, NY 10027-6902 (United States); Meyer, S. S. [Departments of Astrophysics and Physics, KICP and EFI, University of Chicago, Chicago, IL 60637 (United States); Tucker, G. S., E-mail: cbennett@jhu.edu [Department of Physics, Brown University, 182 Hope Street, Providence, RI 02912-1843 (United States); and others

    2013-10-01

    of 68,000 for the standard six-parameter ΛCDM model, based on CMB data alone. For a model including tensors, the allowed seven-parameter volume has been reduced by a factor 117,000. Other cosmological observations are in accord with the CMB predictions, and the combined data reduces the cosmological parameter volume even further. With no significant anomalies and an adequate goodness of fit, the inflationary flat ΛCDM model and its precise and accurate parameters rooted in WMAP data stands as the standard model of cosmology.

  7. NINE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) OBSERVATIONS: FINAL MAPS AND RESULTS

    International Nuclear Information System (INIS)

    Bennett, C. L.; Larson, D.; Weiland, J. L.; Jarosik, N.; Page, L.; Hinshaw, G.; Halpern, M.; Odegard, N.; Hill, R. S.; Smith, K. M.; Gold, B.; Komatsu, E.; Nolta, M. R.; Spergel, D. N.; Wollack, E.; Kogut, A.; Dunkley, J.; Limon, M.; Meyer, S. S.; Tucker, G. S.

    2013-01-01

    , based on CMB data alone. For a model including tensors, the allowed seven-parameter volume has been reduced by a factor 117,000. Other cosmological observations are in accord with the CMB predictions, and the combined data reduces the cosmological parameter volume even further. With no significant anomalies and an adequate goodness of fit, the inflationary flat ΛCDM model and its precise and accurate parameters rooted in WMAP data stands as the standard model of cosmology

  8. Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results

    Science.gov (United States)

    Bennett, C. L.; Larson, D.; Weiland, J. L.; Jaorsik, N.; Hinshaw, G.; Odegard, N.; Smith, K. M.; Hill, R. S.; Gold, B.; Halpern, M; hide

    2013-01-01

    -parameter ?Lambda-CDM model, based on CMB data alone. For a model including tensors, the allowed seven-parameter volume has been reduced by a factor 117,000. Other cosmological observations are in accord with the CMB predictions, and the combined data reduces the cosmological parameter volume even further.With no significant anomalies and an adequate goodness of fit, the inflationary flat Lambda-CDM model and its precise and accurate parameters rooted in WMAP data stands as the standard model of cosmology.

  9. Intermediate inflation in light of the three-year WMAP observations

    International Nuclear Information System (INIS)

    Barrow, John D.; Liddle, Andrew R.; Pahud, Cedric

    2006-01-01

    The three-year observations from the Wilkinson Microwave Anisotropy Probe have been hailed as giving the first clear indication of a spectral index n s s =1 and allowing the tensor-to-scalar ratio r to be nonzero. The combination n s =1 and r>0 is given (within the slow-roll approximation) by a version of the intermediate inflation model with expansion rate H(t)∝t -1/3 . We assess the status of this model in light of the WMAP3 data

  10. ON THE NATURE OF THE SMALL-SCALE STRUCTURE IN THE COSMIC MICROWAVE BACKGROUND OBSERVED BY PLANCK AND WMAP

    Energy Technology Data Exchange (ETDEWEB)

    Verschuur, G. L.; Schmelz, J. T., E-mail: gverschu@naic.edu [Arecibo Observatory, HC-3 Box 53995, Arecibo PR 00612 (Puerto Rico)

    2016-12-01

    Small-scale features observed by Wilkinson Microwave Anisotropy Probe  ( WMAP ) and PLANCK in the frequency range of 22–90 GHz show a nearly flat spectrum, which meets with expectations that they originate in the early universe. However, free–free emission from electrons in small angular scale galactic sources that suffer beam dilution very closely mimic the observed spectrum in this frequency range. Fitting such a model to the PLANCK and WMAP data shows that the angular size required to fit the data is comparable to the angular width of associated H i filaments found in the Galactic Arecibo L-Band Feed Array-H isurvey data. Also, the temperature of the electrons is found to be in the range of 100–300 K. The phenomenon revealed by these data may contribute to a more precise characterization of the foreground masks required to interpret the cosmological aspect of PLANCK and WMAP data.

  11. First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Galactic Signal Contamination from Sidelobe Pickup

    Science.gov (United States)

    Barnes, C.; Hill, R. S.; Hinshaw, G.; Page, L.; Bennett, C. L.; Halpern, M.; Jarosik, N.; Kogut, A.; Limon, M.; Meyer, S. S.; Tucker, G. S.; Wollack, E.; Wright, E. L.

    2003-09-01

    Since the Galactic center is ~1000 times brighter than fluctuations in the cosmic microwave background (CMB), CMB experiments must carefully account for stray Galactic pickup. We present the level of contamination due to sidelobes for the first-year CMB maps produced by the Wilkinson Microwave Anisotropy Probe (WMAP) observatory. For each radiometer, full 4π sr antenna gain patterns are determined from a combination of numerical prediction and ground-based and space-based measurements. These patterns are convolved with the WMAP first-year sky maps and observatory scan pattern to generate the expected sidelobe signal contamination, for both intensity and polarized microwave sky maps. When the main beams are outside of the Galactic plane, we find rms values for the expected sidelobe pickup of 15, 2.1, 2.0, 0.3, and 0.5 μK for the K, Ka, Q, V, and W bands, respectively. Except for at the K band, the rms polarized contamination is the Galactic pickup are presented. WMAP is the result of a partnership between Princeton University and the NASA Goddard Space Flight Center. Scientific guidance is provided by the WMAP Science Team.

  12. Fermi LAT and WMAP observations of the supernova remnant HB 21

    Energy Technology Data Exchange (ETDEWEB)

    Pivato, G. [Dipartimento di Fisica e Astronomia " G. Galilei," Università di Padova, I-35131 Padova (Italy); Hewitt, J. W. [CRESST, University of Maryland, Baltimore County, Baltimore, MD 21250 (United States); Tibaldo, L. [W. W. Hansen Experimental Physics Laboratory, Kavli Institute for Particle Astrophysics and Cosmology, Department of Physics and SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94305 (United States); Acero, F.; Brandt, T. J. [NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Ballet, J. [Laboratoire AIM, CEA-IRFU/CNRS/Université Paris Diderot, Service d' Astrophysique, CEA Saclay, F-91191 Gif sur Yvette (France); De Palma, F.; Giordano, F. [Dipartimento di Fisica " M. Merlin" dell' Università e del Politecnico di Bari, I-70126 Bari (Italy); Janssen, G. H. [University of Manchester, Manchester, M13 9PL (United Kingdom); Jóhannesson, G. [Science Institute, University of Iceland, IS-107 Reykjavik (Iceland); Smith, D. A., E-mail: giovanna.pivato@pd.infn.it, E-mail: john.w.hewitt@nasa.gov, E-mail: ltibaldo@slac.stanford.edu [Centre d' Études Nucléaires de Bordeaux Gradignan, IN2P3/CNRS, Université Bordeaux 1, BP120, F-33175 Gradignan Cedex (France)

    2013-12-20

    We present the analysis of Fermi Large Area Telescope γ-ray observations of HB 21 (G89.0+4.7). We detect significant γ-ray emission associated with the remnant: the flux >100 MeV is 9.4 ± 0.8 (stat) ± 1.6 (syst) × 10{sup –11} erg cm{sup –2} s{sup –1}. HB 21 is well modeled by a uniform disk centered at l = 88.°75 ± 0.°04, b = +4.°65 ± 0.°06 with a radius of 1.°19 ± 0.°06. The γ-ray spectrum shows clear evidence of curvature, suggesting a cutoff or break in the underlying particle population at an energy of a few GeV. We complement γ-ray observations with the analysis of the WMAP 7 yr data from 23 to 93 GHz, achieving the first detection of HB 21 at these frequencies. In combination with archival radio data, the radio spectrum shows a spectral break, which helps to constrain the relativistic electron spectrum, and, in turn, parameters of simple non-thermal radiation models. In one-zone models multiwavelength data favor the origin of γ rays from nucleon-nucleon collisions. A single population of electrons cannot produce both γ rays through bremsstrahlung and radio emission through synchrotron radiation. A predominantly inverse-Compton origin of the γ-ray emission is disfavored because it requires lower interstellar densities than are inferred for HB 21. In the hadronic-dominated scenarios, accelerated nuclei contribute a total energy of ∼3 × 10{sup 49} erg, while, in a two-zone bremsstrahlung-dominated scenario, the total energy in accelerated particles is ∼1 × 10{sup 49} erg.

  13. NINE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) OBSERVATIONS: COSMOLOGICAL PARAMETER RESULTS

    International Nuclear Information System (INIS)

    Hinshaw, G.; Halpern, M.; Larson, D.; Bennett, C. L.; Weiland, J. L.; Komatsu, E.; Spergel, D. N.; Dunkley, J.; Nolta, M. R.; Hill, R. S.; Odegard, N.; Page, L.; Jarosik, N.; Smith, K. M.; Gold, B.; Kogut, A.; Wollack, E.; Limon, M.; Meyer, S. S.; Tucker, G. S.

    2013-01-01

    We present cosmological parameter constraints based on the final nine-year Wilkinson Microwave Anisotropy Probe (WMAP) data, in conjunction with a number of additional cosmological data sets. The WMAP data alone, and in combination, continue to be remarkably well fit by a six-parameter ΛCDM model. When WMAP data are combined with measurements of the high-l cosmic microwave background anisotropy, the baryon acoustic oscillation scale, and the Hubble constant, the matter and energy densities, Ω b h 2 , Ω c h 2 , and Ω Λ , are each determined to a precision of ∼1.5%. The amplitude of the primordial spectrum is measured to within 3%, and there is now evidence for a tilt in the primordial spectrum at the 5σ level, confirming the first detection of tilt based on the five-year WMAP data. At the end of the WMAP mission, the nine-year data decrease the allowable volume of the six-dimensional ΛCDM parameter space by a factor of 68,000 relative to pre-WMAP measurements. We investigate a number of data combinations and show that their ΛCDM parameter fits are consistent. New limits on deviations from the six-parameter model are presented, for example: the fractional contribution of tensor modes is limited to r k = -0.0027 +0.0039 -0.0038 ; the summed mass of neutrinos is limited to Σm ν eff = 3.84 ± 0.40, when the full data are analyzed. The joint constraint on N eff and the primordial helium abundance, Y He , agrees with the prediction of standard big bang nucleosynthesis. We compare recent Planck measurements of the Sunyaev-Zel'dovich effect with our seven-year measurements, and show their mutual agreement. Our analysis of the polarization pattern around temperature extrema is updated. This confirms a fundamental prediction of the standard cosmological model and provides a striking illustration of acoustic oscillations and adiabatic initial conditions in the early universe

  14. Testing the dark matter origin of the WMAP-Planck haze with radio observations of spiral galaxies

    Energy Technology Data Exchange (ETDEWEB)

    Carlson, Eric; Linden, Tim; Profumo, Stefano [Department of Physics, University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA, 95064 (United States); Hooper, Dan, E-mail: erccarls@ucsc.edu, E-mail: dhooper@fnal.gov, E-mail: tlinden@ucsc.edu, E-mail: profumo@ucsc.edu [Center for Particle Astrophysics, Fermi National Accelerator Laboratory, Batavia, IL 60510 (United States)

    2013-07-01

    If the Galactic WMAP radio haze, as recently confirmed by Planck, is produced by dark matter annihilation or decay, similar diffuse radio halos should exist around other galaxies with physical properties comparable to the Milky Way. If instead the haze is due to an astrophysical mechanism peculiar to the Milky Way or to a transient event, a similar halo need not exist around all Milky Way ''twins''. We use radio observations of 66 spiral galaxies to test the dark matter origin of the haze. We select galaxies based on morphological type and maximal rotational velocity, and obtain their luminosities from a 1.49 GHz catalog and additional radio observations at other frequencies. We find many instances of galaxies with radio emission that is less than 5% as bright as naively expected from dark matter models that could produce the Milky Way haze, and at least 3 galaxies that are less than 1% as bright as expected, assuming dark matter distributions, magnetic fields, and cosmic ray propagation parameters equal to those of the Milky Way. For reasonable ranges for the variation of these parameters, we estimate the fraction of galaxies that should be expected to be significantly less bright in radio, and argue that this is marginally compatible with the observed distribution. While our findings therefore cannot rule out a dark matter origin for the radio haze at this time, we find numerous examples (including the Andromeda Galaxy) where, if dark matter is indeed the origin of the Milky Way haze, some mechanism must be in place to suppress the corresponding haze of the external galaxy. We point out that Planck data will offer opportunities to improve this type of constraint in a highly relevant frequency range and for a potentially larger set of candidate galaxies.

  15. Confronting quasi-exponential inflation with WMAP seven

    International Nuclear Information System (INIS)

    Pal, Barun Kumar; Pal, Supratik; Basu, B.

    2012-01-01

    We confront quasi-exponential models of inflation with WMAP seven years dataset using Hamilton Jacobi formalism. With a phenomenological Hubble parameter, representing quasi exponential inflation, we develop the formalism and subject the analysis to confrontation with WMAP seven using the publicly available code CAMB. The observable parameters are found to fair extremely well with WMAP seven. We also obtain a ratio of tensor to scalar amplitudes which may be detectable in PLANCK

  16. Forecasting neutrino masses from combining KATRIN and the CMB observations: Frequentist and Bayesian analyses

    Science.gov (United States)

    Host, Ole; Lahav, Ofer; Abdalla, Filipe B.; Eitel, Klaus

    2007-12-01

    We present a showcase for deriving bounds on the neutrino masses from laboratory experiments and cosmological observations. We compare the frequentist and Bayesian bounds on the effective electron neutrino mass mβ which the KATRIN neutrino mass experiment is expected to obtain, using both an analytical likelihood function and Monte Carlo simulations of KATRIN. Assuming a uniform prior in mβ, we find that a null result yields an upper bound of about 0.17 eV at 90% confidence in the Bayesian analysis, to be compared with the frequentist KATRIN reference value of 0.20 eV. This is a significant difference when judged relative to the systematic and statistical uncertainties of the experiment. On the other hand, an input mβ=0.35eV, which is the KATRIN 5σ detection threshold, would be detected at virtually the same level. Finally, we combine the simulated KATRIN results with cosmological data in the form of present (post-WMAP) and future (simulated Planck) observations. If an input of mβ=0.2eV is assumed in our simulations, KATRIN alone excludes a zero neutrino mass at 2.2σ. Adding Planck data increases the probability of detection to a median 2.7σ. The analysis highlights the importance of combining cosmological and laboratory data on an equal footing.

  17. Forecasting neutrino masses from combining KATRIN and the CMB observations: Frequentist and Bayesian analyses

    International Nuclear Information System (INIS)

    Host, Ole; Lahav, Ofer; Abdalla, Filipe B.; Eitel, Klaus

    2007-01-01

    We present a showcase for deriving bounds on the neutrino masses from laboratory experiments and cosmological observations. We compare the frequentist and Bayesian bounds on the effective electron neutrino mass m β which the KATRIN neutrino mass experiment is expected to obtain, using both an analytical likelihood function and Monte Carlo simulations of KATRIN. Assuming a uniform prior in m β , we find that a null result yields an upper bound of about 0.17 eV at 90% confidence in the Bayesian analysis, to be compared with the frequentist KATRIN reference value of 0.20 eV. This is a significant difference when judged relative to the systematic and statistical uncertainties of the experiment. On the other hand, an input m β =0.35 eV, which is the KATRIN 5σ detection threshold, would be detected at virtually the same level. Finally, we combine the simulated KATRIN results with cosmological data in the form of present (post-WMAP) and future (simulated Planck) observations. If an input of m β =0.2 eV is assumed in our simulations, KATRIN alone excludes a zero neutrino mass at 2.2σ. Adding Planck data increases the probability of detection to a median 2.7σ. The analysis highlights the importance of combining cosmological and laboratory data on an equal footing

  18. Evidence Estimation for Bayesian Partially Observed MRFs

    NARCIS (Netherlands)

    Chen, Y.; Welling, M.

    2013-01-01

    Bayesian estimation in Markov random fields is very hard due to the intractability of the partition function. The introduction of hidden units makes the situation even worse due to the presence of potentially very many modes in the posterior distribution. For the first time we propose a

  19. Large-scale alignments from WMAP and Planck

    CERN Document Server

    Copi, Craig J.; Schwarz, Dominik J.; Starkman, Glenn D.

    2015-01-01

    We revisit the alignments of the largest structures observed in the cosmic microwave background (CMB) using the seven and nine-year WMAP and first-year Planck data releases. The observed alignments -- the quadrupole with the octopole and their joint alignment with the direction of our motion with respect to the CMB (the dipole direction) and the geometry of the Solar System (defined by the Ecliptic plane) -- are generally in good agreement with results from the previous WMAP data releases. However, a closer look at full-sky data on the largest scales reveals discrepancies between the earlier WMAP data releases (three to seven-year) and the final nine-year release. There are also discrepancies between all the WMAP data releases and the first-year Planck release. Nevertheless, both the WMAP and Planck data confirm the alignments of the largest observable CMB modes in the Universe. In particular, the p-values for the mutual alignment between the quadrupole and octopole, and the alignment of the plane defined by ...

  20. Running-mass inflation model and WMAP

    International Nuclear Information System (INIS)

    Covi, Laura; Lyth, David H.; Melchiorri, Alessandro; Odman, Carolina J.

    2004-01-01

    We consider the observational constraints on the running-mass inflationary model, and, in particular, on the scale dependence of the spectral index, from the new cosmic microwave background (CMB) anisotropy measurements performed by WMAP and from new clustering data from the SLOAN survey. We find that the data strongly constraints a significant positive scale dependence of n, and we translate the analysis into bounds on the physical parameters of the inflaton potential. Looking deeper into specific types of interaction (gauge and Yukawa) we find that the parameter space is significantly constrained by the new data, but that the running-mass model remains viable

  1. The running-mass inflation model and WMAP

    OpenAIRE

    Covi, Laura; Lyth, David H.; Melchiorri, Alessandro; Odman, Carolina J.

    2004-01-01

    We consider the observational constraints on the running-mass inflationary model, and in particular on the scale-dependence of the spectral index, from the new Cosmic Microwave Background (CMB) anisotropy measurements performed by WMAP and from new clustering data from the SLOAN survey. We find that the data strongly constraints a significant positive scale-dependence of $n$, and we translate the analysis into bounds on the physical parameters of the inflaton potential. Looking deeper into sp...

  2. Optimal projection of observations in a Bayesian setting

    KAUST Repository

    Giraldi, Loic

    2018-03-18

    Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on information theory: the projection that minimizes the Kullback–Leibler divergence between the posterior distributions of the original and the projected models, the one that minimizes the expected Kullback–Leibler divergence between the same distributions, and the one that maximizes the mutual information between the parameter of interest and the projected observations. The first two optimization problems are formulated as the determination of an optimal subspace and therefore the solution is computed using Riemannian optimization algorithms on the Grassmann manifold. Regarding the maximization of the mutual information, it is shown that there exists an optimal subspace that minimizes the entropy of the posterior distribution of the reduced model; a basis of the subspace can be computed as the solution to a generalized eigenvalue problem; an a priori error estimate on the mutual information is available for this particular solution; and that the dimensionality of the subspace to exactly conserve the mutual information between the input and the output of the models is less than the number of parameters to be inferred. Numerical applications to linear and nonlinear models are used to assess the efficiency of the proposed approaches, and to highlight their advantages compared to standard approaches based on the principal component analysis of the observations.

  3. Bayesian inference for Markov jump processes with informative observations.

    Science.gov (United States)

    Golightly, Andrew; Wilkinson, Darren J

    2015-04-01

    In this paper we consider the problem of parameter inference for Markov jump process (MJP) representations of stochastic kinetic models. Since transition probabilities are intractable for most processes of interest yet forward simulation is straightforward, Bayesian inference typically proceeds through computationally intensive methods such as (particle) MCMC. Such methods ostensibly require the ability to simulate trajectories from the conditioned jump process. When observations are highly informative, use of the forward simulator is likely to be inefficient and may even preclude an exact (simulation based) analysis. We therefore propose three methods for improving the efficiency of simulating conditioned jump processes. A conditioned hazard is derived based on an approximation to the jump process, and used to generate end-point conditioned trajectories for use inside an importance sampling algorithm. We also adapt a recently proposed sequential Monte Carlo scheme to our problem. Essentially, trajectories are reweighted at a set of intermediate time points, with more weight assigned to trajectories that are consistent with the next observation. We consider two implementations of this approach, based on two continuous approximations of the MJP. We compare these constructs for a simple tractable jump process before using them to perform inference for a Lotka-Volterra system. The best performing construct is used to infer the parameters governing a simple model of motility regulation in Bacillus subtilis.

  4. Observing the observer (I): meta-bayesian models of learning and decision-making.

    Science.gov (United States)

    Daunizeau, Jean; den Ouden, Hanneke E M; Pessiglione, Matthias; Kiebel, Stefan J; Stephan, Klaas E; Friston, Karl J

    2010-12-14

    In this paper, we present a generic approach that can be used to infer how subjects make optimal decisions under uncertainty. This approach induces a distinction between a subject's perceptual model, which underlies the representation of a hidden "state of affairs" and a response model, which predicts the ensuing behavioural (or neurophysiological) responses to those inputs. We start with the premise that subjects continuously update a probabilistic representation of the causes of their sensory inputs to optimise their behaviour. In addition, subjects have preferences or goals that guide decisions about actions given the above uncertain representation of these hidden causes or state of affairs. From a Bayesian decision theoretic perspective, uncertain representations are so-called "posterior" beliefs, which are influenced by subjective "prior" beliefs. Preferences and goals are encoded through a "loss" (or "utility") function, which measures the cost incurred by making any admissible decision for any given (hidden) state of affair. By assuming that subjects make optimal decisions on the basis of updated (posterior) beliefs and utility (loss) functions, one can evaluate the likelihood of observed behaviour. Critically, this enables one to "observe the observer", i.e. identify (context- or subject-dependent) prior beliefs and utility-functions using psychophysical or neurophysiological measures. In this paper, we describe the main theoretical components of this meta-Bayesian approach (i.e. a Bayesian treatment of Bayesian decision theoretic predictions). In a companion paper ('Observing the observer (II): deciding when to decide'), we describe a concrete implementation of it and demonstrate its utility by applying it to simulated and real reaction time data from an associative learning task.

  5. Observing the observer (I: meta-bayesian models of learning and decision-making.

    Directory of Open Access Journals (Sweden)

    Jean Daunizeau

    2010-12-01

    Full Text Available In this paper, we present a generic approach that can be used to infer how subjects make optimal decisions under uncertainty. This approach induces a distinction between a subject's perceptual model, which underlies the representation of a hidden "state of affairs" and a response model, which predicts the ensuing behavioural (or neurophysiological responses to those inputs. We start with the premise that subjects continuously update a probabilistic representation of the causes of their sensory inputs to optimise their behaviour. In addition, subjects have preferences or goals that guide decisions about actions given the above uncertain representation of these hidden causes or state of affairs. From a Bayesian decision theoretic perspective, uncertain representations are so-called "posterior" beliefs, which are influenced by subjective "prior" beliefs. Preferences and goals are encoded through a "loss" (or "utility" function, which measures the cost incurred by making any admissible decision for any given (hidden state of affair. By assuming that subjects make optimal decisions on the basis of updated (posterior beliefs and utility (loss functions, one can evaluate the likelihood of observed behaviour. Critically, this enables one to "observe the observer", i.e. identify (context- or subject-dependent prior beliefs and utility-functions using psychophysical or neurophysiological measures. In this paper, we describe the main theoretical components of this meta-Bayesian approach (i.e. a Bayesian treatment of Bayesian decision theoretic predictions. In a companion paper ('Observing the observer (II: deciding when to decide', we describe a concrete implementation of it and demonstrate its utility by applying it to simulated and real reaction time data from an associative learning task.

  6. Natural inflation: Status after WMAP 3-year data

    International Nuclear Information System (INIS)

    Savage, Christopher; Freese, Katherine; Kinney, William H.

    2006-01-01

    The model of natural inflation is examined in light of recent 3-year data from the Wilkinson Microwave Anisotropy Probe and shown to provide a good fit. The inflaton potential is naturally flat due to shift symmetries, and in the simplest version takes the form V(φ)=Λ 4 [1±cos(Nφ/f)]. The model agrees with WMAP3 measurements as long as f>0.7m Pl (where m Pl =1.22x10 19 GeV) and Λ∼m GUT . The running of the scalar spectral index is shown to be small--an order of magnitude below the sensitivity of WMAP3. The location of the field in the potential when perturbations on observable scales are produced is examined; for f>5m Pl , the relevant part of the potential is indistinguishable from a quadratic, yet has the advantage that the required flatness is well-motivated. Depending on the value of f, the model falls into the large field (f≥1.5m Pl ) or small field (f Pl ) classification scheme that has been applied to inflation models. Natural inflation provides a good fit to WMAP3 data

  7. WMAP constraints on k-inflation

    International Nuclear Information System (INIS)

    Devi, N. Chandrachani; Sen, Anjan A.; Nautiyal, Akhilesh

    2011-01-01

    We study the k-inflation models where the inflaton field has a noncanonical kinetic term. In particular, we consider the Dirac-Born-Infeld (DBI) form for the kinetic energy of the inflaton field. We consider quadratic and quartic potentials as well as the potential for the natural inflation. We use a modified version of MODECODE[M. J. Mortonson, H. V. Peiris, and R. Easther, Phys. Rev. D 83, 043505 (2011).] to calculate the power spectrum of the primordial perturbations generated by the inflaton field and subsequently use the WMAP7 results to constrain the models. Interestingly, with the DBI type kinetic term, less gravity waves are produced as one approaches scale invariance. This is true for all the potentials considered. Unlike the canonical case, this feature, in particular, helps the quartic (λφ 4 ) potential with the DBI type kinetic term to be consistent with the WMAP data.

  8. WMAP five-year constraints on lepton asymmetry and radiation energy density: implications for Planck

    International Nuclear Information System (INIS)

    Popa, L A; Vasile, A

    2008-01-01

    In this paper we set bounds on the radiation content of the Universe and neutrino properties by using the WMAP (Wilkinson microwave anisotropy probe) five-year CMB (cosmic microwave background) measurements complemented with most of the existing CMB and LSS (large scale structure) data (WMAP5+All), imposing also self-consistent BBN (big bang nucleosynthesis) constraints on the primordial helium abundance. We consider lepton asymmetric cosmological models parametrized by the neutrino degeneracy parameter ξ ν and the variation of the relativistic degrees of freedom, ΔN eff oth , due to possible other physical processes occurring between BBN and structure formation epochs. We get a mean value of the effective number of relativistic neutrino species of N eff = 2.98  2.27 3.60   1.65 4.37 , providing an important improvement over the similar result obtained from WMAP5+BAO+SN+HST (BAO: baryonic acoustic oscillations; SN: supernovae; HST: Hubble Space Telescope) data (Komatsu et al (WMAP Collaboration), 2008 Astrophys. J. Suppl. submitted [0803.0547]). We also find a strong correlation between Ω m h 2 and z eq , showing that we observe N eff mainly via the effect of z eq , rather than via neutrino anisotropic stress as claimed by the WMAP team (Komatsu et al (WMAP Collaboration), 2008 Astrophys. J. Suppl. submitted [0803.0547]). WMAP5+All data provide a strong bound on the helium mass fraction of Y p = 0.2486 ± 0.0085 (68% CL), that rivals the bound on Y p obtained from the conservative analysis of the present data on helium abundance. For the neutrino degeneracy parameter we find a bound of −0.216≤ξ ν ≤0.226 (68% CL), which represents an important improvement over the similar result obtained by using the WMAP three-year data. The inclusion in the analysis of LSS data reduces the upper limit of the neutrino mass to m ν ν and Y p down to σ(ξ ν )≅0.089 (68% CL) and σ(Y p ) = 0.013 (68% CL) respectively, values fully consistent with the BBN bounds on

  9. WMAP - A Glimpse of the Early Universe

    Science.gov (United States)

    Wollack, Edward

    2009-01-01

    The early Universe was incredibly hot, dense, and homogeneous. A powerful probe of this time is provided by the relic radiation which we refer to today as the Cosmic Microwave Background (CMB). Images produced from this light contain the earliest glimpse of the Universe after the "Big Bang" and the signature of the evolution of its contents. By exploiting these clues, precise constraints on the age, mass density, and geometry of the early Universe can be derived. The history of this intriguing cosmological detective story will be reviewed. Recent results from NASA's Wilkinson Microwave Anisotropy Probe (WMAP) will be presented.

  10. Bayesian updating and decision making using correlated structural health monitoring observations

    DEFF Research Database (Denmark)

    Nielsen, Jannie Sønderkær

    2018-01-01

    A Bayesian approach is often applied when updating a deterioration model using observations from expected structural health monitoring or condition monitoring. Usually, observations are assumed to be independent conditioned on the damage size, but this assumption does not always hold, especially ...... is properly modeled. In case of correlated observations, an advanced decision model using all past observations for decision making is needed to make monitoring feasible compared to only using inspections....

  11. Cosmological parameters from SDSS and WMAP

    International Nuclear Information System (INIS)

    Tegmark, Max; Strauss, Michael A.; Bahcall, Neta A.; Schlegel, David; Finkbeiner, Douglas; Gunn, James E.; Ostriker, Jeremiah P.; Seljak, Uros; Ivezic, Zeljko; Knapp, Gillian R.; Lupton, Robert H.; Blanton, Michael R.; Scoccimarro, Roman; Hogg, David W.; Abazajian, Kevork; Xu Yongzhong; Dodelson, Scott; Sandvik, Havard; Wang Xiaomin; Jain, Bhuvnesh

    2004-01-01

    We measure cosmological parameters using the three-dimensional power spectrum P(k) from over 200 000 galaxies in the Sloan Digital Sky Survey (SDSS) in combination with Wilkinson Microwave Anisotropy Probe (WMAP) and other data. Our results are consistent with a 'vanilla' flat adiabatic cold dark matter model with a cosmological constant without tilt (n s =1), running tilt, tensor modes, or massive neutrinos. Adding SDSS information more than halves the WMAP-only error bars on some parameters, tightening 1σ constraints on the Hubble parameter from h≅0.74 -0.07 +0.18 to h≅0.70 -0.03 +0.04 , on the matter density from Ω m ≅0.25±0.10 to Ω m ≅0.30±0.04 (1σ) and on neutrino masses from 0 ≅16.3 -1.8 +2.3 Gyr to t 0 ≅14.1 -0.9 +1.0 Gyr by adding SDSS and SN Ia data. Including tensors, running tilt, neutrino mass and equation of state in the list of free parameters, many constraints are still quite weak, but future cosmological measurements from SDSS and other sources should allow these to be substantially tightened

  12. Accelerating inference for diffusions observed with measurement error and large sample sizes using approximate Bayesian computation

    DEFF Research Database (Denmark)

    Picchini, Umberto; Forman, Julie Lyng

    2016-01-01

    a nonlinear stochastic differential equation model observed with correlated measurement errors and an application to protein folding modelling. An approximate Bayesian computation (ABC)-MCMC algorithm is suggested to allow inference for model parameters within reasonable time constraints. The ABC algorithm......In recent years, dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However, it is often computationally unfeasible to apply exact statistical methodologies in the context of large data sets and complex models. This paper considers...... applications. A simulation study is conducted to compare our strategy with exact Bayesian inference, the latter resulting two orders of magnitude slower than ABC-MCMC for the considered set-up. Finally, the ABC algorithm is applied to a large size protein data. The suggested methodology is fairly general...

  13. Optimal projection of observations in a Bayesian setting

    KAUST Repository

    Giraldi, Loic; Le Maî tre, Olivier P.; Hoteit, Ibrahim; Knio, Omar

    2018-01-01

    , and the one that maximizes the mutual information between the parameter of interest and the projected observations. The first two optimization problems are formulated as the determination of an optimal subspace and therefore the solution is computed using

  14. Dark matter implications of the WMAP-Planck Haze

    International Nuclear Information System (INIS)

    Egorov, Andrey E.; Pierpaoli, Elena; Gaskins, Jennifer M.; Pietrobon, Davide

    2016-01-01

    Gamma rays and microwave observations of the Galactic Center and surrounding areas indicate the presence of anomalous emission, whose origin remains ambiguous. The possibility of dark matter annihilation explaining both signals through prompt emission at gamma rays and secondary emission at microwave frequencies from interactions of high-energy electrons produced in annihilation with the Galactic magnetic fields has attracted much interest in recent years. We investigate the dark matter interpretation of the Galactic Center gamma-ray excess by searching for the associated synchrotron emission in the WMAP and Planck microwave data. Considering various magnetic field and cosmic-ray propagation models, we predict the synchrotron emission due to dark matter annihilation in our Galaxy, and compare it with the WMAP and Planck data at 23–70 GHz. In addition to standard microwave foregrounds, we separately model the microwave counterpart to the Fermi Bubbles and the signal due to dark matter annihilation, and use component separation techniques to extract the signal associated with each template from the total emission. We confirm the presence of the Haze at the level of ≈7% of the total sky intensity at 23 GHz in our chosen region of interest, with a harder spectrum (I ∼ ν −0.8 ) than the synchrotron from regular cosmic-ray electrons. The data do not show a strong preference towards fitting the Haze by either the Bubbles or dark matter emission only. Inclusion of both components provides a better fit with a dark matter contribution to the Haze emission of ≈20% at 23 GHz, however, due to significant uncertainties in foreground modeling, we do not consider this a clear detection of a dark matter signal. We set robust upper limits on the annihilation cross section by ignoring foregrounds, and also report best-fit dark matter annihilation parameters obtained from a complete template analysis. We conclude that the WMAP and Planck data are consistent with a dark

  15. Dark matter implications of the WMAP-Planck Haze

    Energy Technology Data Exchange (ETDEWEB)

    Egorov, Andrey E.; Pierpaoli, Elena [University of Southern California, 3620 McClintock Ave., SGM 408, Los Angeles, CA 90089 (United States); Gaskins, Jennifer M. [California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125 (United States); Pietrobon, Davide, E-mail: egorov@usc.edu, E-mail: jgaskins@uva.nl, E-mail: pierpaol@usc.edu, E-mail: daddeptr@gmail.com [University of California, Berkeley, Space Sciences Laboratory, 7 Gauss Rd, Berkeley CA 94720 (United States)

    2016-03-01

    Gamma rays and microwave observations of the Galactic Center and surrounding areas indicate the presence of anomalous emission, whose origin remains ambiguous. The possibility of dark matter annihilation explaining both signals through prompt emission at gamma rays and secondary emission at microwave frequencies from interactions of high-energy electrons produced in annihilation with the Galactic magnetic fields has attracted much interest in recent years. We investigate the dark matter interpretation of the Galactic Center gamma-ray excess by searching for the associated synchrotron emission in the WMAP and Planck microwave data. Considering various magnetic field and cosmic-ray propagation models, we predict the synchrotron emission due to dark matter annihilation in our Galaxy, and compare it with the WMAP and Planck data at 23–70 GHz. In addition to standard microwave foregrounds, we separately model the microwave counterpart to the Fermi Bubbles and the signal due to dark matter annihilation, and use component separation techniques to extract the signal associated with each template from the total emission. We confirm the presence of the Haze at the level of ≈7% of the total sky intensity at 23 GHz in our chosen region of interest, with a harder spectrum (I ∼ ν{sup −0.8}) than the synchrotron from regular cosmic-ray electrons. The data do not show a strong preference towards fitting the Haze by either the Bubbles or dark matter emission only. Inclusion of both components provides a better fit with a dark matter contribution to the Haze emission of ≈20% at 23 GHz, however, due to significant uncertainties in foreground modeling, we do not consider this a clear detection of a dark matter signal. We set robust upper limits on the annihilation cross section by ignoring foregrounds, and also report best-fit dark matter annihilation parameters obtained from a complete template analysis. We conclude that the WMAP and Planck data are consistent with a

  16. Predicting Plasma Glucose From Interstitial Glucose Observations Using Bayesian Methods

    DEFF Research Database (Denmark)

    Hansen, Alexander Hildenbrand; Duun-Henriksen, Anne Katrine; Juhl, Rune

    2014-01-01

    One way of constructing a control algorithm for an artificial pancreas is to identify a model capable of predicting plasma glucose (PG) from interstitial glucose (IG) observations. Stochastic differential equations (SDEs) make it possible to account both for the unknown influence of the continuous...... glucose monitor (CGM) and for unknown physiological influences. Combined with prior knowledge about the measurement devices, this approach can be used to obtain a robust predictive model. A stochastic-differential-equation-based gray box (SDE-GB) model is formulated on the basis of an identifiable...

  17. Searching for planar signatures in WMAP

    International Nuclear Information System (INIS)

    Abramo, L. Raul; Bernui, Armando; Pereira, Thiago S.

    2009-01-01

    We search for planar deviations of statistical isotropy in the Wilkinson Microwave Anisotropy Probe (WMAP) data by applying a recently introduced angular-planar statistics both to full-sky and to masked temperature maps, including in our analysis the effect of the residual foreground contamination and systematics in the foreground removing process as sources of error. We confirm earlier findings that full-sky maps exhibit anomalies at the planar (l) and angular (l) scales (l,l) = (2,5),(4,7), and (6,8), which seem to be due to unremoved foregrounds since this features are present in the full-sky map but not in the masked maps. On the other hand, our test detects slightly anomalous results at the scales (l,l) = (10,8) and (2,9) in the masked maps but not in the full-sky one, indicating that the foreground cleaning procedure (used to generate the full-sky map) could not only be creating false anomalies but also hiding existing ones. We also find a significant trace of an anomaly in the full-sky map at the scale (l,l) = (10,5), which is still present when we consider galactic cuts of 18.3% and 28.4%. As regards the quadrupole (l = 2), we find a coherent over-modulation over the whole celestial sphere, for all full-sky and cut-sky maps. Overall, our results seem to indicate that current CMB maps derived from WMAP data do not show significant signs of anisotropies, as measured by our angular-planar estimator. However, we have detected a curious coherence of planar modulations at angular scales of the order of the galaxy's plane, which may be an indication of residual contaminations in the full- and cut-sky maps

  18. An imprecise Dirichlet model for Bayesian analysis of failure data including right-censored observations

    International Nuclear Information System (INIS)

    Coolen, F.P.A.

    1997-01-01

    This paper is intended to make researchers in reliability theory aware of a recently introduced Bayesian model with imprecise prior distributions for statistical inference on failure data, that can also be considered as a robust Bayesian model. The model consists of a multinomial distribution with Dirichlet priors, making the approach basically nonparametric. New results for the model are presented, related to right-censored observations, where estimation based on this model is closely related to the product-limit estimator, which is an important statistical method to deal with reliability or survival data including right-censored observations. As for the product-limit estimator, the model considered in this paper aims at not using any information other than that provided by observed data, but our model fits into the robust Bayesian context which has the advantage that all inferences can be based on probabilities or expectations, or bounds for probabilities or expectations. The model uses a finite partition of the time-axis, and as such it is also related to life-tables

  19. Assimilating irregularly spaced sparsely observed turbulent signals with hierarchical Bayesian reduced stochastic filters

    International Nuclear Information System (INIS)

    Brown, Kristen A.; Harlim, John

    2013-01-01

    In this paper, we consider a practical filtering approach for assimilating irregularly spaced, sparsely observed turbulent signals through a hierarchical Bayesian reduced stochastic filtering framework. The proposed hierarchical Bayesian approach consists of two steps, blending a data-driven interpolation scheme and the Mean Stochastic Model (MSM) filter. We examine the potential of using the deterministic piecewise linear interpolation scheme and the ordinary kriging scheme in interpolating irregularly spaced raw data to regularly spaced processed data and the importance of dynamical constraint (through MSM) in filtering the processed data on a numerically stiff state estimation problem. In particular, we test this approach on a two-layer quasi-geostrophic model in a two-dimensional domain with a small radius of deformation to mimic ocean turbulence. Our numerical results suggest that the dynamical constraint becomes important when the observation noise variance is large. Second, we find that the filtered estimates with ordinary kriging are superior to those with linear interpolation when observation networks are not too sparse; such robust results are found from numerical simulations with many randomly simulated irregularly spaced observation networks, various observation time intervals, and observation error variances. Third, when the observation network is very sparse, we find that both the kriging and linear interpolations are comparable

  20. Bayesian inference for multivariate point processes observed at sparsely distributed times

    DEFF Research Database (Denmark)

    Rasmussen, Jakob Gulddahl; Møller, Jesper; Aukema, B.H.

    We consider statistical and computational aspects of simulation-based Bayesian inference for a multivariate point process which is only observed at sparsely distributed times. For specicity we consider a particular data set which has earlier been analyzed by a discrete time model involving unknown...... normalizing constants. We discuss the advantages and disadvantages of using continuous time processes compared to discrete time processes in the setting of the present paper as well as other spatial-temporal situations. Keywords: Bark beetle, conditional intensity, forest entomology, Markov chain Monte Carlo...

  1. Model independent foreground power spectrum estimation using WMAP 5-year data

    International Nuclear Information System (INIS)

    Ghosh, Tuhin; Souradeep, Tarun; Saha, Rajib; Jain, Pankaj

    2009-01-01

    In this paper, we propose and implement on WMAP 5 yr data a model independent approach of foreground power spectrum estimation for multifrequency observations of the CMB experiments. Recently, a model independent approach of CMB power spectrum estimation was proposed by Saha et al. 2006. This methodology demonstrates that the CMB power spectrum can be reliably estimated solely from WMAP data without assuming any template models for the foreground components. In the current paper, we extend this work to estimate the galactic foreground power spectrum using the WMAP 5 yr maps following a self-contained analysis. We apply the model independent method in harmonic basis to estimate the foreground power spectrum and frequency dependence of combined foregrounds. We also study the behavior of synchrotron spectral index variation over different regions of the sky. We use the full sky Haslam map as an external template to increase the degrees of freedom, while computing the synchrotron spectral index over the frequency range from 408 MHz to 94 GHz. We compare our results with those obtained from maximum entropy method foreground maps, which are formed in pixel space. We find that relative to our model independent estimates maximum entropy method maps overestimate the foreground power close to galactic plane and underestimates it at high latitudes.

  2. BAYESIAN TECHNIQUES FOR COMPARING TIME-DEPENDENT GRMHD SIMULATIONS TO VARIABLE EVENT HORIZON TELESCOPE OBSERVATIONS

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Junhan; Marrone, Daniel P.; Chan, Chi-Kwan; Medeiros, Lia; Özel, Feryal; Psaltis, Dimitrios, E-mail: junhankim@email.arizona.edu [Department of Astronomy and Steward Observatory, University of Arizona, 933 N. Cherry Avenue, Tucson, AZ 85721 (United States)

    2016-12-01

    The Event Horizon Telescope (EHT) is a millimeter-wavelength, very-long-baseline interferometry (VLBI) experiment that is capable of observing black holes with horizon-scale resolution. Early observations have revealed variable horizon-scale emission in the Galactic Center black hole, Sagittarius A* (Sgr A*). Comparing such observations to time-dependent general relativistic magnetohydrodynamic (GRMHD) simulations requires statistical tools that explicitly consider the variability in both the data and the models. We develop here a Bayesian method to compare time-resolved simulation images to variable VLBI data, in order to infer model parameters and perform model comparisons. We use mock EHT data based on GRMHD simulations to explore the robustness of this Bayesian method and contrast it to approaches that do not consider the effects of variability. We find that time-independent models lead to offset values of the inferred parameters with artificially reduced uncertainties. Moreover, neglecting the variability in the data and the models often leads to erroneous model selections. We finally apply our method to the early EHT data on Sgr A*.

  3. Cosmic microwave background snapshots: pre-WMAP and post-WMAP.

    Science.gov (United States)

    Bond, J Richard; Contaldi, Carlo; Pogosyan, Dmitry

    2003-11-15

    We highlight the remarkable evolution in the cosmic microwave background (CMB) power spectrum C(l) as a function of multipole l over the past few years, and in the cosmological parameters for minimal inflation models derived from it: from anisotropy results before 2000; in 2000 and 2001 from Boomerang, Maxima and the Degree Angular Scale Interferometer (DASI), extending l to approximately 1000; and in 2002 from the Cosmic Background Imager (CBI), Very Small Array (VSA), ARCHEOPS and Arcminute Cosmology Bolometer Array Receiver (ACBAR), extending l to approximately 3000, with more from Boomerang and DASI as well. Pre-WMAP (pre-Wilkinson Microwave Anisotropy Probe) optimal band powers are in good agreement with each other and with the exquisite one-year WMAP results, unveiled in February 2003, which now dominate the l less, similar 600 bands. These CMB experiments significantly increased the case for accelerated expansion in the early Universe (the inflationary paradigm) and at the current epoch (dark energy dominance) when they were combined with "prior" probabilities on the parameters. The minimal inflation parameter set, [omega(b), omega(cdm), Omega(tot), Omega(Lambda), n(s), tau(C), sigma(8)], is applied in the same way to the evolving data. C(l) database and Monte Carlo Markov Chain (MCMC) methods are shown to give similar values, which are highly stable over time and for different prior choices, with the increasing precision best characterized by decreasing errors on uncorrelated "parameter eigenmodes". Priors applied range from weak ones to stronger constraints from the expansion rate (HST-h), from cosmic acceleration from supernovae (SN1) and from galaxy clustering, gravitational lensing and local cluster abundance (LSS). After marginalizing over the other cosmic and experimental variables for the weak + LSS prior, the pre-WMAP data of January 2003 compared with the post-WMAP data of March 2003 give Omega(tot) = 1.03(-0.04)(+0.05) compared with 1

  4. BAYESIAN SEMI-BLIND COMPONENT SEPARATION FOR FOREGROUND REMOVAL IN INTERFEROMETRIC 21 cm OBSERVATIONS

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Le; Timbie, Peter T. [Department of Physics, University of Wisconsin, Madison, WI 53706 (United States); Bunn, Emory F. [Physics Department, University of Richmond, Richmond, VA 23173 (United States); Karakci, Ata; Korotkov, Andrei; Tucker, Gregory S. [Department of Physics, Brown University, 182 Hope Street, Providence, RI 02912 (United States); Sutter, P. M. [Center for Cosmology and Astro-Particle Physics, Ohio State University, Columbus, OH 43210 (United States); Wandelt, Benjamin D., E-mail: lzhang263@wisc.edu [Department of Physics, University of Illinois at Urbana-Champaign, 1110 W Green Street, Urbana, IL 61801 (United States)

    2016-01-15

    In this paper, we present a new Bayesian semi-blind approach for foreground removal in observations of the 21 cm signal measured by interferometers. The technique, which we call H i Expectation–Maximization Independent Component Analysis (HIEMICA), is an extension of the Independent Component Analysis technique developed for two-dimensional (2D) cosmic microwave background maps to three-dimensional (3D) 21 cm cosmological signals measured by interferometers. This technique provides a fully Bayesian inference of power spectra and maps and separates the foregrounds from the signal based on the diversity of their power spectra. Relying only on the statistical independence of the components, this approach can jointly estimate the 3D power spectrum of the 21 cm signal, as well as the 2D angular power spectrum and the frequency dependence of each foreground component, without any prior assumptions about the foregrounds. This approach has been tested extensively by applying it to mock data from interferometric 21 cm intensity mapping observations under idealized assumptions of instrumental effects. We also discuss the impact when the noise properties are not known completely. As a first step toward solving the 21 cm power spectrum analysis problem, we compare the semi-blind HIEMICA technique to the commonly used Principal Component Analysis. Under the same idealized circumstances, the proposed technique provides significantly improved recovery of the power spectrum. This technique can be applied in a straightforward manner to all 21 cm interferometric observations, including epoch of reionization measurements, and can be extended to single-dish observations as well.

  5. Searching for non-Gaussianity in the WMAP data

    International Nuclear Information System (INIS)

    Bernui, A.; Reboucas, M. J.

    2009-01-01

    Some analyses of recent cosmic microwave background (CMB) data have provided hints that there are deviations from Gaussianity in the WMAP CMB temperature fluctuations. Given the far-reaching consequences of such a non-Gaussianity for our understanding of the physics of the early universe, it is important to employ alternative indicators in order to determine whether the reported non-Gaussianity is of cosmological origin, and/or extract further information that may be helpful for identifying its causes. We propose two new non-Gaussianity indicators, based on skewness and kurtosis of large-angle patches of CMB maps, which provide a measure of departure from Gaussianity on large angular scales. A distinctive feature of these indicators is that they provide sky maps of non-Gaussianity of the CMB temperature data, thus allowing a possible additional window into their origins. Using these indicators, we find no significant deviation from Gaussianity in the three and five-year WMAP Internal Linear Combination (ILC) map with KQ75 mask, while the ILC unmasked map exhibits deviation from Gaussianity, quantifying therefore the WMAP team recommendation to employ the new mask KQ75 for tests of Gaussianity. We also use our indicators to test for Gaussianity the single frequency foreground unremoved WMAP three and five-year maps, and show that the K and Ka maps exhibit a clear indication of deviation from Gaussianity even with the KQ75 mask. We show that our findings are robust with respect to the details of the method.

  6. Estimation of CO2 flux from targeted satellite observations: a Bayesian approach

    International Nuclear Information System (INIS)

    Cox, Graham

    2014-01-01

    We consider the estimation of carbon dioxide flux at the ocean–atmosphere interface, given weighted averages of the mixing ratio in a vertical atmospheric column. In particular we examine the dependence of the posterior covariance on the weighting function used in taking observations, motivated by the fact that this function is instrument-dependent, hence one needs the ability to compare different weights. The estimation problem is considered using a variational data assimilation method, which is shown to admit an equivalent infinite-dimensional Bayesian formulation. The main tool in our investigation is an explicit formula for the posterior covariance in terms of the prior covariance and observation operator. Using this formula, we compare weighting functions concentrated near the surface of the earth with those concentrated near the top of the atmosphere, in terms of the resulting covariance operators. We also consider the problem of observational targeting, and ask if it is possible to reduce the covariance in a prescribed direction through an appropriate choice of weighting function. We find that this is not the case—there exist directions in which one can never gain information, regardless of the choice of weight. (paper)

  7. Measuring the cosmological background of relativistic particles with WMAP

    CERN Document Server

    Crotty, P; Pastor, S; Crotty, Patrick; Lesgourgues, Julien; Pastor, Sergio

    2003-01-01

    We show that the first year results of the Wilkinson Microwave Anisotropy Probe (WMAP) constrain very efficiently the energy density in relativistic particles in the universe. We derive new bounds on additional relativistic degrees of freedom expressed in terms of an excess in the effective number of light neutrinos Delta N_eff. Within the flat LambdaCDM scenario, the allowed range is Delta N_eff < 6 (95% CL) using WMAP data only, or -2.6 < Delta N_eff < 4 with the prior H_0= 72 \\pm 8 km/s/Mpc. When other cosmic microwave background and large scale structure experiments are taken into account, the window shrinks to -1.5 < Delta N_eff < 4.2. These results are in perfect agreement with the bounds from primordial nucleosynthesis. Non-minimal cosmological models with extra relativistic degrees of freedom are now severely restricted.

  8. Mildly mixed coupled models vs. WMAP7 data

    International Nuclear Information System (INIS)

    La Vacca, Giuseppe; Bonometto, Silvio A.

    2011-01-01

    Mildly mixed coupled models include massive ν's and CDM-DE coupling. We present new tests of their likelihood vs. recent data including WMAP7, confirming it to exceed ΛCDM, although at ∼2--σ's. We then show the impact on the physics of the dark components of ν-mass detection in 3 H β-decay or 0νββ-decay experiments.

  9. A Bayesian kriging approach for blending satellite and ground precipitation observations

    Science.gov (United States)

    Verdin, Andrew P.; Rajagopalan, Balaji; Kleiber, William; Funk, Christopher C.

    2015-01-01

    Drought and flood management practices require accurate estimates of precipitation. Gauge observations, however, are often sparse in regions with complicated terrain, clustered in valleys, and of poor quality. Consequently, the spatial extent of wet events is poorly represented. Satellite-derived precipitation data are an attractive alternative, though they tend to underestimate the magnitude of wet events due to their dependency on retrieval algorithms and the indirect relationship between satellite infrared observations and precipitation intensities. Here we offer a Bayesian kriging approach for blending precipitation gauge data and the Climate Hazards Group Infrared Precipitation satellite-derived precipitation estimates for Central America, Colombia, and Venezuela. First, the gauge observations are modeled as a linear function of satellite-derived estimates and any number of other variables—for this research we include elevation. Prior distributions are defined for all model parameters and the posterior distributions are obtained simultaneously via Markov chain Monte Carlo sampling. The posterior distributions of these parameters are required for spatial estimation, and thus are obtained prior to implementing the spatial kriging model. This functional framework is applied to model parameters obtained by sampling from the posterior distributions, and the residuals of the linear model are subject to a spatial kriging model. Consequently, the posterior distributions and uncertainties of the blended precipitation estimates are obtained. We demonstrate this method by applying it to pentadal and monthly total precipitation fields during 2009. The model's performance and its inherent ability to capture wet events are investigated. We show that this blending method significantly improves upon the satellite-derived estimates and is also competitive in its ability to represent wet events. This procedure also provides a means to estimate a full conditional distribution

  10. WMAP constraints on the Cardassian model

    International Nuclear Information System (INIS)

    Sen, A.A.; Sen, S.

    2003-01-01

    We investigate the constraints on the Cardassian model using the recent results from the Wilkinson microwave anisotropy probe for the locations of the peaks of the cosmic microwave background (CMB) anisotropy spectrum. We find that the model is consistent with the recent observational data for a certain range of the model parameter n and the cosmological parameters. We find that the Cardassian model is favored compared to the ΛCDM model for a higher spectral index (n s ≅1) together with a lower value of the Hubble parameter h (h≤0.71). But for smaller values of n s , both ΛCDM and Cardassian models are equally favored. Also, irrespective of supernova constraints, CMB data alone predict the current acceleration of the Universe in this model. We have also studied the constraint on σ 8 , the rms density fluctuations at the 8h -1 Mpc scale

  11. Quantitative Precipitation Estimation over Ocean Using Bayesian Approach from Microwave Observations during the Typhoon Season

    Directory of Open Access Journals (Sweden)

    Jen-Chi Hu

    2009-01-01

    Full Text Available We have developed a new Bayesian approach to retrieve oceanic rain rate from the Tropical Rainfall Measuring Mission (TRMM Microwave Imager (TMI, with an emphasis on typhoon cases in the West Pacific. Retrieved rain rates are validated with measurements of rain gauges located on Japanese islands. To demonstrate improvement, retrievals are also compared with those from the TRMM/Precipitation Radar (PR, the Goddard Profiling Algorithm (GPROF, and a multi-channel linear regression statistical method (MLRS. We have found that qualitatively, all methods retrieved similar horizontal distributions in terms of locations of eyes and rain bands of typhoons. Quantitatively, our new Bayesian retrievals have the best linearity and the smallest root mean square (RMS error against rain gauge data for 16 typhoon over passes in 2004. The correlation coefficient and RMS of our retrievals are 0.95 and ~2 mm hr-1, respectively. In particular, at heavy rain rates, our Bayesian retrievals out perform those retrieved from GPROF and MLRS. Over all, the new Bayesian approach accurately retrieves surface rain rate for typhoon cases. Ac cu rate rain rate estimates from this method can be assimilated in models to improve forecast and prevent potential damages in Taiwan during typhoon seasons.

  12. Inflation and WMAP three year data. Features have a feature.

    Energy Technology Data Exchange (ETDEWEB)

    Covi, L.; Hamann, J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Melchiorri, A. [INFN, Roma (Italy)]|[Rome-3 Univ. (Italy). Dipt. di Fisica; Slosar, A. [Ljubljana Univ. (Slovenia). Faculty of Mathematics and Physics; Sorbera, I. [Rome-3 Univ. (Italy). Dipt. di Fisica

    2006-06-15

    The new three year WMAP data seem to confirm the presence of non-standard large scale features in the Cosmic Microwave Anisotropies power spectrum. While these features may hint at uncorrected experimental systematics, it is also possible to generate, in a cosmological way, oscillations on large angular scales by introducing a sharp step in the inflaton potential. Using current cosmological data, we derive constraints on the position, magnitude and gradient of a possible step in the inflaton potential. We show that a step in the potential, while strongly constrained by current data, is still allowed and may provide an interesting explanation to the currently measured deviations from the standard featureless spectrum. (Orig.)

  13. Inflation and WMAP three year data. Features have a future

    International Nuclear Information System (INIS)

    Covi, L.; Hamann, J.; Melchiorri, A.; Rome-3 Univ.; Slosar, A.; Sorbera, I.

    2006-06-01

    The new three year WMAP data seem to confirm the presence of non-standard large scale features in the Cosmic Microwave Anisotropies power spectrum. While these features may hint at uncorrected experimental systematics, it is also possible to generate, in a cosmological way, oscillations on large angular scales by introducing a sharp step in the inflaton potential. Using current cosmological data, we derive constraints on the position, magnitude and gradient of a possible step in the inflaton potential. We show that a step in the potential, while strongly constrained by current data, is still allowed and may provide an interesting explanation to the currently measured deviations from the standard featureless spectrum. (Orig.)

  14. WMAP constraints on inflationary models with global defects

    International Nuclear Information System (INIS)

    Bevis, Neil; Hindmarsh, Mark; Kunz, Martin

    2004-01-01

    We use the cosmic microwave background angular power spectra to place upper limits on the degree to which global defects may have aided cosmic structure formation. We explore this under the inflationary paradigm, but with the addition of textures resulting from the breaking of a global O(4) symmetry during the early stages of the Universe. As a measure of their contribution, we use the fraction of the temperature power spectrum that is attributed to the defects at a multipole of 10. However, we find a parameter degeneracy enabling a fit to the first-year WMAP data to be made even with a significant defect fraction. This degeneracy involves the baryon fraction and the Hubble constant, plus the normalization and tilt of the primordial power spectrum. Hence, constraints on these cosmological parameters are weakened. Combining the WMAP data with a constraint on the physical baryon fraction from big bang nucleosynthesis calculations and high-redshift deuterium abundance limits the extent of the degeneracy and gives an upper bound on the defect fraction of 0.13 (95% confidence)

  15. Foreground removal from WMAP 7 yr polarization maps using an MLP neural network

    DEFF Research Database (Denmark)

    Nørgaard-Nielsen, Hans Ulrik

    2012-01-01

    . As a concrete example, the WMAP 7-year polarization data, the most reliable determination of the polarization properties of the CMB, has been analyzed. The analysis has adopted the frequency maps, noise models, window functions and the foreground models as provided by the WMAP Team, and no auxiliary data...

  16. Using polarimetric radar observations and probabilistic inference to develop the Bayesian Observationally-constrained Statistical-physical Scheme (BOSS), a novel microphysical parameterization framework

    Science.gov (United States)

    van Lier-Walqui, M.; Morrison, H.; Kumjian, M. R.; Prat, O. P.

    2016-12-01

    Microphysical parameterization schemes have reached an impressive level of sophistication: numerous prognostic hydrometeor categories, and either size-resolved (bin) particle size distributions, or multiple prognostic moments of the size distribution. Yet, uncertainty in model representation of microphysical processes and the effects of microphysics on numerical simulation of weather has not shown a improvement commensurate with the advanced sophistication of these schemes. We posit that this may be caused by unconstrained assumptions of these schemes, such as ad-hoc parameter value choices and structural uncertainties (e.g. choice of a particular form for the size distribution). We present work on development and observational constraint of a novel microphysical parameterization approach, the Bayesian Observationally-constrained Statistical-physical Scheme (BOSS), which seeks to address these sources of uncertainty. Our framework avoids unnecessary a priori assumptions, and instead relies on observations to provide probabilistic constraint of the scheme structure and sensitivities to environmental and microphysical conditions. We harness the rich microphysical information content of polarimetric radar observations to develop and constrain BOSS within a Bayesian inference framework using a Markov Chain Monte Carlo sampler (see Kumjian et al., this meeting for details on development of an associated polarimetric forward operator). Our work shows how knowledge of microphysical processes is provided by polarimetric radar observations of diverse weather conditions, and which processes remain highly uncertain, even after considering observations.

  17. Monte Carlo Algorithms for a Bayesian Analysis of the Cosmic Microwave Background

    Science.gov (United States)

    Jewell, Jeffrey B.; Eriksen, H. K.; ODwyer, I. J.; Wandelt, B. D.; Gorski, K.; Knox, L.; Chu, M.

    2006-01-01

    A viewgraph presentation on the review of Bayesian approach to Cosmic Microwave Background (CMB) analysis, numerical implementation with Gibbs sampling, a summary of application to WMAP I and work in progress with generalizations to polarization, foregrounds, asymmetric beams, and 1/f noise is given.

  18. Peak Bagging of red giant stars observed by Kepler: first results with a new method based on Bayesian nested sampling

    Science.gov (United States)

    Corsaro, Enrico; De Ridder, Joris

    2015-09-01

    The peak bagging analysis, namely the fitting and identification of single oscillation modes in stars' power spectra, coupled to the very high-quality light curves of red giant stars observed by Kepler, can play a crucial role for studying stellar oscillations of different flavor with an unprecedented level of detail. A thorough study of stellar oscillations would thus allow for deeper testing of stellar structure models and new insights in stellar evolution theory. However, peak bagging inferences are in general very challenging problems due to the large number of observed oscillation modes, hence of free parameters that can be involved in the fitting models. Efficiency and robustness in performing the analysis is what may be needed to proceed further. For this purpose, we developed a new code implementing the Nested Sampling Monte Carlo (NSMC) algorithm, a powerful statistical method well suited for Bayesian analyses of complex problems. In this talk we show the peak bagging of a sample of high signal-to-noise red giant stars by exploiting recent Kepler datasets and a new criterion for the detection of an oscillation mode based on the computation of the Bayesian evidence. Preliminary results for frequencies and lifetimes for single oscillation modes, together with acoustic glitches, are therefore presented.

  19. Peak Bagging of red giant stars observed by Kepler: first results with a new method based on Bayesian nested sampling

    Directory of Open Access Journals (Sweden)

    Corsaro Enrico

    2015-01-01

    Full Text Available The peak bagging analysis, namely the fitting and identification of single oscillation modes in stars’ power spectra, coupled to the very high-quality light curves of red giant stars observed by Kepler, can play a crucial role for studying stellar oscillations of different flavor with an unprecedented level of detail. A thorough study of stellar oscillations would thus allow for deeper testing of stellar structure models and new insights in stellar evolution theory. However, peak bagging inferences are in general very challenging problems due to the large number of observed oscillation modes, hence of free parameters that can be involved in the fitting models. Efficiency and robustness in performing the analysis is what may be needed to proceed further. For this purpose, we developed a new code implementing the Nested Sampling Monte Carlo (NSMC algorithm, a powerful statistical method well suited for Bayesian analyses of complex problems. In this talk we show the peak bagging of a sample of high signal-to-noise red giant stars by exploiting recent Kepler datasets and a new criterion for the detection of an oscillation mode based on the computation of the Bayesian evidence. Preliminary results for frequencies and lifetimes for single oscillation modes, together with acoustic glitches, are therefore presented.

  20. A Bayesian method for inferring transmission chains in a partially observed epidemic.

    Energy Technology Data Exchange (ETDEWEB)

    Marzouk, Youssef M.; Ray, Jaideep

    2008-10-01

    We present a Bayesian approach for estimating transmission chains and rates in the Abakaliki smallpox epidemic of 1967. The epidemic affected 30 individuals in a community of 74; only the dates of appearance of symptoms were recorded. Our model assumes stochastic transmission of the infections over a social network. Distinct binomial random graphs model intra- and inter-compound social connections, while disease transmission over each link is treated as a Poisson process. Link probabilities and rate parameters are objects of inference. Dates of infection and recovery comprise the remaining unknowns. Distributions for smallpox incubation and recovery periods are obtained from historical data. Using Markov chain Monte Carlo, we explore the joint posterior distribution of the scalar parameters and provide an expected connectivity pattern for the social graph and infection pathway.

  1. Bayesian evidences for dark energy models in light of current observational data

    Science.gov (United States)

    Lonappan, Anto. I.; Kumar, Sumit; Ruchika; Dinda, Bikash R.; Sen, Anjan A.

    2018-02-01

    We do a comprehensive study of the Bayesian evidences for a large number of dark energy models using a combination of latest cosmological data from SNIa, CMB, BAO, strong lensing time delay, growth measurements, measurements of Hubble parameter at different redshifts and measurements of angular diameter distance by Megamaser Cosmology Project. We consider a variety of scalar field models with different potentials as well as different parametrizations for the dark energy equation of state. Among 21 models that we consider in our study, we do not find strong evidences in favor of any evolving dark energy model compared to Λ CDM . For the evolving dark energy models, we show that purely nonphantom models have much better evidences compared to those models that allow both phantom and nonphantom behaviors. Canonical scalar field with exponential and tachyon field with square potential have highest evidences among all the models considered in this work. We also show that a combination of low redshift measurements decisively favors an accelerating Λ CDM model compared to a nonaccelerating power law model.

  2. Sensitivity of Global Methane Bayesian Inversion to Surface Observation Data Sets and Chemical-Transport Model Resolution

    Science.gov (United States)

    Lew, E. J.; Butenhoff, C. L.; Karmakar, S.; Rice, A. L.; Khalil, A. K.

    2017-12-01

    Methane is the second most important greenhouse gas after carbon dioxide. In efforts to control emissions, a careful examination of the methane budget and source strengths is required. To determine methane surface fluxes, Bayesian methods are often used to provide top-down constraints. Inverse modeling derives unknown fluxes using observed methane concentrations, a chemical transport model (CTM) and prior information. The Bayesian inversion reduces prior flux uncertainties by exploiting information content in the data. While the Bayesian formalism produces internal error estimates of source fluxes, systematic or external errors that arise from user choices in the inversion scheme are often much larger. Here we examine model sensitivity and uncertainty of our inversion under different observation data sets and CTM grid resolution. We compare posterior surface fluxes using the data product GLOBALVIEW-CH4 against the event-level molar mixing ratio data available from NOAA. GLOBALVIEW-CH4 is a collection of CH4 concentration estimates from 221 sites, collected by 12 laboratories, that have been interpolated and extracted to provide weekly records from 1984-2008. Differently, the event-level NOAA data records methane mixing ratios field measurements from 102 sites, containing sampling frequency irregularities and gaps in time. Furthermore, the sampling platform types used by the data sets may influence the posterior flux estimates, namely fixed surface, tower, ship and aircraft sites. To explore the sensitivity of the posterior surface fluxes to the observation network geometry, inversions composed of all sites, only aircraft, only ship, only tower and only fixed surface sites, are performed and compared. Also, we investigate the sensitivity of the error reduction associated with the resolution of the GEOS-Chem simulation (4°×5° vs 2°×2.5°) used to calculate the response matrix. Using a higher resolution grid decreased the model-data error at most sites, thereby

  3. Evaluating Observational Learning in a Competitive Two-Sided Crowdsourcing Market: A Bayesian Inferential Approach

    Science.gov (United States)

    Ayaburi, Emmanuel Wusuhon Yanibo

    2017-01-01

    This dissertation investigates the effect of observational learning in crowdsourcing markets as a lens to identify appropriate mechanism(s) for sustaining this increasingly popular business model. Observational learning occurs when crowdsourcing participating agents obtain knowledge from signals they observe in the marketplace and incorporate such…

  4. Multiple player tracking in sports video: a dual-mode two-way bayesian inference approach with progressive observation modeling.

    Science.gov (United States)

    Xing, Junliang; Ai, Haizhou; Liu, Liwei; Lao, Shihong

    2011-06-01

    Multiple object tracking (MOT) is a very challenging task yet of fundamental importance for many practical applications. In this paper, we focus on the problem of tracking multiple players in sports video which is even more difficult due to the abrupt movements of players and their complex interactions. To handle the difficulties in this problem, we present a new MOT algorithm which contributes both in the observation modeling level and in the tracking strategy level. For the observation modeling, we develop a progressive observation modeling process that is able to provide strong tracking observations and greatly facilitate the tracking task. For the tracking strategy, we propose a dual-mode two-way Bayesian inference approach which dynamically switches between an offline general model and an online dedicated model to deal with single isolated object tracking and multiple occluded object tracking integrally by forward filtering and backward smoothing. Extensive experiments on different kinds of sports videos, including football, basketball, as well as hockey, demonstrate the effectiveness and efficiency of the proposed method.

  5. Sunyaev-Zeldovich effect in WMAP and its effect on cosmological parameters

    International Nuclear Information System (INIS)

    Huffenberger, Kevin M.; Seljak, Uros; Makarov, Alexey

    2004-01-01

    We use multifrequency information in first year Wilkinson microwave anisotropy probe (WMAP) data to search for the Sunyaev-Zeldovich (SZ) effect. WMAP has sufficiently broad frequency coverage to constrain the SZ effect without the addition of higher frequency data: the SZ power spectrum amplitude is expected to increase 50% from W to Q frequency band. This, in combination with the low noise in WMAP, allows us to strongly constrain the SZ contribution. We derive an optimal frequency combination of WMAP cross-spectra to extract the SZ effect in the presence of noise, cosmic microwave background (CMB), and radio point sources, which are marginalized over. We find that the SZ contribution is less than 2% (95% C.L.) at the first acoustic peak in W band. Under the assumption that the removed radio point sources are not correlated with the SZ effect this limit implies σ 8 <1.07 at 95% C.L. We investigate the effect on the cosmological parameters of allowing an SZ component. We run Monte Carlo Markov chains with and without an SZ component and find that the addition of the SZ effect does not affect any of the cosmological conclusions. We conclude that the SZ effect does not contaminate the WMAP CMB or change cosmological parameters, refuting the recent claims that they may be corrupted

  6. Foreground removal from WMAP 5 yr temperature maps using an MLP neural network

    Science.gov (United States)

    Nørgaard-Nielsen, H. U.

    2010-09-01

    Aims: One of the main obstacles for extracting the cosmic microwave background (CMB) signal from observations in the mm/sub-mm range is the foreground contamination by emission from Galactic component: mainly synchrotron, free-free, and thermal dust emission. The statistical nature of the intrinsic CMB signal makes it essential to minimize the systematic errors in the CMB temperature determinations. Methods: The feasibility of using simple neural networks to extract the CMB signal from detailed simulated data has already been demonstrated. Here, simple neural networks are applied to the WMAP 5 yr temperature data without using any auxiliary data. Results: A simple multilayer perceptron neural network with two hidden layers provides temperature estimates over more than 75 per cent of the sky with random errors significantly below those previously extracted from these data. Also, the systematic errors, i.e. errors correlated with the Galactic foregrounds, are very small. Conclusions: With these results the neural network method is well prepared for dealing with the high - quality CMB data from the ESA Planck Surveyor satellite. unknown author type, collab

  7. On the Origins of the CMB: Insight from the COBE, WMAP, and Relikt-1 Satellites

    Directory of Open Access Journals (Sweden)

    Robitaille P.-M.

    2007-01-01

    Full Text Available The powerful “Cosmic Microwave Background (CMB” signal currently associated with the origins of the Universe is examined from a historical perspective and relative to the experimental context in which it was measured. Results from the COBE satellite are reviewed, with particular emphasis on the systematic error observed in determining the CMB temperature. The nature of the microwave signal emanating from the oceans is also discussed. From this analysis, it is demonstrated that it is improper for the COBE team to model the Earth as a 285 K blackbody source. The assignment of temperatures to objects that fail to meet the requirements set forth in Kirchhoff’s law constitutes a serious overextension of the laws of thermal emission. Using this evidence, and the general rule that powerful signals are associated with proximal sources, the CMB monopole signal is reassigned to the oceans. In turn, through the analysis of COBE, WMAP, and Relikt-1 data, the dipole signal is attributed to motion through a much weaker microwave field present both at the position of the Earth and at the second Lagrange point.

  8. Testing general relativity using Bayesian model selection: Applications to observations of gravitational waves from compact binary systems

    International Nuclear Information System (INIS)

    Del Pozzo, Walter; Veitch, John; Vecchio, Alberto

    2011-01-01

    Second-generation interferometric gravitational-wave detectors, such as Advanced LIGO and Advanced Virgo, are expected to begin operation by 2015. Such instruments plan to reach sensitivities that will offer the unique possibility to test general relativity in the dynamical, strong-field regime and investigate departures from its predictions, in particular, using the signal from coalescing binary systems. We introduce a statistical framework based on Bayesian model selection in which the Bayes factor between two competing hypotheses measures which theory is favored by the data. Probability density functions of the model parameters are then used to quantify the inference on individual parameters. We also develop a method to combine the information coming from multiple independent observations of gravitational waves, and show how much stronger inference could be. As an introduction and illustration of this framework-and a practical numerical implementation through the Monte Carlo integration technique of nested sampling-we apply it to gravitational waves from the inspiral phase of coalescing binary systems as predicted by general relativity and a very simple alternative theory in which the graviton has a nonzero mass. This method can (and should) be extended to more realistic and physically motivated theories.

  9. From Neutron Star Observables to the Equation of State. II. Bayesian Inference of Equation of State Pressures

    Science.gov (United States)

    Raithel, Carolyn A.; Özel, Feryal; Psaltis, Dimitrios

    2017-08-01

    One of the key goals of observing neutron stars is to infer the equation of state (EoS) of the cold, ultradense matter in their interiors. Here, we present a Bayesian statistical method of inferring the pressures at five fixed densities, from a sample of mock neutron star masses and radii. We show that while five polytropic segments are needed for maximum flexibility in the absence of any prior knowledge of the EoS, regularizers are also necessary to ensure that simple underlying EoS are not over-parameterized. For ideal data with small measurement uncertainties, we show that the pressure at roughly twice the nuclear saturation density, {ρ }{sat}, can be inferred to within 0.3 dex for many realizations of potential sources of uncertainties. The pressures of more complicated EoS with significant phase transitions can also be inferred to within ˜30%. We also find that marginalizing the multi-dimensional parameter space of pressure to infer a mass-radius relation can lead to biases of nearly 1 km in radius, toward larger radii. Using the full, five-dimensional posterior likelihoods avoids this bias.

  10. A Bayesian spatial assimilation scheme for snow coverage observations in a gridded snow model

    Directory of Open Access Journals (Sweden)

    S. Kolberg

    2006-01-01

    Full Text Available A method for assimilating remotely sensed snow covered area (SCA into the snow subroutine of a grid distributed precipitation-runoff model (PRM is presented. The PRM is assumed to simulate the snow state in each grid cell by a snow depletion curve (SDC, which relates that cell's SCA to its snow cover mass balance. The assimilation is based on Bayes' theorem, which requires a joint prior distribution of the SDC variables in all the grid cells. In this paper we propose a spatial model for this prior distribution, and include similarities and dependencies among the grid cells. Used to represent the PRM simulated snow cover state, our joint prior model regards two elevation gradients and a degree-day factor as global variables, rather than describing their effect separately for each cell. This transformation results in smooth normalised surfaces for the two related mass balance variables, supporting a strong inter-cell dependency in their joint prior model. The global features and spatial interdependency in the prior model cause each SCA observation to provide information for many grid cells. The spatial approach similarly facilitates the utilisation of observed discharge. Assimilation of SCA data using the proposed spatial model is evaluated in a 2400 km2 mountainous region in central Norway (61° N, 9° E, based on two Landsat 7 ETM+ images generalized to 1 km2 resolution. An image acquired on 11 May, a week before the peak flood, removes 78% of the variance in the remaining snow storage. Even an image from 4 May, less than a week after the melt onset, reduces this variance by 53%. These results are largely improved compared to a cell-by-cell independent assimilation routine previously reported. Including observed discharge in the updating information improves the 4 May results, but has weak effect on 11 May. Estimated elevation gradients are shown to be sensitive to informational deficits occurring at high altitude, where snowmelt has not started

  11. Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives

    NARCIS (Netherlands)

    Durbin, J.; Koopman, S.J.M.

    1998-01-01

    The analysis of non-Gaussian time series using state space models is considered from both classical and Bayesian perspectives. The treatment in both cases is based on simulation using importance sampling and antithetic variables; Monte Carlo Markov chain methods are not employed. Non-Gaussian

  12. A LAST LOOK AT THE MICROWAVE HAZE/BUBBLES WITH WMAP

    Energy Technology Data Exchange (ETDEWEB)

    Dobler, Gregory, E-mail: dobler@kitp.ucsb.edu [Kavli Institute for Theoretical Physics, University of California, Santa Barbara Kohn Hall, Santa Barbara, CA 93106 (United States)

    2012-05-01

    The microwave 'haze' was first discovered with the initial release of the full sky data from the Wilkinson Microwave Anisotropy Probe (WMAP). It is diffuse emission toward the center of our Galaxy with spectral behavior that makes it difficult to categorize as any of the previously known emission mechanisms at those wavelengths. With now seven years of WMAP data publicly available, we have learned much about the nature of the haze, and with the release of data from the Fermi Gamma-Ray Space Telescope and the discovery of the gamma-ray haze/bubbles, we have had a spectacular confirmation of its existence at other wavelengths. As the WMAP mission winds down and the Planck mission prepares to release data, I take a last look at what WMAP has to tell us about the origin of this unique Galactic feature. Much like the gamma rays, the microwave haze/bubbles is/are elongated in latitude with respect to longitude by a factor of roughly two, and at high latitudes, the microwave emission cuts off sharply above {approx}35 Degree-Sign (compared to {approx}50 Degree-Sign in the gammas). The hard spectrum of electrons required to generate the microwave synchrotron is consistent with that required to generate gamma-ray emission via inverse Compton scattering, though it is likely that these signals result from distinct regions of the spectrum ({approx}10 GeV for the microwaves and {approx}1 TeV for the gammas). While there is no evidence for significant haze polarization in the seven-year WMAP data, I demonstrate explicitly that it is unlikely such a signal would be detectable above the noise.

  13. PROBING THE DARK FLOW SIGNAL IN WMAP 9 -YEAR AND PLANCK COSMIC MICROWAVE BACKGROUND MAPS

    Energy Technology Data Exchange (ETDEWEB)

    Atrio-Barandela, F. [Física Teórica, Universidad de Salamanca, E-37008 Salamanca (Spain); Kashlinsky, A. [NASA Goddard Space Flight Center and SSAI, Observational Cosmology Lab, Greenbelt, MD 20771 (United States); Ebeling, H. [Institute for Astronomy, University of Hawaii, Honolulu, HI 96822 (United States); Fixsen, D. J. [NASA Goddard Space Flight Center and UMCP, Observational Cosmology Lab, Greenbelt, MD 20771 (United States); Kocevski, D., E-mail: atrio@usal.es, E-mail: Alexander.Kashlinsky@nasa.gov, E-mail: ebeling@ifa.hawaii.edu, E-mail: Dale.Fixsen@nasa.gov, E-mail: dale.kocevski@colby.edu [Physics and Astronomy, 5800 Mayflower Hill, Waterville, ME 04901 (United States)

    2015-09-10

    The “dark flow” dipole is a statistically significant dipole found at the position of galaxy clusters in filtered maps of Cosmic Microwave Background (CMB) temperature anisotropies. The dipole measured in WMAP 3-, 5-, and 7- year data releases was (1) mutually consistent, (2) roughly aligned with the all-sky CMB dipole, and (3) correlated with clusters’ X-ray luminosities. We analyzed WMAP 9 -year and Planck 1st- year data releases using a catalog of 980 clusters outside of the Kp0 mask to test our earlier findings. The dipoles measured on these new data sets are fully compatible with our earlier estimates, are similar in amplitude and direction to our previous results, and are in disagreement with the results of an earlier study by the Planck Collaboration. Furthermore, in the Planck data sets dipoles are found to be independent of frequency, ruling out the thermal Sunyaev–Zeldovich as the source of the effect. In the data of both WMAP and Planck we find a clear correlation between the dipole measured at the cluster location in filtered maps and the average anisotropy on the original maps, further proving that the dipole is associated with clusters. The dipole signal is dominated by the most massive clusters, with a statistical significance that is better than 99%, slightly larger than in WMAP. Since both data sets differ in foreground contributions, instrumental noise, and other systematics, the agreement between the WMAP and Planck dipoles argues against them being due to systematic effects in either of the experiments.

  14. Bayesian biostatistics

    CERN Document Server

    Lesaffre, Emmanuel

    2012-01-01

    The growth of biostatistics has been phenomenal in recent years and has been marked by considerable technical innovation in both methodology and computational practicality. One area that has experienced significant growth is Bayesian methods. The growing use of Bayesian methodology has taken place partly due to an increasing number of practitioners valuing the Bayesian paradigm as matching that of scientific discovery. In addition, computational advances have allowed for more complex models to be fitted routinely to realistic data sets. Through examples, exercises and a combination of introd

  15. Searching for CPT violation with cosmic microwave background data from WMAP and BOOMERANG.

    Science.gov (United States)

    Feng, Bo; Li, Mingzhe; Xia, Jun-Qing; Chen, Xuelei; Zhang, Xinmin

    2006-06-09

    We search for signatures of Lorentz and violations in the cosmic microwave background (CMB) temperature and polarization anisotropies by using the Wilkinson Microwave Anisotropy Probe (WMAP) and the 2003 flight of BOOMERANG (B03) data. We note that if the Lorentz and symmetries are broken by a Chern-Simons term in the effective Lagrangian, which couples the dual electromagnetic field strength tensor to an external four-vector, the polarization vectors of propagating CMB photons will get rotated. Using the WMAP data alone, one could put an interesting constraint on the size of such a term. Combined with the B03 data, we found that a nonzero rotation angle of the photons is mildly favored: [Formula: See Text].

  16. CORRELATION ANALYSIS BETWEEN TIBET AS-γ TeV COSMIC RAY AND WMAP NINE-YEAR DATA

    Energy Technology Data Exchange (ETDEWEB)

    Yin, Qian-Qing; Zhang, Shuang-Nan, E-mail: zhangsn@ihep.ac.cn [Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Beijing 100049 (China)

    2015-08-01

    The WMAP team subtracted template-based foreground models to produce foreground-reduced maps, and masked point sources and uncertain sky regions directly; however, whether foreground residuals exist in the WMAP foreground-reduced maps is still an open question. Here, we use Pearson correlation coefficient analysis with AS-γ TeV cosmic ray (CR) data to probe possible foreground residuals in the WMAP nine-year data. The correlation results between the CR and foreground-contained maps (WMAP foreground-unreduced maps, WMAP template-based, and Maximum Entropy Method foreground models) suggest that: (1) CRs can trace foregrounds in the WMAP data; (2) at least some TeV CRs originate from the Milky Way; (3) foregrounds may be related to the existence of CR anisotropy (loss-cone and tail-in structures); (4) there exist differences among different types of foregrounds in the decl. range of <15°. Then, we generate 10,000 mock cosmic microwave background (CMB) sky maps to describe the cosmic variance, which is used to measure the effect of the fluctuations of all possible CMB maps to the correlations between CR and CMB maps. Finally, we do correlation analysis between the CR and WMAP foreground-reduced maps, and find that: (1) there are significant anticorrelations; and (2) the WMAP foreground-reduced maps are credible. However, the significant anticorrelations may be accidental, and the higher signal-to-noise ratio Planck SMICA map cannot reject the hypothesis of accidental correlations. We therefore can only conclude that the foreground residuals exist with ∼95% probability.

  17. Bayesian Utilitarianism

    OpenAIRE

    ZHOU, Lin

    1996-01-01

    In this paper I consider social choices under uncertainty. I prove that any social choice rule that satisfies independence of irrelevant alternatives, translation invariance, and weak anonymity is consistent with ex post Bayesian utilitarianism

  18. Bayesian analysis in plant pathology.

    Science.gov (United States)

    Mila, A L; Carriquiry, A L

    2004-09-01

    ABSTRACT Bayesian methods are currently much discussed and applied in several disciplines from molecular biology to engineering. Bayesian inference is the process of fitting a probability model to a set of data and summarizing the results via probability distributions on the parameters of the model and unobserved quantities such as predictions for new observations. In this paper, after a short introduction of Bayesian inference, we present the basic features of Bayesian methodology using examples from sequencing genomic fragments and analyzing microarray gene-expressing levels, reconstructing disease maps, and designing experiments.

  19. Hybrid inflation revisited in light of WMAP5 data

    International Nuclear Information System (INIS)

    Rehman, Mansoor Ur; Shafi, Qaisar; Wickman, Joshua R.

    2009-01-01

    We study the effects of including one-loop radiative corrections in a nonsupersymmetric hybrid inflationary model. These corrections can arise from Yukawa couplings between the inflaton and right-handed neutrinos, and induce a maximum in the potential which admits hilltop-type solutions in addition to the standard hybrid solutions. We obtain a red-tilted spectral index n s , consistent with Wilkinson Microwave Anisotropy Probe 5 yr analysis data, for sub-Planckian values of the field. This is in contrast to the tree level hybrid analysis, in which a red-tilted spectrum is achieved only for trans-Planckian values of the field. Successful reheating is obtained at the end of the inflationary phase via a conversion of the inflaton and waterfall fields into right-handed neutrinos, whose subsequent decay can explain the observed baryon asymmetry via leptogenesis.

  20. Bayesian maximum entropy integration of ozone observations and model predictions: an application for attainment demonstration in North Carolina.

    Science.gov (United States)

    de Nazelle, Audrey; Arunachalam, Saravanan; Serre, Marc L

    2010-08-01

    States in the USA are required to demonstrate future compliance of criteria air pollutant standards by using both air quality monitors and model outputs. In the case of ozone, the demonstration tests aim at relying heavily on measured values, due to their perceived objectivity and enforceable quality. Weight given to numerical models is diminished by integrating them in the calculations only in a relative sense. For unmonitored locations, the EPA has suggested the use of a spatial interpolation technique to assign current values. We demonstrate that this approach may lead to erroneous assignments of nonattainment and may make it difficult for States to establish future compliance. We propose a method that combines different sources of information to map air pollution, using the Bayesian Maximum Entropy (BME) Framework. The approach gives precedence to measured values and integrates modeled data as a function of model performance. We demonstrate this approach in North Carolina, using the State's ozone monitoring network in combination with outputs from the Multiscale Air Quality Simulation Platform (MAQSIP) modeling system. We show that the BME data integration approach, compared to a spatial interpolation of measured data, improves the accuracy and the precision of ozone estimations across the state.

  1. Adaptive framework to better characterize errors of apriori fluxes and observational residuals in a Bayesian setup for the urban flux inversions.

    Science.gov (United States)

    Ghosh, S.; Lopez-Coto, I.; Prasad, K.; Karion, A.; Mueller, K.; Gourdji, S.; Martin, C.; Whetstone, J. R.

    2017-12-01

    The National Institute of Standards and Technology (NIST) supports the North-East Corridor Baltimore Washington (NEC-B/W) project and Indianapolis Flux Experiment (INFLUX) aiming to quantify sources of Greenhouse Gas (GHG) emissions as well as their uncertainties. These projects employ different flux estimation methods including top-down inversion approaches. The traditional Bayesian inversion method estimates emission distributions by updating prior information using atmospheric observations of Green House Gases (GHG) coupled to an atmospheric and dispersion model. The magnitude of the update is dependent upon the observed enhancement along with the assumed errors such as those associated with prior information and the atmospheric transport and dispersion model. These errors are specified within the inversion covariance matrices. The assumed structure and magnitude of the specified errors can have large impact on the emission estimates from the inversion. The main objective of this work is to build a data-adaptive model for these covariances matrices. We construct a synthetic data experiment using a Kalman Filter inversion framework (Lopez et al., 2017) employing different configurations of transport and dispersion model and an assumed prior. Unlike previous traditional Bayesian approaches, we estimate posterior emissions using regularized sample covariance matrices associated with prior errors to investigate whether the structure of the matrices help to better recover our hypothetical true emissions. To incorporate transport model error, we use ensemble of transport models combined with space-time analytical covariance to construct a covariance that accounts for errors in space and time. A Kalman Filter is then run using these covariances along with Maximum Likelihood Estimates (MLE) of the involved parameters. Preliminary results indicate that specifying sptio-temporally varying errors in the error covariances can improve the flux estimates and uncertainties. We

  2. Taking the Measure of the Universe: Cosmology from the WMAP Mission

    Science.gov (United States)

    Hinshaw, Gary F.

    2007-01-01

    The data from the first three years of operation of the Wilkinson Microwave Anisotropy Probe (WMAP) satellite provide detailed full-sky maps of the cosmic microwave background temperature anisotropy and new full-sky maps of the polarization. Together, the data provide a wealth of cosmological information, including the age of the universe, the epoch when the first stars formed, and the overall composition of baryonic matter, dark matter, and dark energy. The results also provide constraints on the period of inflationary expansion in the very first moments of time. These and other aspects of the mission will be discussed.

  3. FERMI-LAT AND WMAP OBSERVATIONS OF THE PUPPIS A SUPERNOVA REMNANT

    Energy Technology Data Exchange (ETDEWEB)

    Hewitt, J. W. [NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Grondin, M.-H. [Max-Planck-Institut fuer Kernphysik, D-69029 Heidelberg (Germany); Lemoine-Goumard, M.; Reposeur, T. [Centre d' Etudes Nucleaires de Bordeaux-Gradignan, Universite Bordeaux 1, CNRS/IN2p3, F-33175 Gradignan (France); Ballet, J. [Laboratoire AIM, CEA-IRFU/CNRS/Universite Paris Diderot, Service d' Astrophysique, CEA Saclay, F-91191 Gif sur Yvette (France); Tanaka, T., E-mail: john.w.hewitt@nasa.gov, E-mail: marie-helene.grondin@mpi-hd.mpg.de, E-mail: lemoine@cenbg.in2p3.fr [W. W. Hansen Experimental Physics Laboratory, Kavli Institute for Particle Astrophysics and Cosmology, Department of Physics and SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94305 (United States)

    2012-11-10

    We report the detection of GeV {gamma}-ray emission from the supernova remnant (SNR) Puppis A with the Fermi Gamma-Ray Space Telescope. Puppis A is among the faintest SNRs yet detected at GeV energies, with a luminosity of only 2.7 Multiplication-Sign 10{sup 34} (D/2.2 kpc){sup 2} erg s{sup -1} between 1 and 100 GeV. The {gamma}-ray emission from the remnant is spatially extended, with a morphology matching that of the radio and X-ray emission, and is well described by a simple power law with an index of 2.1. We attempt to model the broadband spectral energy distribution (SED), from radio to {gamma}-rays, using standard nonthermal emission mechanisms. To constrain the relativistic electron population we use 7 years of Wilkinson Microwave Anisotropy Probe data to extend the radio spectrum up to 93 GHz. Both leptonic- and hadronic-dominated models can reproduce the nonthermal SED, requiring a total content of cosmic-ray electrons and protons accelerated in Puppis A of at least W {sub CR} Almost-Equal-To (1-5) Multiplication-Sign 10{sup 49} erg.

  4. Uncertainty Quantification of GEOS-5 L-band Radiative Transfer Model Parameters Using Bayesian Inference and SMOS Observations

    Science.gov (United States)

    DeLannoy, Gabrielle J. M.; Reichle, Rolf H.; Vrugt, Jasper A.

    2013-01-01

    Uncertainties in L-band (1.4 GHz) radiative transfer modeling (RTM) affect the simulation of brightness temperatures (Tb) over land and the inversion of satellite-observed Tb into soil moisture retrievals. In particular, accurate estimates of the microwave soil roughness, vegetation opacity and scattering albedo for large-scale applications are difficult to obtain from field studies and often lack an uncertainty estimate. Here, a Markov Chain Monte Carlo (MCMC) simulation method is used to determine satellite-scale estimates of RTM parameters and their posterior uncertainty by minimizing the misfit between long-term averages and standard deviations of simulated and observed Tb at a range of incidence angles, at horizontal and vertical polarization, and for morning and evening overpasses. Tb simulations are generated with the Goddard Earth Observing System (GEOS-5) and confronted with Tb observations from the Soil Moisture Ocean Salinity (SMOS) mission. The MCMC algorithm suggests that the relative uncertainty of the RTM parameter estimates is typically less than 25 of the maximum a posteriori density (MAP) parameter value. Furthermore, the actual root-mean-square-differences in long-term Tb averages and standard deviations are found consistent with the respective estimated total simulation and observation error standard deviations of m3.1K and s2.4K. It is also shown that the MAP parameter values estimated through MCMC simulation are in close agreement with those obtained with Particle Swarm Optimization (PSO).

  5. Monte Carlo Bayesian inference on a statistical model of sub-gridcolumn moisture variability using high-resolution cloud observations. Part 1: Method

    Science.gov (United States)

    Norris, Peter M.; da Silva, Arlindo M.

    2018-01-01

    A method is presented to constrain a statistical model of sub-gridcolumn moisture variability using high-resolution satellite cloud data. The method can be used for large-scale model parameter estimation or cloud data assimilation. The gridcolumn model includes assumed probability density function (PDF) intra-layer horizontal variability and a copula-based inter-layer correlation model. The observables used in the current study are Moderate Resolution Imaging Spectroradiometer (MODIS) cloud-top pressure, brightness temperature and cloud optical thickness, but the method should be extensible to direct cloudy radiance assimilation for a small number of channels. The algorithm is a form of Bayesian inference with a Markov chain Monte Carlo (MCMC) approach to characterizing the posterior distribution. This approach is especially useful in cases where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach is not gradient-based and allows jumps into regions of non-zero cloud probability. The current study uses a skewed-triangle distribution for layer moisture. The article also includes a discussion of the Metropolis and multiple-try Metropolis versions of MCMC. PMID:29618847

  6. Monte Carlo Bayesian Inference on a Statistical Model of Sub-Gridcolumn Moisture Variability Using High-Resolution Cloud Observations. Part 1: Method

    Science.gov (United States)

    Norris, Peter M.; Da Silva, Arlindo M.

    2016-01-01

    A method is presented to constrain a statistical model of sub-gridcolumn moisture variability using high-resolution satellite cloud data. The method can be used for large-scale model parameter estimation or cloud data assimilation. The gridcolumn model includes assumed probability density function (PDF) intra-layer horizontal variability and a copula-based inter-layer correlation model. The observables used in the current study are Moderate Resolution Imaging Spectroradiometer (MODIS) cloud-top pressure, brightness temperature and cloud optical thickness, but the method should be extensible to direct cloudy radiance assimilation for a small number of channels. The algorithm is a form of Bayesian inference with a Markov chain Monte Carlo (MCMC) approach to characterizing the posterior distribution. This approach is especially useful in cases where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach is not gradient-based and allows jumps into regions of non-zero cloud probability. The current study uses a skewed-triangle distribution for layer moisture. The article also includes a discussion of the Metropolis and multiple-try Metropolis versions of MCMC.

  7. Bayesian programming

    CERN Document Server

    Bessiere, Pierre; Ahuactzin, Juan Manuel; Mekhnacha, Kamel

    2013-01-01

    Probability as an Alternative to Boolean LogicWhile logic is the mathematical foundation of rational reasoning and the fundamental principle of computing, it is restricted to problems where information is both complete and certain. However, many real-world problems, from financial investments to email filtering, are incomplete or uncertain in nature. Probability theory and Bayesian computing together provide an alternative framework to deal with incomplete and uncertain data. Decision-Making Tools and Methods for Incomplete and Uncertain DataEmphasizing probability as an alternative to Boolean

  8. Bayesian image restoration, using configurations

    OpenAIRE

    Thorarinsdottir, Thordis

    2006-01-01

    In this paper, we develop a Bayesian procedure for removing noise from images that can be viewed as noisy realisations of random sets in the plane. The procedure utilises recent advances in configuration theory for noise free random sets, where the probabilities of observing the different boundary configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the re...

  9. Uncertainty quantification of GEOS-5 L-band radiative transfer model parameters using Bayesian inference and SMOS observations

    NARCIS (Netherlands)

    De Lannoy, G.J.M.; Reichle, R.H.; Vrugt, J.A.

    2014-01-01

    Uncertainties in L-band (1.4 GHz) microwave radiative transfer modeling (RTM) affect the simulation of brightness temperatures (Tb) over land and the inversion of satellite-observed Tb into soil moisture retrievals. In particular, accurate estimates of the microwave soil roughness, vegetation

  10. ANALYSIS OF WMAP 7 YEAR TEMPERATURE DATA: ASTROPHYSICS OF THE GALACTIC HAZE

    Energy Technology Data Exchange (ETDEWEB)

    Pietrobon, Davide; Gorski, Krzysztof M.; Bartlett, James; Colombo, Loris P. L.; Jewell, Jeffrey B.; Pagano, Luca; Rocha, Graca; Lawrence, Charles R. [Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109-8099 (United States); Banday, A. J. [Universie de Toulouse, UPS-OMP, IRAP, Toulouse (France); Dobler, Gregory [Kavli Institute for Theoretical Physics, University of California, Santa Barbara Kohn Hall, Santa Barbara, CA 93106 (United States); Hildebrandt, Sergi R. [Division of Physics, Mathematics and Astronomy, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125 (United States); Eriksen, Hans Kristian [Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029, Blindern, N-0315 Oslo (Norway); Saha, Rajib, E-mail: davide.pietrobon@jpl.nasa.gov [Physics Department, Indian Institute of Science Education and Research Bhopal, Bhopal, MP 462023 (India)

    2012-08-10

    We perform a joint analysis of the cosmic microwave background (CMB) and Galactic emission from the WMAP 7 year temperature data. Using the Commander code, based on Gibbs sampling, we simultaneously derive the CMB and Galactic components on scales larger than 1 Degree-Sign with improved sensitivity over previous work. We conduct a detailed study of the low-frequency Galactic foreground, focusing on the 'microwave haze' emission around the Galactic center. We demonstrate improved performance in quantifying the diffuse Galactic emission when including Haslam 408 MHz data and when jointly modeling the spinning and thermal dust emission. We examine whether the hypothetical Galactic haze can be explained by a spatial variation of the synchrotron spectral index, and find that the excess of emission around the Galactic center is stable with respect to variations of the foreground model. Our results demonstrate that the new Galactic foreground component-the microwave haze-is indeed present.

  11. Foreground removal from WMAP 5 yr temperature maps using an MLP neural network

    DEFF Research Database (Denmark)

    Nørgaard-Nielsen, Hans Ulrik

    2010-01-01

    CMB signal makes it essential to minimize the systematic errors in the CMB temperature determinations. Methods. The feasibility of using simple neural networks to extract the CMB signal from detailed simulated data has already been demonstrated. Here, simple neural networks are applied to the WMAP 5...... yr temperature data without using any auxiliary data. Results. A simple multilayer perceptron neural network with two hidden layers provides temperature estimates over more than 75 per cent of the sky with random errors significantly below those previously extracted from these data. Also......, the systematic errors, i.e. errors correlated with the Galactic foregrounds, are very small. Conclusions. With these results the neural network method is well prepared for dealing with the high-quality CMB data from the ESA Planck Surveyor satellite. © ESO, 2010....

  12. Bayesian Graphical Models

    DEFF Research Database (Denmark)

    Jensen, Finn Verner; Nielsen, Thomas Dyhre

    2016-01-01

    Mathematically, a Bayesian graphical model is a compact representation of the joint probability distribution for a set of variables. The most frequently used type of Bayesian graphical models are Bayesian networks. The structural part of a Bayesian graphical model is a graph consisting of nodes...

  13. A Bayesian model for binary Markov chains

    Directory of Open Access Journals (Sweden)

    Belkheir Essebbar

    2004-02-01

    Full Text Available This note is concerned with Bayesian estimation of the transition probabilities of a binary Markov chain observed from heterogeneous individuals. The model is founded on the Jeffreys' prior which allows for transition probabilities to be correlated. The Bayesian estimator is approximated by means of Monte Carlo Markov chain (MCMC techniques. The performance of the Bayesian estimates is illustrated by analyzing a small simulated data set.

  14. Monte Carlo Bayesian inference on a statistical model of sub-gridcolumn moisture variability using high-resolution cloud observations. Part 2: Sensitivity tests and results

    Science.gov (United States)

    Norris, Peter M.; da Silva, Arlindo M.

    2018-01-01

    Part 1 of this series presented a Monte Carlo Bayesian method for constraining a complex statistical model of global circulation model (GCM) sub-gridcolumn moisture variability using high-resolution Moderate Resolution Imaging Spectroradiometer (MODIS) cloud data, thereby permitting parameter estimation and cloud data assimilation for large-scale models. This article performs some basic testing of this new approach, verifying that it does indeed reduce mean and standard deviation biases significantly with respect to the assimilated MODIS cloud optical depth, brightness temperature and cloud-top pressure and that it also improves the simulated rotational–Raman scattering cloud optical centroid pressure (OCP) against independent (non-assimilated) retrievals from the Ozone Monitoring Instrument (OMI). Of particular interest, the Monte Carlo method does show skill in the especially difficult case where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach allows non-gradient-based jumps into regions of non-zero cloud probability. In the example provided, the method is able to restore marine stratocumulus near the Californian coast, where the background state has a clear swath. This article also examines a number of algorithmic and physical sensitivities of the new method and provides guidance for its cost-effective implementation. One obvious difficulty for the method, and other cloud data assimilation methods as well, is the lack of information content in passive-radiometer-retrieved cloud observables on cloud vertical structure, beyond cloud-top pressure and optical thickness, thus necessitating strong dependence on the background vertical moisture structure. It is found that a simple flow-dependent correlation modification from Riishojgaard provides some help in this respect, by

  15. Monte Carlo Bayesian Inference on a Statistical Model of Sub-gridcolumn Moisture Variability Using High-resolution Cloud Observations . Part II; Sensitivity Tests and Results

    Science.gov (United States)

    da Silva, Arlindo M.; Norris, Peter M.

    2013-01-01

    Part I presented a Monte Carlo Bayesian method for constraining a complex statistical model of GCM sub-gridcolumn moisture variability using high-resolution MODIS cloud data, thereby permitting large-scale model parameter estimation and cloud data assimilation. This part performs some basic testing of this new approach, verifying that it does indeed significantly reduce mean and standard deviation biases with respect to the assimilated MODIS cloud optical depth, brightness temperature and cloud top pressure, and that it also improves the simulated rotational-Ramman scattering cloud optical centroid pressure (OCP) against independent (non-assimilated) retrievals from the OMI instrument. Of particular interest, the Monte Carlo method does show skill in the especially difficult case where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach allows finite jumps into regions of non-zero cloud probability. In the example provided, the method is able to restore marine stratocumulus near the Californian coast where the background state has a clear swath. This paper also examines a number of algorithmic and physical sensitivities of the new method and provides guidance for its cost-effective implementation. One obvious difficulty for the method, and other cloud data assimilation methods as well, is the lack of information content in the cloud observables on cloud vertical structure, beyond cloud top pressure and optical thickness, thus necessitating strong dependence on the background vertical moisture structure. It is found that a simple flow-dependent correlation modification due to Riishojgaard (1998) provides some help in this respect, by better honoring inversion structures in the background state.

  16. Monte Carlo Bayesian Inference on a Statistical Model of Sub-Gridcolumn Moisture Variability Using High-Resolution Cloud Observations. Part 2: Sensitivity Tests and Results

    Science.gov (United States)

    Norris, Peter M.; da Silva, Arlindo M.

    2016-01-01

    Part 1 of this series presented a Monte Carlo Bayesian method for constraining a complex statistical model of global circulation model (GCM) sub-gridcolumn moisture variability using high-resolution Moderate Resolution Imaging Spectroradiometer (MODIS) cloud data, thereby permitting parameter estimation and cloud data assimilation for large-scale models. This article performs some basic testing of this new approach, verifying that it does indeed reduce mean and standard deviation biases significantly with respect to the assimilated MODIS cloud optical depth, brightness temperature and cloud-top pressure and that it also improves the simulated rotational-Raman scattering cloud optical centroid pressure (OCP) against independent (non-assimilated) retrievals from the Ozone Monitoring Instrument (OMI). Of particular interest, the Monte Carlo method does show skill in the especially difficult case where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach allows non-gradient-based jumps into regions of non-zero cloud probability. In the example provided, the method is able to restore marine stratocumulus near the Californian coast, where the background state has a clear swath. This article also examines a number of algorithmic and physical sensitivities of the new method and provides guidance for its cost-effective implementation. One obvious difficulty for the method, and other cloud data assimilation methods as well, is the lack of information content in passive-radiometer-retrieved cloud observables on cloud vertical structure, beyond cloud-top pressure and optical thickness, thus necessitating strong dependence on the background vertical moisture structure. It is found that a simple flow-dependent correlation modification from Riishojgaard provides some help in this respect, by

  17. Probability biases as Bayesian inference

    Directory of Open Access Journals (Sweden)

    Andre; C. R. Martins

    2006-11-01

    Full Text Available In this article, I will show how several observed biases in human probabilistic reasoning can be partially explained as good heuristics for making inferences in an environment where probabilities have uncertainties associated to them. Previous results show that the weight functions and the observed violations of coalescing and stochastic dominance can be understood from a Bayesian point of view. We will review those results and see that Bayesian methods should also be used as part of the explanation behind other known biases. That means that, although the observed errors are still errors under the be understood as adaptations to the solution of real life problems. Heuristics that allow fast evaluations and mimic a Bayesian inference would be an evolutionary advantage, since they would give us an efficient way of making decisions. %XX In that sense, it should be no surprise that humans reason with % probability as it has been observed.

  18. Assessing the association between natural food folate intake and blood folate concentrations: a systematic review and Bayesian meta-analysis of trials and observational studies.

    Science.gov (United States)

    Marchetta, Claire M; Devine, Owen J; Crider, Krista S; Tsang, Becky L; Cordero, Amy M; Qi, Yan Ping; Guo, Jing; Berry, Robert J; Rosenthal, Jorge; Mulinare, Joseph; Mersereau, Patricia; Hamner, Heather C

    2015-04-10

    Folate is found naturally in foods or as synthetic folic acid in dietary supplements and fortified foods. Adequate periconceptional folic acid intake can prevent neural tube defects. Folate intake impacts blood folate concentration; however, the dose-response between natural food folate and blood folate concentrations has not been well described. We estimated this association among healthy females. A systematic literature review identified studies (1 1992-3 2014) with both natural food folate intake alone and blood folate concentration among females aged 12-49 years. Bayesian methods were used to estimate regression model parameters describing the association between natural food folate intake and subsequent blood folate concentration. Seven controlled trials and 29 observational studies met the inclusion criteria. For the six studies using microbiologic assay (MA) included in the meta-analysis, we estimate that a 6% (95% Credible Interval (CrI): 4%, 9%) increase in red blood cell (RBC) folate concentration and a 7% (95% CrI: 1%, 12%) increase in serum/plasma folate concentration can occur for every 10% increase in natural food folate intake. Using modeled results, we estimate that a natural food folate intake of ≥ 450 μg dietary folate equivalents (DFE)/day could achieve the lower bound of an RBC folate concentration (~ 1050 nmol/L) associated with the lowest risk of a neural tube defect. Natural food folate intake affects blood folate concentration and adequate intakes could help women achieve a RBC folate concentration associated with a risk of 6 neural tube defects/10,000 live births.

  19. Assessing the Association between Natural Food Folate Intake and Blood Folate Concentrations: A Systematic Review and Bayesian Meta-Analysis of Trials and Observational Studies

    Directory of Open Access Journals (Sweden)

    Claire M. Marchetta

    2015-04-01

    Full Text Available Folate is found naturally in foods or as synthetic folic acid in dietary supplements and fortified foods. Adequate periconceptional folic acid intake can prevent neural tube defects. Folate intake impacts blood folate concentration; however, the dose-response between natural food folate and blood folate concentrations has not been well described. We estimated this association among healthy females. A systematic literature review identified studies (1 1992–3 2014 with both natural food folate intake alone and blood folate concentration among females aged 12–49 years. Bayesian methods were used to estimate regression model parameters describing the association between natural food folate intake and subsequent blood folate concentration. Seven controlled trials and 29 observational studies met the inclusion criteria. For the six studies using microbiologic assay (MA included in the meta-analysis, we estimate that a 6% (95% Credible Interval (CrI: 4%, 9% increase in red blood cell (RBC folate concentration and a 7% (95% CrI: 1%, 12% increase in serum/plasma folate concentration can occur for every 10% increase in natural food folate intake. Using modeled results, we estimate that a natural food folate intake of ≥450 μg dietary folate equivalents (DFE/day could achieve the lower bound of an RBC folate concentration (~1050 nmol/L associated with the lowest risk of a neural tube defect. Natural food folate intake affects blood folate concentration and adequate intakes could help women achieve a RBC folate concentration associated with a risk of 6 neural tube defects/10,000 live births.

  20. Are all modes created equal? An analysis of the WMAP 5- and 7-year data without inflationary prejudice

    International Nuclear Information System (INIS)

    Gjerloew, Eirik; Elgaroey, Oystein

    2011-01-01

    We submit recent claims of hints of primordial tensor perturbations and a scale-dependent spectral index in the WMAP data to a closer scrutiny. Our approach differs in that we use different best-fit values at which to fix the parameters not to be varied, and in that we use CosmoMC, thus incorporating the WMAP likelihood code and EE and BB mode data. We introduce a new parameter to test the claims of a scale-dependent spectral index. While we do find some hints of a scale-dependent spectral index over the multipole range l=2-220, the change in maximum likelihood is too small to justify introducing a new parameter. We conclude that there is no significant detection of primordial tensor perturbations, and that the assumption of a scale-independent spectral index in this multipole range has little effect on the amount of primordial gravitational waves found.

  1. Introduction to Bayesian statistics

    CERN Document Server

    Bolstad, William M

    2017-01-01

    There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this Third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian staistics. The author continues to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inferenfe cfor discrete random variables, bionomial proprotion, Poisson, normal mean, and simple linear regression. In addition, newly-developing topics in the field are presented in four new chapters: Bayesian inference with unknown mean and variance; Bayesian inference for Multivariate Normal mean vector; Bayesian inference for Multiple Linear RegressionModel; and Computati...

  2. Spectrum of the Anomalous Microwave Emission in the North Celestial Pole with WMAP 7-Year Data

    Directory of Open Access Journals (Sweden)

    Anna Bonaldi

    2012-01-01

    Full Text Available We estimate the frequency spectrum of the diffuse anomalous microwave emission (AME on the North Celestial Pole (NCP region of the sky with the Correlated Component Analysis (CCA component separation method applied to WMAP 7-yr data. The NCP is a suitable region for this analysis because the AME is weakly contaminated by synchrotron and free-free emission. By modeling the AME component as a peaked spectrum we estimate the peak frequency to be 21.7±0.8 GHz, in agreement with previous analyses which favored νp < 23 GHz. The ability of our method to correctly recover the position of the peak is verified through simulations. We compare the estimated AME spectrum with theoretical spinning dust models to constrain the hydrogen density nH. The best results are obtained with densities around 0.2–0.3 cm−3, typical of warm ionised medium (WIM to warm neutral medium (WNM conditions. The degeneracy with the gas temperature prevents an accurate determination of nH, especially for low hydrogen ionization fractions, where densities of a few cm−3 are also allowed.

  3. Neutrino cosmology after WMAP 7-year data and LHC first Z' bounds.

    Science.gov (United States)

    Anchordoqui, Luis Alfredo; Goldberg, Haim

    2012-02-24

    The gauge-extended U(1)(C)×SU(2)(L)×U(1)(I(R))×U(1)(L) model elevates the global symmetries of the standard model (baryon number B and lepton number L) to local gauge symmetries. The U(1)(L) symmetry leads to three superweakly interacting right-handed neutrinos. This also renders a B-L symmetry nonanomalous. The superweak interactions of these Dirac states permit ν(R) decoupling just above the QCD phase transition: 175 is < or approximately equal to T(ν(R))(dec)/MeV is < or approximately equal to 250. In this transitional region, the residual temperature ratio between ν(L) and ν(R) generates extra relativistic degrees of freedom at BBN and at the CMB epochs. Consistency with both WMAP 7-year data and recent estimates of the primordial 4He mass fraction is achieved for 3

  4. Bayesian artificial intelligence

    CERN Document Server

    Korb, Kevin B

    2010-01-01

    Updated and expanded, Bayesian Artificial Intelligence, Second Edition provides a practical and accessible introduction to the main concepts, foundation, and applications of Bayesian networks. It focuses on both the causal discovery of networks and Bayesian inference procedures. Adopting a causal interpretation of Bayesian networks, the authors discuss the use of Bayesian networks for causal modeling. They also draw on their own applied research to illustrate various applications of the technology.New to the Second EditionNew chapter on Bayesian network classifiersNew section on object-oriente

  5. Bayesian artificial intelligence

    CERN Document Server

    Korb, Kevin B

    2003-01-01

    As the power of Bayesian techniques has become more fully realized, the field of artificial intelligence has embraced Bayesian methodology and integrated it to the point where an introduction to Bayesian techniques is now a core course in many computer science programs. Unlike other books on the subject, Bayesian Artificial Intelligence keeps mathematical detail to a minimum and covers a broad range of topics. The authors integrate all of Bayesian net technology and learning Bayesian net technology and apply them both to knowledge engineering. They emphasize understanding and intuition but also provide the algorithms and technical background needed for applications. Software, exercises, and solutions are available on the authors' website.

  6. Bayesian Analysis of the Cosmic Microwave Background

    Science.gov (United States)

    Jewell, Jeffrey

    2007-01-01

    There is a wealth of cosmological information encoded in the spatial power spectrum of temperature anisotropies of the cosmic microwave background! Experiments designed to map the microwave sky are returning a flood of data (time streams of instrument response as a beam is swept over the sky) at several different frequencies (from 30 to 900 GHz), all with different resolutions and noise properties. The resulting analysis challenge is to estimate, and quantify our uncertainty in, the spatial power spectrum of the cosmic microwave background given the complexities of "missing data", foreground emission, and complicated instrumental noise. Bayesian formulation of this problem allows consistent treatment of many complexities including complicated instrumental noise and foregrounds, and can be numerically implemented with Gibbs sampling. Gibbs sampling has now been validated as an efficient, statistically exact, and practically useful method for low-resolution (as demonstrated on WMAP 1 and 3 year temperature and polarization data). Continuing development for Planck - the goal is to exploit the unique capabilities of Gibbs sampling to directly propagate uncertainties in both foreground and instrument models to total uncertainty in cosmological parameters.

  7. Bayesian Mediation Analysis

    OpenAIRE

    Yuan, Ying; MacKinnon, David P.

    2009-01-01

    This article proposes Bayesian analysis of mediation effects. Compared to conventional frequentist mediation analysis, the Bayesian approach has several advantages. First, it allows researchers to incorporate prior information into the mediation analysis, thus potentially improving the efficiency of estimates. Second, under the Bayesian mediation analysis, inference is straightforward and exact, which makes it appealing for studies with small samples. Third, the Bayesian approach is conceptua...

  8. Application of Bayesian model averaging to measurements of the primordial power spectrum

    International Nuclear Information System (INIS)

    Parkinson, David; Liddle, Andrew R.

    2010-01-01

    Cosmological parameter uncertainties are often stated assuming a particular model, neglecting the model uncertainty, even when Bayesian model selection is unable to identify a conclusive best model. Bayesian model averaging is a method for assessing parameter uncertainties in situations where there is also uncertainty in the underlying model. We apply model averaging to the estimation of the parameters associated with the primordial power spectra of curvature and tensor perturbations. We use CosmoNest and MultiNest to compute the model evidences and posteriors, using cosmic microwave data from WMAP, ACBAR, BOOMERanG, and CBI, plus large-scale structure data from the SDSS DR7. We find that the model-averaged 95% credible interval for the spectral index using all of the data is 0.940 s s is specified at a pivot scale 0.015 Mpc -1 . For the tensors model averaging can tighten the credible upper limit, depending on prior assumptions.

  9. Bayesian benefits with JASP

    NARCIS (Netherlands)

    Marsman, M.; Wagenmakers, E.-J.

    2017-01-01

    We illustrate the Bayesian approach to data analysis using the newly developed statistical software program JASP. With JASP, researchers are able to take advantage of the benefits that the Bayesian framework has to offer in terms of parameter estimation and hypothesis testing. The Bayesian

  10. Customized vs population-based growth charts to identify neonates at risk of adverse outcome: systematic review and Bayesian meta-analysis of observational studies.

    Science.gov (United States)

    Chiossi, G; Pedroza, C; Costantine, M M; Truong, V T T; Gargano, G; Saade, G R

    2017-08-01

    To compare the effectiveness of customized vs population-based growth charts for the prediction of adverse pregnancy outcomes. MEDLINE, ClinicalTrials.gov and The Cochrane Library were searched up to 31 May 2016 to identify interventional and observational studies comparing adverse outcomes among large- (LGA) and small- (SGA) for-gestational-age neonates, when classified according to customized vs population-based growth charts. Perinatal mortality and admission to the neonatal intensive care unit (NICU) of both SGA and LGA neonates, intrauterine fetal demise (IUFD) and neonatal mortality of SGA neonates, and neonatal shoulder dystocia and hypoglycemia as well as maternal third- and fourth-degree perineal lacerations in LGA pregnancies were evaluated. The electronic search identified 237 records that were examined based on title and abstract, of which 27 full-text articles were examined for eligibility. After excluding seven articles, 20 observational studies were included in a Bayesian meta-analysis. Neonates classified as SGA according to customized growth charts had higher risks of IUFD (odds ratio (OR), 7.8 (95% CI, 4.2-12.3)), neonatal death (OR, 3.5 (95% CI, 1.1-8.0)), perinatal death (OR, 5.8 (95% CI, 3.8-7.8)) and NICU admission (OR, 3.6 (95% CI, 2.0-5.5)) than did non-SGA cases. Neonates classified as SGA according to population-based growth charts also had increased risk for adverse outcomes, albeit the point estimates of the pooled ORs were smaller: IUFD (OR, 3.3 (95% CI, 1.9-5.0)), neonatal death (OR, 2.9 (95% CI, 1.2-4.5)), perinatal death (OR, 4.0 (95% CI, 2.8-5.1)) and NICU admission (OR, 2.4 (95% CI, 1.7-3.2)). For LGA vs non-LGA, there were no differences in pooled ORs for perinatal death, NICU admission, hypoglycemia and maternal third- and fourth-degree perineal lacerations when classified according to either the customized or the population-based approach. In contrast, both approaches indicated that LGA neonates are at increased risk for

  11. Approximate Bayesian computation.

    Directory of Open Access Journals (Sweden)

    Mikael Sunnåker

    Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.

  12. Understanding Computational Bayesian Statistics

    CERN Document Server

    Bolstad, William M

    2011-01-01

    A hands-on introduction to computational statistics from a Bayesian point of view Providing a solid grounding in statistics while uniquely covering the topics from a Bayesian perspective, Understanding Computational Bayesian Statistics successfully guides readers through this new, cutting-edge approach. With its hands-on treatment of the topic, the book shows how samples can be drawn from the posterior distribution when the formula giving its shape is all that is known, and how Bayesian inferences can be based on these samples from the posterior. These ideas are illustrated on common statistic

  13. Bayesian statistics an introduction

    CERN Document Server

    Lee, Peter M

    2012-01-01

    Bayesian Statistics is the school of thought that combines prior beliefs with the likelihood of a hypothesis to arrive at posterior beliefs. The first edition of Peter Lee’s book appeared in 1989, but the subject has moved ever onwards, with increasing emphasis on Monte Carlo based techniques. This new fourth edition looks at recent techniques such as variational methods, Bayesian importance sampling, approximate Bayesian computation and Reversible Jump Markov Chain Monte Carlo (RJMCMC), providing a concise account of the way in which the Bayesian approach to statistics develops as wel

  14. Bayesian analysis of rare events

    Energy Technology Data Exchange (ETDEWEB)

    Straub, Daniel, E-mail: straub@tum.de; Papaioannou, Iason; Betz, Wolfgang

    2016-06-01

    In many areas of engineering and science there is an interest in predicting the probability of rare events, in particular in applications related to safety and security. Increasingly, such predictions are made through computer models of physical systems in an uncertainty quantification framework. Additionally, with advances in IT, monitoring and sensor technology, an increasing amount of data on the performance of the systems is collected. This data can be used to reduce uncertainty, improve the probability estimates and consequently enhance the management of rare events and associated risks. Bayesian analysis is the ideal method to include the data into the probabilistic model. It ensures a consistent probabilistic treatment of uncertainty, which is central in the prediction of rare events, where extrapolation from the domain of observation is common. We present a framework for performing Bayesian updating of rare event probabilities, termed BUS. It is based on a reinterpretation of the classical rejection-sampling approach to Bayesian analysis, which enables the use of established methods for estimating probabilities of rare events. By drawing upon these methods, the framework makes use of their computational efficiency. These methods include the First-Order Reliability Method (FORM), tailored importance sampling (IS) methods and Subset Simulation (SuS). In this contribution, we briefly review these methods in the context of the BUS framework and investigate their applicability to Bayesian analysis of rare events in different settings. We find that, for some applications, FORM can be highly efficient and is surprisingly accurate, enabling Bayesian analysis of rare events with just a few model evaluations. In a general setting, BUS implemented through IS and SuS is more robust and flexible.

  15. Maximum a posteriori probability estimates in infinite-dimensional Bayesian inverse problems

    International Nuclear Information System (INIS)

    Helin, T; Burger, M

    2015-01-01

    A demanding challenge in Bayesian inversion is to efficiently characterize the posterior distribution. This task is problematic especially in high-dimensional non-Gaussian problems, where the structure of the posterior can be very chaotic and difficult to analyse. Current inverse problem literature often approaches the problem by considering suitable point estimators for the task. Typically the choice is made between the maximum a posteriori (MAP) or the conditional mean (CM) estimate. The benefits of either choice are not well-understood from the perspective of infinite-dimensional theory. Most importantly, there exists no general scheme regarding how to connect the topological description of a MAP estimate to a variational problem. The recent results by Dashti and others (Dashti et al 2013 Inverse Problems 29 095017) resolve this issue for nonlinear inverse problems in Gaussian framework. In this work we improve the current understanding by introducing a novel concept called the weak MAP (wMAP) estimate. We show that any MAP estimate in the sense of Dashti et al (2013 Inverse Problems 29 095017) is a wMAP estimate and, moreover, how the wMAP estimate connects to a variational formulation in general infinite-dimensional non-Gaussian problems. The variational formulation enables to study many properties of the infinite-dimensional MAP estimate that were earlier impossible to study. In a recent work by the authors (Burger and Lucka 2014 Maximum a posteriori estimates in linear inverse problems with logconcave priors are proper bayes estimators preprint) the MAP estimator was studied in the context of the Bayes cost method. Using Bregman distances, proper convex Bayes cost functions were introduced for which the MAP estimator is the Bayes estimator. Here, we generalize these results to the infinite-dimensional setting. Moreover, we discuss the implications of our results for some examples of prior models such as the Besov prior and hierarchical prior. (paper)

  16. Bayesian Mediation Analysis

    Science.gov (United States)

    Yuan, Ying; MacKinnon, David P.

    2009-01-01

    In this article, we propose Bayesian analysis of mediation effects. Compared with conventional frequentist mediation analysis, the Bayesian approach has several advantages. First, it allows researchers to incorporate prior information into the mediation analysis, thus potentially improving the efficiency of estimates. Second, under the Bayesian…

  17. The Bayesian Score Statistic

    NARCIS (Netherlands)

    Kleibergen, F.R.; Kleijn, R.; Paap, R.

    2000-01-01

    We propose a novel Bayesian test under a (noninformative) Jeffreys'priorspecification. We check whether the fixed scalar value of the so-calledBayesian Score Statistic (BSS) under the null hypothesis is aplausiblerealization from its known and standardized distribution under thealternative. Unlike

  18. Bayesian Probability Theory

    Science.gov (United States)

    von der Linden, Wolfgang; Dose, Volker; von Toussaint, Udo

    2014-06-01

    Preface; Part I. Introduction: 1. The meaning of probability; 2. Basic definitions; 3. Bayesian inference; 4. Combinatrics; 5. Random walks; 6. Limit theorems; 7. Continuous distributions; 8. The central limit theorem; 9. Poisson processes and waiting times; Part II. Assigning Probabilities: 10. Transformation invariance; 11. Maximum entropy; 12. Qualified maximum entropy; 13. Global smoothness; Part III. Parameter Estimation: 14. Bayesian parameter estimation; 15. Frequentist parameter estimation; 16. The Cramer-Rao inequality; Part IV. Testing Hypotheses: 17. The Bayesian way; 18. The frequentist way; 19. Sampling distributions; 20. Bayesian vs frequentist hypothesis tests; Part V. Real World Applications: 21. Regression; 22. Inconsistent data; 23. Unrecognized signal contributions; 24. Change point problems; 25. Function estimation; 26. Integral equations; 27. Model selection; 28. Bayesian experimental design; Part VI. Probabilistic Numerical Techniques: 29. Numerical integration; 30. Monte Carlo methods; 31. Nested sampling; Appendixes; References; Index.

  19. Features in the primordial spectrum: New constraints from WMAP7 and ACT data and prospects for the Planck mission

    International Nuclear Information System (INIS)

    Benetti, Micol; Lattanzi, Massimiliano; Calabrese, Erminia; Melchiorri, Alessandro

    2011-01-01

    We update the constraints on possible features in the primordial inflationary density perturbation spectrum by using the latest data from the WMAP7 and ACT (Atacama Cosmology Telescope) cosmic microwave background experiments. The inclusion of new data significantly improves the constraints with respect to older work, especially to smaller angular scales. While we found no clear statistical evidence in the data for extensions to the simplest, featureless, inflationary model, models with a step provide a significantly better fit than standard featureless power-law spectra. We show that the possibility of a step in the inflationary potential like the one preferred by current data will soon be tested by the forthcoming temperature and polarization data from the Planck satellite mission.

  20. BAYESIAN IMAGE RESTORATION, USING CONFIGURATIONS

    Directory of Open Access Journals (Sweden)

    Thordis Linda Thorarinsdottir

    2011-05-01

    Full Text Available In this paper, we develop a Bayesian procedure for removing noise from images that can be viewed as noisy realisations of random sets in the plane. The procedure utilises recent advances in configuration theory for noise free random sets, where the probabilities of observing the different boundary configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for salt and pepper noise. The inference in the model is discussed in detail for 3 X 3 and 5 X 5 configurations and examples of the performance of the procedure are given.

  1. Bayesian computation with R

    CERN Document Server

    Albert, Jim

    2009-01-01

    There has been a dramatic growth in the development and application of Bayesian inferential methods. Some of this growth is due to the availability of powerful simulation-based algorithms to summarize posterior distributions. There has been also a growing interest in the use of the system R for statistical analyses. R's open source nature, free availability, and large number of contributor packages have made R the software of choice for many statisticians in education and industry. Bayesian Computation with R introduces Bayesian modeling by the use of computation using the R language. The earl

  2. Bayesian data analysis for newcomers.

    Science.gov (United States)

    Kruschke, John K; Liddell, Torrin M

    2018-02-01

    This article explains the foundational concepts of Bayesian data analysis using virtually no mathematical notation. Bayesian ideas already match your intuitions from everyday reasoning and from traditional data analysis. Simple examples of Bayesian data analysis are presented that illustrate how the information delivered by a Bayesian analysis can be directly interpreted. Bayesian approaches to null-value assessment are discussed. The article clarifies misconceptions about Bayesian methods that newcomers might have acquired elsewhere. We discuss prior distributions and explain how they are not a liability but an important asset. We discuss the relation of Bayesian data analysis to Bayesian models of mind, and we briefly discuss what methodological problems Bayesian data analysis is not meant to solve. After you have read this article, you should have a clear sense of how Bayesian data analysis works and the sort of information it delivers, and why that information is so intuitive and useful for drawing conclusions from data.

  3. Holographic dark energy models: a comparison from the latest observational data

    International Nuclear Information System (INIS)

    Li, Miao; Li, Xiao-Dong; Wang, Shuang; Zhang, Xin

    2009-01-01

    The holographic principle of quantum gravity theory has been applied to the dark energy (DE) problem, and so far three holographic DE models have been proposed: the original holographic dark energy (HDE) model, the agegraphic dark energy (ADE) model, and the holographic Ricci dark energy (RDE) model. In this work, we perform the best-fit analysis on these three models, by using the latest observational data including the Union+CFA3 sample of 397 Type Ia supernovae (SNIa), the shift parameter of the cosmic microwave background (CMB) given by the five-year Wilkinson Microwave Anisotropy Probe (WMAP5) observations, and the baryon acoustic oscillation (BAO) measurement from the Sloan Digital Sky Survey (SDSS). The analysis shows that for HDE, χ min 2 = 465.912; for RDE, χ min 2 = 483.130; for ADE, χ min 2 = 481.694. Among these models, HDE model can give the smallest χ 2 min . Besides, we also use the Bayesian evidence (BE) as a model selection criterion to make a comparison. It is found that for HDE, ADE, and RDE, Δln BE = −0.86, −5.17, and −8.14, respectively. So, it seems that the HDE model is more favored by the observational data

  4. Bayesian methods for data analysis

    CERN Document Server

    Carlin, Bradley P.

    2009-01-01

    Approaches for statistical inference Introduction Motivating Vignettes Defining the Approaches The Bayes-Frequentist Controversy Some Basic Bayesian Models The Bayes approach Introduction Prior Distributions Bayesian Inference Hierarchical Modeling Model Assessment Nonparametric Methods Bayesian computation Introduction Asymptotic Methods Noniterative Monte Carlo Methods Markov Chain Monte Carlo Methods Model criticism and selection Bayesian Modeling Bayesian Robustness Model Assessment Bayes Factors via Marginal Density Estimation Bayes Factors

  5. Noncausal Bayesian Vector Autoregression

    DEFF Research Database (Denmark)

    Lanne, Markku; Luoto, Jani

    We propose a Bayesian inferential procedure for the noncausal vector autoregressive (VAR) model that is capable of capturing nonlinearities and incorporating effects of missing variables. In particular, we devise a fast and reliable posterior simulator that yields the predictive distribution...

  6. Statistics: a Bayesian perspective

    National Research Council Canada - National Science Library

    Berry, Donald A

    1996-01-01

    ...: it is the only introductory textbook based on Bayesian ideas, it combines concepts and methods, it presents statistics as a means of integrating data into the significant process, it develops ideas...

  7. Bayesian psychometric scaling

    NARCIS (Netherlands)

    Fox, Gerardus J.A.; van den Berg, Stéphanie Martine; Veldkamp, Bernard P.; Irwing, P.; Booth, T.; Hughes, D.

    2015-01-01

    In educational and psychological studies, psychometric methods are involved in the measurement of constructs, and in constructing and validating measurement instruments. Assessment results are typically used to measure student proficiency levels and test characteristics. Recently, Bayesian item

  8. Bayesian Networks An Introduction

    CERN Document Server

    Koski, Timo

    2009-01-01

    Bayesian Networks: An Introduction provides a self-contained introduction to the theory and applications of Bayesian networks, a topic of interest and importance for statisticians, computer scientists and those involved in modelling complex data sets. The material has been extensively tested in classroom teaching and assumes a basic knowledge of probability, statistics and mathematics. All notions are carefully explained and feature exercises throughout. Features include:.: An introduction to Dirichlet Distribution, Exponential Families and their applications.; A detailed description of learni

  9. A Bayesian encourages dropout

    OpenAIRE

    Maeda, Shin-ichi

    2014-01-01

    Dropout is one of the key techniques to prevent the learning from overfitting. It is explained that dropout works as a kind of modified L2 regularization. Here, we shed light on the dropout from Bayesian standpoint. Bayesian interpretation enables us to optimize the dropout rate, which is beneficial for learning of weight parameters and prediction after learning. The experiment result also encourages the optimization of the dropout.

  10. Basics of Bayesian methods.

    Science.gov (United States)

    Ghosh, Sujit K

    2010-01-01

    Bayesian methods are rapidly becoming popular tools for making statistical inference in various fields of science including biology, engineering, finance, and genetics. One of the key aspects of Bayesian inferential method is its logical foundation that provides a coherent framework to utilize not only empirical but also scientific information available to a researcher. Prior knowledge arising from scientific background, expert judgment, or previously collected data is used to build a prior distribution which is then combined with current data via the likelihood function to characterize the current state of knowledge using the so-called posterior distribution. Bayesian methods allow the use of models of complex physical phenomena that were previously too difficult to estimate (e.g., using asymptotic approximations). Bayesian methods offer a means of more fully understanding issues that are central to many practical problems by allowing researchers to build integrated models based on hierarchical conditional distributions that can be estimated even with limited amounts of data. Furthermore, advances in numerical integration methods, particularly those based on Monte Carlo methods, have made it possible to compute the optimal Bayes estimators. However, there is a reasonably wide gap between the background of the empirically trained scientists and the full weight of Bayesian statistical inference. Hence, one of the goals of this chapter is to bridge the gap by offering elementary to advanced concepts that emphasize linkages between standard approaches and full probability modeling via Bayesian methods.

  11. Estimating mental states of a depressed person with bayesian networks

    NARCIS (Netherlands)

    Klein, Michel C.A.; Modena, Gabriele

    2013-01-01

    In this work in progress paper we present an approach based on Bayesian Networks to model the relationship between mental states and empirical observations in a depressed person. We encode relationships and domain expertise as a Hierarchical Bayesian Network. Mental states are represented as latent

  12. Bayesian Methods for Radiation Detection and Dosimetry

    CERN Document Server

    Groer, Peter G

    2002-01-01

    We performed work in three areas: radiation detection, external and internal radiation dosimetry. In radiation detection we developed Bayesian techniques to estimate the net activity of high and low activity radioactive samples. These techniques have the advantage that the remaining uncertainty about the net activity is described by probability densities. Graphs of the densities show the uncertainty in pictorial form. Figure 1 below demonstrates this point. We applied stochastic processes for a method to obtain Bayesian estimates of 222Rn-daughter products from observed counting rates. In external radiation dosimetry we studied and developed Bayesian methods to estimate radiation doses to an individual with radiation induced chromosome aberrations. We analyzed chromosome aberrations after exposure to gammas and neutrons and developed a method for dose-estimation after criticality accidents. The research in internal radiation dosimetry focused on parameter estimation for compartmental models from observed comp...

  13. Bayesian Nonparametric Longitudinal Data Analysis.

    Science.gov (United States)

    Quintana, Fernando A; Johnson, Wesley O; Waetjen, Elaine; Gold, Ellen

    2016-01-01

    Practical Bayesian nonparametric methods have been developed across a wide variety of contexts. Here, we develop a novel statistical model that generalizes standard mixed models for longitudinal data that include flexible mean functions as well as combined compound symmetry (CS) and autoregressive (AR) covariance structures. AR structure is often specified through the use of a Gaussian process (GP) with covariance functions that allow longitudinal data to be more correlated if they are observed closer in time than if they are observed farther apart. We allow for AR structure by considering a broader class of models that incorporates a Dirichlet Process Mixture (DPM) over the covariance parameters of the GP. We are able to take advantage of modern Bayesian statistical methods in making full predictive inferences and about characteristics of longitudinal profiles and their differences across covariate combinations. We also take advantage of the generality of our model, which provides for estimation of a variety of covariance structures. We observe that models that fail to incorporate CS or AR structure can result in very poor estimation of a covariance or correlation matrix. In our illustration using hormone data observed on women through the menopausal transition, biology dictates the use of a generalized family of sigmoid functions as a model for time trends across subpopulation categories.

  14. New natural shapes of non-Gaussianity from high-derivative interactions and their optimal limits from WMAP 9-year data

    International Nuclear Information System (INIS)

    Behbahani, Siavosh R.; Mirbabayi, Mehrdad; Senatore, Leonardo; Smith, Kendrick M.

    2014-01-01

    Given the fantastic experimental effort, it is important to thoroughly explore the signature space of inflationary models. The fact that higher derivative operators do not renormalize lower derivative ones allows us to find a large class of technically natural single-clock inflationary models where, in the context of the Effective Field Theory of Inflation, the leading interactions have many derivatives. We systematically explore the 3-point function induced by these models and their overlap with the standard equilateral and orthogonal templates. We find that in order to satisfactorily cover the signature space of these models, two new additional templates need to be included. We then perform the optimal analysis of the WMAP 9-year data for the resulting four templates, finding that the overall significance of a non-zero signal is between 2–2.5σ, depending on the choice of parameter space, partially driven by the preference for nonzero f NL orth in WMAP9

  15. Bayesian networks with examples in R

    CERN Document Server

    Scutari, Marco

    2014-01-01

    Introduction. The Discrete Case: Multinomial Bayesian Networks. The Continuous Case: Gaussian Bayesian Networks. More Complex Cases. Theory and Algorithms for Bayesian Networks. Real-World Applications of Bayesian Networks. Appendices. Bibliography.

  16. Bayesian methods in reliability

    Science.gov (United States)

    Sander, P.; Badoux, R.

    1991-11-01

    The present proceedings from a course on Bayesian methods in reliability encompasses Bayesian statistical methods and their computational implementation, models for analyzing censored data from nonrepairable systems, the traits of repairable systems and growth models, the use of expert judgment, and a review of the problem of forecasting software reliability. Specific issues addressed include the use of Bayesian methods to estimate the leak rate of a gas pipeline, approximate analyses under great prior uncertainty, reliability estimation techniques, and a nonhomogeneous Poisson process. Also addressed are the calibration sets and seed variables of expert judgment systems for risk assessment, experimental illustrations of the use of expert judgment for reliability testing, and analyses of the predictive quality of software-reliability growth models such as the Weibull order statistics.

  17. Bayesian policy reuse

    CSIR Research Space (South Africa)

    Rosman, Benjamin

    2016-02-01

    Full Text Available Keywords Policy Reuse · Reinforcement Learning · Online Learning · Online Bandits · Transfer Learning · Bayesian Optimisation · Bayesian Decision Theory. 1 Introduction As robots and software agents are becoming more ubiquitous in many applications.... The agent has access to a library of policies (pi1, pi2 and pi3), and has previously experienced a set of task instances (τ1, τ2, τ3, τ4), as well as samples of the utilities of the library policies on these instances (the black dots indicate the means...

  18. Nonparametric Bayesian Modeling of Complex Networks

    DEFF Research Database (Denmark)

    Schmidt, Mikkel Nørgaard; Mørup, Morten

    2013-01-01

    an infinite mixture model as running example, we go through the steps of deriving the model as an infinite limit of a finite parametric model, inferring the model parameters by Markov chain Monte Carlo, and checking the model?s fit and predictive performance. We explain how advanced nonparametric models......Modeling structure in complex networks using Bayesian nonparametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This article provides a gentle introduction to nonparametric Bayesian modeling of complex networks: Using...

  19. Bayesian methods for hackers probabilistic programming and Bayesian inference

    CERN Document Server

    Davidson-Pilon, Cameron

    2016-01-01

    Bayesian methods of inference are deeply natural and extremely powerful. However, most discussions of Bayesian inference rely on intensely complex mathematical analyses and artificial examples, making it inaccessible to anyone without a strong mathematical background. Now, though, Cameron Davidson-Pilon introduces Bayesian inference from a computational perspective, bridging theory to practice–freeing you to get results using computing power. Bayesian Methods for Hackers illuminates Bayesian inference through probabilistic programming with the powerful PyMC language and the closely related Python tools NumPy, SciPy, and Matplotlib. Using this approach, you can reach effective solutions in small increments, without extensive mathematical intervention. Davidson-Pilon begins by introducing the concepts underlying Bayesian inference, comparing it with other techniques and guiding you through building and training your first Bayesian model. Next, he introduces PyMC through a series of detailed examples a...

  20. Bayesian logistic regression analysis

    NARCIS (Netherlands)

    Van Erp, H.R.N.; Van Gelder, P.H.A.J.M.

    2012-01-01

    In this paper we present a Bayesian logistic regression analysis. It is found that if one wishes to derive the posterior distribution of the probability of some event, then, together with the traditional Bayes Theorem and the integrating out of nuissance parameters, the Jacobian transformation is an

  1. Bayesian Dark Knowledge

    NARCIS (Netherlands)

    Korattikara, A.; Rathod, V.; Murphy, K.; Welling, M.; Cortes, C.; Lawrence, N.D.; Lee, D.D.; Sugiyama, M.; Garnett, R.

    2015-01-01

    We consider the problem of Bayesian parameter estimation for deep neural networks, which is important in problem settings where we may have little data, and/ or where we need accurate posterior predictive densities p(y|x, D), e.g., for applications involving bandits or active learning. One simple

  2. Bayesian Geostatistical Design

    DEFF Research Database (Denmark)

    Diggle, Peter; Lophaven, Søren Nymand

    2006-01-01

    locations to, or deletion of locations from, an existing design, and prospective design, which consists of choosing positions for a new set of sampling locations. We propose a Bayesian design criterion which focuses on the goal of efficient spatial prediction whilst allowing for the fact that model...

  3. Bayesian statistical inference

    Directory of Open Access Journals (Sweden)

    Bruno De Finetti

    2017-04-01

    Full Text Available This work was translated into English and published in the volume: Bruno De Finetti, Induction and Probability, Biblioteca di Statistica, eds. P. Monari, D. Cocchi, Clueb, Bologna, 1993.Bayesian statistical Inference is one of the last fundamental philosophical papers in which we can find the essential De Finetti's approach to the statistical inference.

  4. Bayesian grid matching

    DEFF Research Database (Denmark)

    Hartelius, Karsten; Carstensen, Jens Michael

    2003-01-01

    A method for locating distorted grid structures in images is presented. The method is based on the theories of template matching and Bayesian image restoration. The grid is modeled as a deformable template. Prior knowledge of the grid is described through a Markov random field (MRF) model which r...

  5. Bayesian Independent Component Analysis

    DEFF Research Database (Denmark)

    Winther, Ole; Petersen, Kaare Brandt

    2007-01-01

    In this paper we present an empirical Bayesian framework for independent component analysis. The framework provides estimates of the sources, the mixing matrix and the noise parameters, and is flexible with respect to choice of source prior and the number of sources and sensors. Inside the engine...

  6. Bayesian Exponential Smoothing.

    OpenAIRE

    Forbes, C.S.; Snyder, R.D.; Shami, R.S.

    2000-01-01

    In this paper, a Bayesian version of the exponential smoothing method of forecasting is proposed. The approach is based on a state space model containing only a single source of error for each time interval. This model allows us to improve current practices surrounding exponential smoothing by providing both point predictions and measures of the uncertainty surrounding them.

  7. Large-Scale Analysis of Relationships between Mineral Dust, Ice Cloud Properties, and Precipitation from Satellite Observations Using a Bayesian Approach: Theoretical Basis and First Results for the Tropical Atlantic Ocean

    Directory of Open Access Journals (Sweden)

    Lars Klüser

    2017-01-01

    Full Text Available Mineral dust and ice cloud observations from the Infrared Atmospheric Sounding Interferometer (IASI are used to assess the relationships between desert dust aerosols and ice clouds over the tropical Atlantic Ocean during the hurricane season 2008. Cloud property histograms are first adjusted for varying cloud top temperature or ice water path distributions with a Bayesian approach to account for meteorological constraints on the cloud variables. Then, histogram differences between dust load classes are used to describe the impact of dust load on cloud property statistics. The analysis of the histogram differences shows that ice crystal sizes are reduced with increasing aerosol load and ice cloud optical depth and ice water path are increased. The distributions of all three variables broaden and get less skewed in dusty environments. For ice crystal size the significant bimodality is reduced and the order of peaks is reversed. Moreover, it is shown that not only are distributions of ice cloud variables simply shifted linearly but also variance, skewness, and complexity of the cloud variable distributions are significantly affected. This implies that the whole cloud variable distributions have to be considered for indirect aerosol effects in any application for climate modelling.

  8. Bayesian optimization for materials science

    CERN Document Server

    Packwood, Daniel

    2017-01-01

    This book provides a short and concise introduction to Bayesian optimization specifically for experimental and computational materials scientists. After explaining the basic idea behind Bayesian optimization and some applications to materials science in Chapter 1, the mathematical theory of Bayesian optimization is outlined in Chapter 2. Finally, Chapter 3 discusses an application of Bayesian optimization to a complicated structure optimization problem in computational surface science. Bayesian optimization is a promising global optimization technique that originates in the field of machine learning and is starting to gain attention in materials science. For the purpose of materials design, Bayesian optimization can be used to predict new materials with novel properties without extensive screening of candidate materials. For the purpose of computational materials science, Bayesian optimization can be incorporated into first-principles calculations to perform efficient, global structure optimizations. While re...

  9. First observational tests of eternal inflation.

    Science.gov (United States)

    Feeney, Stephen M; Johnson, Matthew C; Mortlock, Daniel J; Peiris, Hiranya V

    2011-08-12

    The eternal inflation scenario predicts that our observable Universe resides inside a single bubble embedded in a vast inflating multiverse. We present the first observational tests of eternal inflation, performing a search for cosmological signatures of collisions with other bubble universes in cosmic microwave background data from the WMAP satellite. We conclude that the WMAP 7-year data do not warrant augmenting the cold dark matter model with a cosmological constant with bubble collisions, constraining the average number of detectable bubble collisions on the full sky N(s) < 1.6 at 68% C.L. Data from the Planck satellite can be used to more definitively test the bubble-collision hypothesis.

  10. Bayesian ensemble refinement by replica simulations and reweighting

    Science.gov (United States)

    Hummer, Gerhard; Köfinger, Jürgen

    2015-12-01

    We describe different Bayesian ensemble refinement methods, examine their interrelation, and discuss their practical application. With ensemble refinement, the properties of dynamic and partially disordered (bio)molecular structures can be characterized by integrating a wide range of experimental data, including measurements of ensemble-averaged observables. We start from a Bayesian formulation in which the posterior is a functional that ranks different configuration space distributions. By maximizing this posterior, we derive an optimal Bayesian ensemble distribution. For discrete configurations, this optimal distribution is identical to that obtained by the maximum entropy "ensemble refinement of SAXS" (EROS) formulation. Bayesian replica ensemble refinement enhances the sampling of relevant configurations by imposing restraints on averages of observables in coupled replica molecular dynamics simulations. We show that the strength of the restraints should scale linearly with the number of replicas to ensure convergence to the optimal Bayesian result in the limit of infinitely many replicas. In the "Bayesian inference of ensembles" method, we combine the replica and EROS approaches to accelerate the convergence. An adaptive algorithm can be used to sample directly from the optimal ensemble, without replicas. We discuss the incorporation of single-molecule measurements and dynamic observables such as relaxation parameters. The theoretical analysis of different Bayesian ensemble refinement approaches provides a basis for practical applications and a starting point for further investigations.

  11. Probability and Bayesian statistics

    CERN Document Server

    1987-01-01

    This book contains selected and refereed contributions to the "Inter­ national Symposium on Probability and Bayesian Statistics" which was orga­ nized to celebrate the 80th birthday of Professor Bruno de Finetti at his birthplace Innsbruck in Austria. Since Professor de Finetti died in 1985 the symposium was dedicated to the memory of Bruno de Finetti and took place at Igls near Innsbruck from 23 to 26 September 1986. Some of the pa­ pers are published especially by the relationship to Bruno de Finetti's scientific work. The evolution of stochastics shows growing importance of probability as coherent assessment of numerical values as degrees of believe in certain events. This is the basis for Bayesian inference in the sense of modern statistics. The contributions in this volume cover a broad spectrum ranging from foundations of probability across psychological aspects of formulating sub­ jective probability statements, abstract measure theoretical considerations, contributions to theoretical statistics an...

  12. Bayesian community detection

    DEFF Research Database (Denmark)

    Mørup, Morten; Schmidt, Mikkel N

    2012-01-01

    Many networks of scientific interest naturally decompose into clusters or communities with comparatively fewer external than internal links; however, current Bayesian models of network communities do not exert this intuitive notion of communities. We formulate a nonparametric Bayesian model...... for community detection consistent with an intuitive definition of communities and present a Markov chain Monte Carlo procedure for inferring the community structure. A Matlab toolbox with the proposed inference procedure is available for download. On synthetic and real networks, our model detects communities...... consistent with ground truth, and on real networks, it outperforms existing approaches in predicting missing links. This suggests that community structure is an important structural property of networks that should be explicitly modeled....

  13. Approximate Bayesian recursive estimation

    Czech Academy of Sciences Publication Activity Database

    Kárný, Miroslav

    2014-01-01

    Roč. 285, č. 1 (2014), s. 100-111 ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Approximate parameter estimation * Bayesian recursive estimation * Kullback–Leibler divergence * Forgetting Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.038, year: 2014 http://library.utia.cas.cz/separaty/2014/AS/karny-0425539.pdf

  14. Subjective Bayesian Beliefs

    DEFF Research Database (Denmark)

    Antoniou, Constantinos; Harrison, Glenn W.; Lau, Morten I.

    2015-01-01

    A large literature suggests that many individuals do not apply Bayes’ Rule when making decisions that depend on them correctly pooling prior information and sample data. We replicate and extend a classic experimental study of Bayesian updating from psychology, employing the methods of experimenta...... economics, with careful controls for the confounding effects of risk aversion. Our results show that risk aversion significantly alters inferences on deviations from Bayes’ Rule....

  15. Bayesian Hypothesis Testing

    Energy Technology Data Exchange (ETDEWEB)

    Andrews, Stephen A. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Sigeti, David E. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2017-11-15

    These are a set of slides about Bayesian hypothesis testing, where many hypotheses are tested. The conclusions are the following: The value of the Bayes factor obtained when using the median of the posterior marginal is almost the minimum value of the Bayes factor. The value of τ2 which minimizes the Bayes factor is a reasonable choice for this parameter. This allows a likelihood ratio to be computed with is the least favorable to H0.

  16. Introduction to Bayesian statistics

    CERN Document Server

    Koch, Karl-Rudolf

    2007-01-01

    This book presents Bayes' theorem, the estimation of unknown parameters, the determination of confidence regions and the derivation of tests of hypotheses for the unknown parameters. It does so in a simple manner that is easy to comprehend. The book compares traditional and Bayesian methods with the rules of probability presented in a logical way allowing an intuitive understanding of random variables and their probability distributions to be formed.

  17. Bayesian ARTMAP for regression.

    Science.gov (United States)

    Sasu, L M; Andonie, R

    2013-10-01

    Bayesian ARTMAP (BA) is a recently introduced neural architecture which uses a combination of Fuzzy ARTMAP competitive learning and Bayesian learning. Training is generally performed online, in a single-epoch. During training, BA creates input data clusters as Gaussian categories, and also infers the conditional probabilities between input patterns and categories, and between categories and classes. During prediction, BA uses Bayesian posterior probability estimation. So far, BA was used only for classification. The goal of this paper is to analyze the efficiency of BA for regression problems. Our contributions are: (i) we generalize the BA algorithm using the clustering functionality of both ART modules, and name it BA for Regression (BAR); (ii) we prove that BAR is a universal approximator with the best approximation property. In other words, BAR approximates arbitrarily well any continuous function (universal approximation) and, for every given continuous function, there is one in the set of BAR approximators situated at minimum distance (best approximation); (iii) we experimentally compare the online trained BAR with several neural models, on the following standard regression benchmarks: CPU Computer Hardware, Boston Housing, Wisconsin Breast Cancer, and Communities and Crime. Our results show that BAR is an appropriate tool for regression tasks, both for theoretical and practical reasons. Copyright © 2013 Elsevier Ltd. All rights reserved.

  18. Bayesian theory and applications

    CERN Document Server

    Dellaportas, Petros; Polson, Nicholas G; Stephens, David A

    2013-01-01

    The development of hierarchical models and Markov chain Monte Carlo (MCMC) techniques forms one of the most profound advances in Bayesian analysis since the 1970s and provides the basis for advances in virtually all areas of applied and theoretical Bayesian statistics. This volume guides the reader along a statistical journey that begins with the basic structure of Bayesian theory, and then provides details on most of the past and present advances in this field. The book has a unique format. There is an explanatory chapter devoted to each conceptual advance followed by journal-style chapters that provide applications or further advances on the concept. Thus, the volume is both a textbook and a compendium of papers covering a vast range of topics. It is appropriate for a well-informed novice interested in understanding the basic approach, methods and recent applications. Because of its advanced chapters and recent work, it is also appropriate for a more mature reader interested in recent applications and devel...

  19. Non-linear Bayesian update of PCE coefficients

    KAUST Repository

    Litvinenko, Alexander

    2014-01-06

    Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(?), a measurement operator Y (u(q), q), where u(q, ?) uncertain solution. Aim: to identify q(?). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(!) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a unctional approximation, e.g. polynomial chaos expansion (PCE). New: We apply Bayesian update to the PCE coefficients of the random coefficient q(?) (not to the probability density function of q).

  20. Non-linear Bayesian update of PCE coefficients

    KAUST Repository

    Litvinenko, Alexander; Matthies, Hermann G.; Pojonk, Oliver; Rosic, Bojana V.; Zander, Elmar

    2014-01-01

    Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(?), a measurement operator Y (u(q), q), where u(q, ?) uncertain solution. Aim: to identify q(?). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(!) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a unctional approximation, e.g. polynomial chaos expansion (PCE). New: We apply Bayesian update to the PCE coefficients of the random coefficient q(?) (not to the probability density function of q).

  1. BAYESIAN ESTIMATION OF THERMONUCLEAR REACTION RATES

    Energy Technology Data Exchange (ETDEWEB)

    Iliadis, C.; Anderson, K. S. [Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3255 (United States); Coc, A. [Centre de Sciences Nucléaires et de Sciences de la Matière (CSNSM), CNRS/IN2P3, Univ. Paris-Sud, Université Paris–Saclay, Bâtiment 104, F-91405 Orsay Campus (France); Timmes, F. X.; Starrfield, S., E-mail: iliadis@unc.edu [School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287-1504 (United States)

    2016-11-01

    The problem of estimating non-resonant astrophysical S -factors and thermonuclear reaction rates, based on measured nuclear cross sections, is of major interest for nuclear energy generation, neutrino physics, and element synthesis. Many different methods have been applied to this problem in the past, almost all of them based on traditional statistics. Bayesian methods, on the other hand, are now in widespread use in the physical sciences. In astronomy, for example, Bayesian statistics is applied to the observation of extrasolar planets, gravitational waves, and Type Ia supernovae. However, nuclear physics, in particular, has been slow to adopt Bayesian methods. We present astrophysical S -factors and reaction rates based on Bayesian statistics. We develop a framework that incorporates robust parameter estimation, systematic effects, and non-Gaussian uncertainties in a consistent manner. The method is applied to the reactions d(p, γ ){sup 3}He, {sup 3}He({sup 3}He,2p){sup 4}He, and {sup 3}He( α , γ ){sup 7}Be, important for deuterium burning, solar neutrinos, and Big Bang nucleosynthesis.

  2. Bayesian Estimation and Inference using Stochastic Hardware

    Directory of Open Access Journals (Sweden)

    Chetan Singh Thakur

    2016-03-01

    Full Text Available In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker, demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND, we show how inference can be performed in a Directed Acyclic Graph (DAG using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream.

  3. Bayesian Estimation and Inference Using Stochastic Electronics.

    Science.gov (United States)

    Thakur, Chetan Singh; Afshar, Saeed; Wang, Runchun M; Hamilton, Tara J; Tapson, Jonathan; van Schaik, André

    2016-01-01

    In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker), demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM) to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise) probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND), we show how inference can be performed in a Directed Acyclic Graph (DAG) using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC) technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream.

  4. Bayesian nonparametric data analysis

    CERN Document Server

    Müller, Peter; Jara, Alejandro; Hanson, Tim

    2015-01-01

    This book reviews nonparametric Bayesian methods and models that have proven useful in the context of data analysis. Rather than providing an encyclopedic review of probability models, the book’s structure follows a data analysis perspective. As such, the chapters are organized by traditional data analysis problems. In selecting specific nonparametric models, simpler and more traditional models are favored over specialized ones. The discussed methods are illustrated with a wealth of examples, including applications ranging from stylized examples to case studies from recent literature. The book also includes an extensive discussion of computational methods and details on their implementation. R code for many examples is included in on-line software pages.

  5. Applied Bayesian modelling

    CERN Document Server

    Congdon, Peter

    2014-01-01

    This book provides an accessible approach to Bayesian computing and data analysis, with an emphasis on the interpretation of real data sets. Following in the tradition of the successful first edition, this book aims to make a wide range of statistical modeling applications accessible using tested code that can be readily adapted to the reader's own applications. The second edition has been thoroughly reworked and updated to take account of advances in the field. A new set of worked examples is included. The novel aspect of the first edition was the coverage of statistical modeling using WinBU

  6. Inference in hybrid Bayesian networks

    DEFF Research Database (Denmark)

    Lanseth, Helge; Nielsen, Thomas Dyhre; Rumí, Rafael

    2009-01-01

    Since the 1980s, Bayesian Networks (BNs) have become increasingly popular for building statistical models of complex systems. This is particularly true for boolean systems, where BNs often prove to be a more efficient modelling framework than traditional reliability-techniques (like fault trees...... decade's research on inference in hybrid Bayesian networks. The discussions are linked to an example model for estimating human reliability....

  7. Searching Algorithm Using Bayesian Updates

    Science.gov (United States)

    Caudle, Kyle

    2010-01-01

    In late October 1967, the USS Scorpion was lost at sea, somewhere between the Azores and Norfolk Virginia. Dr. Craven of the U.S. Navy's Special Projects Division is credited with using Bayesian Search Theory to locate the submarine. Bayesian Search Theory is a straightforward and interesting application of Bayes' theorem which involves searching…

  8. Bayesian Data Analysis (lecture 2)

    CERN Multimedia

    CERN. Geneva

    2018-01-01

    framework but we will also go into more detail and discuss for example the role of the prior. The second part of the lecture will cover further examples and applications that heavily rely on the bayesian approach, as well as some computational tools needed to perform a bayesian analysis.

  9. Bayesian Data Analysis (lecture 1)

    CERN Multimedia

    CERN. Geneva

    2018-01-01

    framework but we will also go into more detail and discuss for example the role of the prior. The second part of the lecture will cover further examples and applications that heavily rely on the bayesian approach, as well as some computational tools needed to perform a bayesian analysis.

  10. Bayesian network learning for natural hazard assessments

    Science.gov (United States)

    Vogel, Kristin

    2016-04-01

    Even though quite different in occurrence and consequences, from a modelling perspective many natural hazards share similar properties and challenges. Their complex nature as well as lacking knowledge about their driving forces and potential effects make their analysis demanding. On top of the uncertainty about the modelling framework, inaccurate or incomplete event observations and the intrinsic randomness of the natural phenomenon add up to different interacting layers of uncertainty, which require a careful handling. Thus, for reliable natural hazard assessments it is crucial not only to capture and quantify involved uncertainties, but also to express and communicate uncertainties in an intuitive way. Decision-makers, who often find it difficult to deal with uncertainties, might otherwise return to familiar (mostly deterministic) proceedings. In the scope of the DFG research training group „NatRiskChange" we apply the probabilistic framework of Bayesian networks for diverse natural hazard and vulnerability studies. The great potential of Bayesian networks was already shown in previous natural hazard assessments. Treating each model component as random variable, Bayesian networks aim at capturing the joint distribution of all considered variables. Hence, each conditional distribution of interest (e.g. the effect of precautionary measures on damage reduction) can be inferred. The (in-)dependencies between the considered variables can be learned purely data driven or be given by experts. Even a combination of both is possible. By translating the (in-)dependences into a graph structure, Bayesian networks provide direct insights into the workings of the system and allow to learn about the underlying processes. Besides numerous studies on the topic, learning Bayesian networks from real-world data remains challenging. In previous studies, e.g. on earthquake induced ground motion and flood damage assessments, we tackled the problems arising with continuous variables

  11. The Bayesian Covariance Lasso.

    Science.gov (United States)

    Khondker, Zakaria S; Zhu, Hongtu; Chu, Haitao; Lin, Weili; Ibrahim, Joseph G

    2013-04-01

    Estimation of sparse covariance matrices and their inverse subject to positive definiteness constraints has drawn a lot of attention in recent years. The abundance of high-dimensional data, where the sample size ( n ) is less than the dimension ( d ), requires shrinkage estimation methods since the maximum likelihood estimator is not positive definite in this case. Furthermore, when n is larger than d but not sufficiently larger, shrinkage estimation is more stable than maximum likelihood as it reduces the condition number of the precision matrix. Frequentist methods have utilized penalized likelihood methods, whereas Bayesian approaches rely on matrix decompositions or Wishart priors for shrinkage. In this paper we propose a new method, called the Bayesian Covariance Lasso (BCLASSO), for the shrinkage estimation of a precision (covariance) matrix. We consider a class of priors for the precision matrix that leads to the popular frequentist penalties as special cases, develop a Bayes estimator for the precision matrix, and propose an efficient sampling scheme that does not precalculate boundaries for positive definiteness. The proposed method is permutation invariant and performs shrinkage and estimation simultaneously for non-full rank data. Simulations show that the proposed BCLASSO performs similarly as frequentist methods for non-full rank data.

  12. Bayesian dynamic mediation analysis.

    Science.gov (United States)

    Huang, Jing; Yuan, Ying

    2017-12-01

    Most existing methods for mediation analysis assume that mediation is a stationary, time-invariant process, which overlooks the inherently dynamic nature of many human psychological processes and behavioral activities. In this article, we consider mediation as a dynamic process that continuously changes over time. We propose Bayesian multilevel time-varying coefficient models to describe and estimate such dynamic mediation effects. By taking the nonparametric penalized spline approach, the proposed method is flexible and able to accommodate any shape of the relationship between time and mediation effects. Simulation studies show that the proposed method works well and faithfully reflects the true nature of the mediation process. By modeling mediation effect nonparametrically as a continuous function of time, our method provides a valuable tool to help researchers obtain a more complete understanding of the dynamic nature of the mediation process underlying psychological and behavioral phenomena. We also briefly discuss an alternative approach of using dynamic autoregressive mediation model to estimate the dynamic mediation effect. The computer code is provided to implement the proposed Bayesian dynamic mediation analysis. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

  13. Bayesian inference with ecological applications

    CERN Document Server

    Link, William A

    2009-01-01

    This text is written to provide a mathematically sound but accessible and engaging introduction to Bayesian inference specifically for environmental scientists, ecologists and wildlife biologists. It emphasizes the power and usefulness of Bayesian methods in an ecological context. The advent of fast personal computers and easily available software has simplified the use of Bayesian and hierarchical models . One obstacle remains for ecologists and wildlife biologists, namely the near absence of Bayesian texts written specifically for them. The book includes many relevant examples, is supported by software and examples on a companion website and will become an essential grounding in this approach for students and research ecologists. Engagingly written text specifically designed to demystify a complex subject Examples drawn from ecology and wildlife research An essential grounding for graduate and research ecologists in the increasingly prevalent Bayesian approach to inference Companion website with analyt...

  14. Bayesian Inference on Gravitational Waves

    Directory of Open Access Journals (Sweden)

    Asad Ali

    2015-12-01

    Full Text Available The Bayesian approach is increasingly becoming popular among the astrophysics data analysis communities. However, the Pakistan statistics communities are unaware of this fertile interaction between the two disciplines. Bayesian methods have been in use to address astronomical problems since the very birth of the Bayes probability in eighteenth century. Today the Bayesian methods for the detection and parameter estimation of gravitational waves have solid theoretical grounds with a strong promise for the realistic applications. This article aims to introduce the Pakistan statistics communities to the applications of Bayesian Monte Carlo methods in the analysis of gravitational wave data with an  overview of the Bayesian signal detection and estimation methods and demonstration by a couple of simplified examples.

  15. How to practise Bayesian statistics outside the Bayesian church: What philosophy for Bayesian statistical modelling?

    NARCIS (Netherlands)

    Borsboom, D.; Haig, B.D.

    2013-01-01

    Unlike most other statistical frameworks, Bayesian statistical inference is wedded to a particular approach in the philosophy of science (see Howson & Urbach, 2006); this approach is called Bayesianism. Rather than being concerned with model fitting, this position in the philosophy of science

  16. The NIFTY way of Bayesian signal inference

    International Nuclear Information System (INIS)

    Selig, Marco

    2014-01-01

    We introduce NIFTY, 'Numerical Information Field Theory', a software package for the development of Bayesian signal inference algorithms that operate independently from any underlying spatial grid and its resolution. A large number of Bayesian and Maximum Entropy methods for 1D signal reconstruction, 2D imaging, as well as 3D tomography, appear formally similar, but one often finds individualized implementations that are neither flexible nor easily transferable. Signal inference in the framework of NIFTY can be done in an abstract way, such that algorithms, prototyped in 1D, can be applied to real world problems in higher-dimensional settings. NIFTY as a versatile library is applicable and already has been applied in 1D, 2D, 3D and spherical settings. A recent application is the D 3 PO algorithm targeting the non-trivial task of denoising, deconvolving, and decomposing photon observations in high energy astronomy

  17. The NIFTy way of Bayesian signal inference

    Science.gov (United States)

    Selig, Marco

    2014-12-01

    We introduce NIFTy, "Numerical Information Field Theory", a software package for the development of Bayesian signal inference algorithms that operate independently from any underlying spatial grid and its resolution. A large number of Bayesian and Maximum Entropy methods for 1D signal reconstruction, 2D imaging, as well as 3D tomography, appear formally similar, but one often finds individualized implementations that are neither flexible nor easily transferable. Signal inference in the framework of NIFTy can be done in an abstract way, such that algorithms, prototyped in 1D, can be applied to real world problems in higher-dimensional settings. NIFTy as a versatile library is applicable and already has been applied in 1D, 2D, 3D and spherical settings. A recent application is the D3PO algorithm targeting the non-trivial task of denoising, deconvolving, and decomposing photon observations in high energy astronomy.

  18. Bayesian component separation: The Planck experience

    Science.gov (United States)

    Wehus, Ingunn Kathrine; Eriksen, Hans Kristian

    2018-05-01

    Bayesian component separation techniques have played a central role in the data reduction process of Planck. The most important strength of this approach is its global nature, in which a parametric and physical model is fitted to the data. Such physical modeling allows the user to constrain very general data models, and jointly probe cosmological, astrophysical and instrumental parameters. This approach also supports statistically robust goodness-of-fit tests in terms of data-minus-model residual maps, which are essential for identifying residual systematic effects in the data. The main challenges are high code complexity and computational cost. Whether or not these costs are justified for a given experiment depends on its final uncertainty budget. We therefore predict that the importance of Bayesian component separation techniques is likely to increase with time for intensity mapping experiments, similar to what has happened in the CMB field, as observational techniques mature, and their overall sensitivity improves.

  19. Bayesian Methods for Radiation Detection and Dosimetry

    International Nuclear Information System (INIS)

    Peter G. Groer

    2002-01-01

    We performed work in three areas: radiation detection, external and internal radiation dosimetry. In radiation detection we developed Bayesian techniques to estimate the net activity of high and low activity radioactive samples. These techniques have the advantage that the remaining uncertainty about the net activity is described by probability densities. Graphs of the densities show the uncertainty in pictorial form. Figure 1 below demonstrates this point. We applied stochastic processes for a method to obtain Bayesian estimates of 222Rn-daughter products from observed counting rates. In external radiation dosimetry we studied and developed Bayesian methods to estimate radiation doses to an individual with radiation induced chromosome aberrations. We analyzed chromosome aberrations after exposure to gammas and neutrons and developed a method for dose-estimation after criticality accidents. The research in internal radiation dosimetry focused on parameter estimation for compartmental models from observed compartmental activities. From the estimated probability densities of the model parameters we were able to derive the densities for compartmental activities for a two compartment catenary model at different times. We also calculated the average activities and their standard deviation for a simple two compartment model

  20. Bayesian Monte Carlo method

    International Nuclear Information System (INIS)

    Rajabalinejad, M.

    2010-01-01

    To reduce cost of Monte Carlo (MC) simulations for time-consuming processes, Bayesian Monte Carlo (BMC) is introduced in this paper. The BMC method reduces number of realizations in MC according to the desired accuracy level. BMC also provides a possibility of considering more priors. In other words, different priors can be integrated into one model by using BMC to further reduce cost of simulations. This study suggests speeding up the simulation process by considering the logical dependence of neighboring points as prior information. This information is used in the BMC method to produce a predictive tool through the simulation process. The general methodology and algorithm of BMC method are presented in this paper. The BMC method is applied to the simplified break water model as well as the finite element model of 17th Street Canal in New Orleans, and the results are compared with the MC and Dynamic Bounds methods.

  1. Bayesian nonparametric hierarchical modeling.

    Science.gov (United States)

    Dunson, David B

    2009-04-01

    In biomedical research, hierarchical models are very widely used to accommodate dependence in multivariate and longitudinal data and for borrowing of information across data from different sources. A primary concern in hierarchical modeling is sensitivity to parametric assumptions, such as linearity and normality of the random effects. Parametric assumptions on latent variable distributions can be challenging to check and are typically unwarranted, given available prior knowledge. This article reviews some recent developments in Bayesian nonparametric methods motivated by complex, multivariate and functional data collected in biomedical studies. The author provides a brief review of flexible parametric approaches relying on finite mixtures and latent class modeling. Dirichlet process mixture models are motivated by the need to generalize these approaches to avoid assuming a fixed finite number of classes. Focusing on an epidemiology application, the author illustrates the practical utility and potential of nonparametric Bayes methods.

  2. Book review: Bayesian analysis for population ecology

    Science.gov (United States)

    Link, William A.

    2011-01-01

    Brian Dennis described the field of ecology as “fertile, uncolonized ground for Bayesian ideas.” He continued: “The Bayesian propagule has arrived at the shore. Ecologists need to think long and hard about the consequences of a Bayesian ecology. The Bayesian outlook is a successful competitor, but is it a weed? I think so.” (Dennis 2004)

  3. Current trends in Bayesian methodology with applications

    CERN Document Server

    Upadhyay, Satyanshu K; Dey, Dipak K; Loganathan, Appaia

    2015-01-01

    Collecting Bayesian material scattered throughout the literature, Current Trends in Bayesian Methodology with Applications examines the latest methodological and applied aspects of Bayesian statistics. The book covers biostatistics, econometrics, reliability and risk analysis, spatial statistics, image analysis, shape analysis, Bayesian computation, clustering, uncertainty assessment, high-energy astrophysics, neural networking, fuzzy information, objective Bayesian methodologies, empirical Bayes methods, small area estimation, and many more topics.Each chapter is self-contained and focuses on

  4. Bayesian methodology for reliability model acceptance

    International Nuclear Information System (INIS)

    Zhang Ruoxue; Mahadevan, Sankaran

    2003-01-01

    This paper develops a methodology to assess the reliability computation model validity using the concept of Bayesian hypothesis testing, by comparing the model prediction and experimental observation, when there is only one computational model available to evaluate system behavior. Time-independent and time-dependent problems are investigated, with consideration of both cases: with and without statistical uncertainty in the model. The case of time-independent failure probability prediction with no statistical uncertainty is a straightforward application of Bayesian hypothesis testing. However, for the life prediction (time-dependent reliability) problem, a new methodology is developed in this paper to make the same Bayesian hypothesis testing concept applicable. With the existence of statistical uncertainty in the model, in addition to the application of a predictor estimator of the Bayes factor, the uncertainty in the Bayes factor is explicitly quantified through treating it as a random variable and calculating the probability that it exceeds a specified value. The developed method provides a rational criterion to decision-makers for the acceptance or rejection of the computational model

  5. Bayesian Networks and Influence Diagrams

    DEFF Research Database (Denmark)

    Kjærulff, Uffe Bro; Madsen, Anders Læsø

     Probabilistic networks, also known as Bayesian networks and influence diagrams, have become one of the most promising technologies in the area of applied artificial intelligence, offering intuitive, efficient, and reliable methods for diagnosis, prediction, decision making, classification......, troubleshooting, and data mining under uncertainty. Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. Intended...

  6. Flood quantile estimation at ungauged sites by Bayesian networks

    Science.gov (United States)

    Mediero, L.; Santillán, D.; Garrote, L.

    2012-04-01

    Estimating flood quantiles at a site for which no observed measurements are available is essential for water resources planning and management. Ungauged sites have no observations about the magnitude of floods, but some site and basin characteristics are known. The most common technique used is the multiple regression analysis, which relates physical and climatic basin characteristic to flood quantiles. Regression equations are fitted from flood frequency data and basin characteristics at gauged sites. Regression equations are a rigid technique that assumes linear relationships between variables and cannot take the measurement errors into account. In addition, the prediction intervals are estimated in a very simplistic way from the variance of the residuals in the estimated model. Bayesian networks are a probabilistic computational structure taken from the field of Artificial Intelligence, which have been widely and successfully applied to many scientific fields like medicine and informatics, but application to the field of hydrology is recent. Bayesian networks infer the joint probability distribution of several related variables from observations through nodes, which represent random variables, and links, which represent causal dependencies between them. A Bayesian network is more flexible than regression equations, as they capture non-linear relationships between variables. In addition, the probabilistic nature of Bayesian networks allows taking the different sources of estimation uncertainty into account, as they give a probability distribution as result. A homogeneous region in the Tagus Basin was selected as case study. A regression equation was fitted taking the basin area, the annual maximum 24-hour rainfall for a given recurrence interval and the mean height as explanatory variables. Flood quantiles at ungauged sites were estimated by Bayesian networks. Bayesian networks need to be learnt from a huge enough data set. As observational data are reduced, a

  7. Dynamic Bayesian Network Modeling of Game Based Diagnostic Assessments. CRESST Report 837

    Science.gov (United States)

    Levy, Roy

    2014-01-01

    Digital games offer an appealing environment for assessing student proficiencies, including skills and misconceptions in a diagnostic setting. This paper proposes a dynamic Bayesian network modeling approach for observations of student performance from an educational video game. A Bayesian approach to model construction, calibration, and use in…

  8. A Bayesian Approach to Person Fit Analysis in Item Response Theory Models. Research Report.

    Science.gov (United States)

    Glas, Cees A. W.; Meijer, Rob R.

    A Bayesian approach to the evaluation of person fit in item response theory (IRT) models is presented. In a posterior predictive check, the observed value on a discrepancy variable is positioned in its posterior distribution. In a Bayesian framework, a Markov Chain Monte Carlo procedure can be used to generate samples of the posterior distribution…

  9. Bayesian linear regression : different conjugate models and their (in)sensitivity to prior-data conflict

    NARCIS (Netherlands)

    Walter, G.M.; Augustin, Th.; Kneib, Thomas; Tutz, Gerhard

    2010-01-01

    The paper is concerned with Bayesian analysis under prior-data conflict, i.e. the situation when observed data are rather unexpected under the prior (and the sample size is not large enough to eliminate the influence of the prior). Two approaches for Bayesian linear regression modeling based on

  10. Bayesian seismic AVO inversion

    Energy Technology Data Exchange (ETDEWEB)

    Buland, Arild

    2002-07-01

    A new linearized AVO inversion technique is developed in a Bayesian framework. The objective is to obtain posterior distributions for P-wave velocity, S-wave velocity and density. Distributions for other elastic parameters can also be assessed, for example acoustic impedance, shear impedance and P-wave to S-wave velocity ratio. The inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the Zoeppritz equation. The solution is represented by a Gaussian posterior distribution with explicit expressions for the posterior expectation and covariance, hence exact prediction intervals for the inverted parameters can be computed under the specified model. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero. With realistic noise levels, acoustic impedance was the best determined parameter, while the inversion provided practically no information about the density. The inversion algorithm has also been tested on a real 3-D dataset from the Sleipner Field. The results show good agreement with well logs but the uncertainty is high. The stochastic model includes uncertainties of both the elastic parameters, the wavelet and the seismic and well log data. The posterior distribution is explored by Markov chain Monte Carlo simulation using the Gibbs sampler algorithm. The inversion algorithm has been tested on a seismic line from the Heidrun Field with two wells located on the line. The uncertainty of the estimated wavelet is low. In the Heidrun examples the effect of including uncertainty of the wavelet and the noise level was marginal with respect to the AVO inversion results. We have developed a 3-D linearized AVO inversion method with spatially coupled model parameters where the objective is to obtain posterior distributions for P-wave velocity, S

  11. Effect on Prediction when Modeling Covariates in Bayesian Nonparametric Models.

    Science.gov (United States)

    Cruz-Marcelo, Alejandro; Rosner, Gary L; Müller, Peter; Stewart, Clinton F

    2013-04-01

    In biomedical research, it is often of interest to characterize biologic processes giving rise to observations and to make predictions of future observations. Bayesian nonparametric methods provide a means for carrying out Bayesian inference making as few assumptions about restrictive parametric models as possible. There are several proposals in the literature for extending Bayesian nonparametric models to include dependence on covariates. Limited attention, however, has been directed to the following two aspects. In this article, we examine the effect on fitting and predictive performance of incorporating covariates in a class of Bayesian nonparametric models by one of two primary ways: either in the weights or in the locations of a discrete random probability measure. We show that different strategies for incorporating continuous covariates in Bayesian nonparametric models can result in big differences when used for prediction, even though they lead to otherwise similar posterior inferences. When one needs the predictive density, as in optimal design, and this density is a mixture, it is better to make the weights depend on the covariates. We demonstrate these points via a simulated data example and in an application in which one wants to determine the optimal dose of an anticancer drug used in pediatric oncology.

  12. Bayesian networks improve causal environmental ...

    Science.gov (United States)

    Rule-based weight of evidence approaches to ecological risk assessment may not account for uncertainties and generally lack probabilistic integration of lines of evidence. Bayesian networks allow causal inferences to be made from evidence by including causal knowledge about the problem, using this knowledge with probabilistic calculus to combine multiple lines of evidence, and minimizing biases in predicting or diagnosing causal relationships. Too often, sources of uncertainty in conventional weight of evidence approaches are ignored that can be accounted for with Bayesian networks. Specifying and propagating uncertainties improve the ability of models to incorporate strength of the evidence in the risk management phase of an assessment. Probabilistic inference from a Bayesian network allows evaluation of changes in uncertainty for variables from the evidence. The network structure and probabilistic framework of a Bayesian approach provide advantages over qualitative approaches in weight of evidence for capturing the impacts of multiple sources of quantifiable uncertainty on predictions of ecological risk. Bayesian networks can facilitate the development of evidence-based policy under conditions of uncertainty by incorporating analytical inaccuracies or the implications of imperfect information, structuring and communicating causal issues through qualitative directed graph formulations, and quantitatively comparing the causal power of multiple stressors on value

  13. Bayesian Latent Class Analysis Tutorial.

    Science.gov (United States)

    Li, Yuelin; Lord-Bessen, Jennifer; Shiyko, Mariya; Loeb, Rebecca

    2018-01-01

    This article is a how-to guide on Bayesian computation using Gibbs sampling, demonstrated in the context of Latent Class Analysis (LCA). It is written for students in quantitative psychology or related fields who have a working knowledge of Bayes Theorem and conditional probability and have experience in writing computer programs in the statistical language R . The overall goals are to provide an accessible and self-contained tutorial, along with a practical computation tool. We begin with how Bayesian computation is typically described in academic articles. Technical difficulties are addressed by a hypothetical, worked-out example. We show how Bayesian computation can be broken down into a series of simpler calculations, which can then be assembled together to complete a computationally more complex model. The details are described much more explicitly than what is typically available in elementary introductions to Bayesian modeling so that readers are not overwhelmed by the mathematics. Moreover, the provided computer program shows how Bayesian LCA can be implemented with relative ease. The computer program is then applied in a large, real-world data set and explained line-by-line. We outline the general steps in how to extend these considerations to other methodological applications. We conclude with suggestions for further readings.

  14. Kernel Bayesian ART and ARTMAP.

    Science.gov (United States)

    Masuyama, Naoki; Loo, Chu Kiong; Dawood, Farhan

    2018-02-01

    Adaptive Resonance Theory (ART) is one of the successful approaches to resolving "the plasticity-stability dilemma" in neural networks, and its supervised learning model called ARTMAP is a powerful tool for classification. Among several improvements, such as Fuzzy or Gaussian based models, the state of art model is Bayesian based one, while solving the drawbacks of others. However, it is known that the Bayesian approach for the high dimensional and a large number of data requires high computational cost, and the covariance matrix in likelihood becomes unstable. This paper introduces Kernel Bayesian ART (KBA) and ARTMAP (KBAM) by integrating Kernel Bayes' Rule (KBR) and Correntropy Induced Metric (CIM) to Bayesian ART (BA) and ARTMAP (BAM), respectively, while maintaining the properties of BA and BAM. The kernel frameworks in KBA and KBAM are able to avoid the curse of dimensionality. In addition, the covariance-free Bayesian computation by KBR provides the efficient and stable computational capability to KBA and KBAM. Furthermore, Correntropy-based similarity measurement allows improving the noise reduction ability even in the high dimensional space. The simulation experiments show that KBA performs an outstanding self-organizing capability than BA, and KBAM provides the superior classification ability than BAM, respectively. Copyright © 2017 Elsevier Ltd. All rights reserved.

  15. A Bayesian concept learning approach to crowdsourcing

    DEFF Research Database (Denmark)

    Viappiani, P.; Zilles, S.; Hamilton, H.J.

    2011-01-01

    techniques, inference methods, and query selection strategies to assist a user charged with choosing a configuration that satisfies some (partially known) concept. Our model is able to simultaneously learn the concept definition and the types of the experts. We evaluate our model with simulations, showing......We develop a Bayesian approach to concept learning for crowdsourcing applications. A probabilistic belief over possible concept definitions is maintained and updated according to (noisy) observations from experts, whose behaviors are modeled using discrete types. We propose recommendation...

  16. Bayesian estimation of core-melt probability

    International Nuclear Information System (INIS)

    Lewis, H.W.

    1984-01-01

    A very simple application of the canonical Bayesian algorithm is made to the problem of estimation of the probability of core melt in a commercial power reactor. An approximation to the results of the Rasmussen study on reactor safety is used as the prior distribution, and the observation that there has been no core melt yet is used as the single experiment. The result is a substantial decrease in the mean probability of core melt--factors of 2 to 4 for reasonable choices of parameters. The purpose is to illustrate the procedure, not to argue for the decrease

  17. Interactive Instruction in Bayesian Inference

    DEFF Research Database (Denmark)

    Khan, Azam; Breslav, Simon; Hornbæk, Kasper

    2018-01-01

    An instructional approach is presented to improve human performance in solving Bayesian inference problems. Starting from the original text of the classic Mammography Problem, the textual expression is modified and visualizations are added according to Mayer’s principles of instruction. These pri......An instructional approach is presented to improve human performance in solving Bayesian inference problems. Starting from the original text of the classic Mammography Problem, the textual expression is modified and visualizations are added according to Mayer’s principles of instruction....... These principles concern coherence, personalization, signaling, segmenting, multimedia, spatial contiguity, and pretraining. Principles of self-explanation and interactivity are also applied. Four experiments on the Mammography Problem showed that these principles help participants answer the questions...... that an instructional approach to improving human performance in Bayesian inference is a promising direction....

  18. Bayesian analysis of CCDM models

    Science.gov (United States)

    Jesus, J. F.; Valentim, R.; Andrade-Oliveira, F.

    2017-09-01

    Creation of Cold Dark Matter (CCDM), in the context of Einstein Field Equations, produces a negative pressure term which can be used to explain the accelerated expansion of the Universe. In this work we tested six different spatially flat models for matter creation using statistical criteria, in light of SNe Ia data: Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Bayesian Evidence (BE). These criteria allow to compare models considering goodness of fit and number of free parameters, penalizing excess of complexity. We find that JO model is slightly favoured over LJO/ΛCDM model, however, neither of these, nor Γ = 3αH0 model can be discarded from the current analysis. Three other scenarios are discarded either because poor fitting or because of the excess of free parameters. A method of increasing Bayesian evidence through reparameterization in order to reducing parameter degeneracy is also developed.

  19. Bayesian analysis of CCDM models

    Energy Technology Data Exchange (ETDEWEB)

    Jesus, J.F. [Universidade Estadual Paulista (Unesp), Câmpus Experimental de Itapeva, Rua Geraldo Alckmin 519, Vila N. Sra. de Fátima, Itapeva, SP, 18409-010 Brazil (Brazil); Valentim, R. [Departamento de Física, Instituto de Ciências Ambientais, Químicas e Farmacêuticas—ICAQF, Universidade Federal de São Paulo (UNIFESP), Unidade José Alencar, Rua São Nicolau No. 210, Diadema, SP, 09913-030 Brazil (Brazil); Andrade-Oliveira, F., E-mail: jfjesus@itapeva.unesp.br, E-mail: valentim.rodolfo@unifesp.br, E-mail: felipe.oliveira@port.ac.uk [Institute of Cosmology and Gravitation—University of Portsmouth, Burnaby Road, Portsmouth, PO1 3FX United Kingdom (United Kingdom)

    2017-09-01

    Creation of Cold Dark Matter (CCDM), in the context of Einstein Field Equations, produces a negative pressure term which can be used to explain the accelerated expansion of the Universe. In this work we tested six different spatially flat models for matter creation using statistical criteria, in light of SNe Ia data: Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Bayesian Evidence (BE). These criteria allow to compare models considering goodness of fit and number of free parameters, penalizing excess of complexity. We find that JO model is slightly favoured over LJO/ΛCDM model, however, neither of these, nor Γ = 3α H {sub 0} model can be discarded from the current analysis. Three other scenarios are discarded either because poor fitting or because of the excess of free parameters. A method of increasing Bayesian evidence through reparameterization in order to reducing parameter degeneracy is also developed.

  20. BAYESIAN MAGNETOHYDRODYNAMIC SEISMOLOGY OF CORONAL LOOPS

    International Nuclear Information System (INIS)

    Arregui, I.; Asensio Ramos, A.

    2011-01-01

    We perform a Bayesian parameter inference in the context of resonantly damped transverse coronal loop oscillations. The forward problem is solved in terms of parametric results for kink waves in one-dimensional flux tubes in the thin tube and thin boundary approximations. For the inverse problem, we adopt a Bayesian approach to infer the most probable values of the relevant parameters, for given observed periods and damping times, and to extract their confidence levels. The posterior probability distribution functions are obtained by means of Markov Chain Monte Carlo simulations, incorporating observed uncertainties in a consistent manner. We find well-localized solutions in the posterior probability distribution functions for two of the three parameters of interest, namely the Alfven travel time and the transverse inhomogeneity length scale. The obtained estimates for the Alfven travel time are consistent with previous inversion results, but the method enables us to additionally constrain the transverse inhomogeneity length scale and to estimate real error bars for each parameter. When observational estimates for the density contrast are used, the method enables us to fully constrain the three parameters of interest. These results can serve to improve our current estimates of unknown physical parameters in coronal loops and to test the assumed theoretical model.

  1. Learning Bayesian networks for discrete data

    KAUST Repository

    Liang, Faming; Zhang, Jian

    2009-01-01

    Bayesian networks have received much attention in the recent literature. In this article, we propose an approach to learn Bayesian networks using the stochastic approximation Monte Carlo (SAMC) algorithm. Our approach has two nice features. Firstly

  2. Bayesian Network Induction via Local Neighborhoods

    National Research Council Canada - National Science Library

    Margaritis, Dimitris

    1999-01-01

    .... We present an efficient algorithm for learning Bayesian networks from data. Our approach constructs Bayesian networks by first identifying each node's Markov blankets, then connecting nodes in a consistent way...

  3. Can a significance test be genuinely Bayesian?

    OpenAIRE

    Pereira, Carlos A. de B.; Stern, Julio Michael; Wechsler, Sergio

    2008-01-01

    The Full Bayesian Significance Test, FBST, is extensively reviewed. Its test statistic, a genuine Bayesian measure of evidence, is discussed in detail. Its behavior in some problems of statistical inference like testing for independence in contingency tables is discussed.

  4. Bayesian modeling using WinBUGS

    CERN Document Server

    Ntzoufras, Ioannis

    2009-01-01

    A hands-on introduction to the principles of Bayesian modeling using WinBUGS Bayesian Modeling Using WinBUGS provides an easily accessible introduction to the use of WinBUGS programming techniques in a variety of Bayesian modeling settings. The author provides an accessible treatment of the topic, offering readers a smooth introduction to the principles of Bayesian modeling with detailed guidance on the practical implementation of key principles. The book begins with a basic introduction to Bayesian inference and the WinBUGS software and goes on to cover key topics, including: Markov Chain Monte Carlo algorithms in Bayesian inference Generalized linear models Bayesian hierarchical models Predictive distribution and model checking Bayesian model and variable evaluation Computational notes and screen captures illustrate the use of both WinBUGS as well as R software to apply the discussed techniques. Exercises at the end of each chapter allow readers to test their understanding of the presented concepts and all ...

  5. BATSE gamma-ray burst line search. 2: Bayesian consistency methodology

    Science.gov (United States)

    Band, D. L.; Ford, L. A.; Matteson, J. L.; Briggs, M.; Paciesas, W.; Pendleton, G.; Preece, R.; Palmer, D.; Teegarden, B.; Schaefer, B.

    1994-01-01

    We describe a Bayesian methodology to evaluate the consistency between the reported Ginga and Burst and Transient Source Experiment (BATSE) detections of absorption features in gamma-ray burst spectra. Currently no features have been detected by BATSE, but this methodology will still be applicable if and when such features are discovered. The Bayesian methodology permits the comparison of hypotheses regarding the two detectors' observations and makes explicit the subjective aspects of our analysis (e.g., the quantification of our confidence in detector performance). We also present non-Bayesian consistency statistics. Based on preliminary calculations of line detectability, we find that both the Bayesian and non-Bayesian techniques show that the BATSE and Ginga observations are consistent given our understanding of these detectors.

  6. Inference in hybrid Bayesian networks

    International Nuclear Information System (INIS)

    Langseth, Helge; Nielsen, Thomas D.; Rumi, Rafael; Salmeron, Antonio

    2009-01-01

    Since the 1980s, Bayesian networks (BNs) have become increasingly popular for building statistical models of complex systems. This is particularly true for boolean systems, where BNs often prove to be a more efficient modelling framework than traditional reliability techniques (like fault trees and reliability block diagrams). However, limitations in the BNs' calculation engine have prevented BNs from becoming equally popular for domains containing mixtures of both discrete and continuous variables (the so-called hybrid domains). In this paper we focus on these difficulties, and summarize some of the last decade's research on inference in hybrid Bayesian networks. The discussions are linked to an example model for estimating human reliability.

  7. 3D Bayesian contextual classifiers

    DEFF Research Database (Denmark)

    Larsen, Rasmus

    2000-01-01

    We extend a series of multivariate Bayesian 2-D contextual classifiers to 3-D by specifying a simultaneous Gaussian distribution for the feature vectors as well as a prior distribution of the class variables of a pixel and its 6 nearest 3-D neighbours.......We extend a series of multivariate Bayesian 2-D contextual classifiers to 3-D by specifying a simultaneous Gaussian distribution for the feature vectors as well as a prior distribution of the class variables of a pixel and its 6 nearest 3-D neighbours....

  8. Bayesian methods for proteomic biomarker development

    Directory of Open Access Journals (Sweden)

    Belinda Hernández

    2015-12-01

    In this review we provide an introduction to Bayesian inference and demonstrate some of the advantages of using a Bayesian framework. We summarize how Bayesian methods have been used previously in proteomics and other areas of bioinformatics. Finally, we describe some popular and emerging Bayesian models from the statistical literature and provide a worked tutorial including code snippets to show how these methods may be applied for the evaluation of proteomic biomarkers.

  9. Bayesian and maximum likelihood estimation of genetic maps

    DEFF Research Database (Denmark)

    York, Thomas L.; Durrett, Richard T.; Tanksley, Steven

    2005-01-01

    There has recently been increased interest in the use of Markov Chain Monte Carlo (MCMC)-based Bayesian methods for estimating genetic maps. The advantage of these methods is that they can deal accurately with missing data and genotyping errors. Here we present an extension of the previous methods...... of genotyping errors. A similar advantage of the Bayesian method was not observed for missing data. We also re-analyse a recently published set of data from the eggplant and show that the use of the MCMC-based method leads to smaller estimates of genetic distances....

  10. Bayesian networks and food security - An introduction

    NARCIS (Netherlands)

    Stein, A.

    2004-01-01

    This paper gives an introduction to Bayesian networks. Networks are defined and put into a Bayesian context. Directed acyclical graphs play a crucial role here. Two simple examples from food security are addressed. Possible uses of Bayesian networks for implementation and further use in decision

  11. Plug & Play object oriented Bayesian networks

    DEFF Research Database (Denmark)

    Bangsø, Olav; Flores, J.; Jensen, Finn Verner

    2003-01-01

    been shown to be quite suitable for dynamic domains as well. However, processing object oriented Bayesian networks in practice does not take advantage of their modular structure. Normally the object oriented Bayesian network is transformed into a Bayesian network and, inference is performed...... dynamic domains. The communication needed between instances is achieved by means of a fill-in propagation scheme....

  12. A Bayesian framework for risk perception

    NARCIS (Netherlands)

    van Erp, H.R.N.

    2017-01-01

    We present here a Bayesian framework of risk perception. This framework encompasses plausibility judgments, decision making, and question asking. Plausibility judgments are modeled by way of Bayesian probability theory, decision making is modeled by way of a Bayesian decision theory, and relevancy

  13. Sequential Inverse Problems Bayesian Principles and the Logistic Map Example

    Science.gov (United States)

    Duan, Lian; Farmer, Chris L.; Moroz, Irene M.

    2010-09-01

    Bayesian statistics provides a general framework for solving inverse problems, but is not without interpretation and implementation problems. This paper discusses difficulties arising from the fact that forward models are always in error to some extent. Using a simple example based on the one-dimensional logistic map, we argue that, when implementation problems are minimal, the Bayesian framework is quite adequate. In this paper the Bayesian Filter is shown to be able to recover excellent state estimates in the perfect model scenario (PMS) and to distinguish the PMS from the imperfect model scenario (IMS). Through a quantitative comparison of the way in which the observations are assimilated in both the PMS and the IMS scenarios, we suggest that one can, sometimes, measure the degree of imperfection.

  14. Nonparametric Bayesian inference for multidimensional compound Poisson processes

    NARCIS (Netherlands)

    Gugushvili, S.; van der Meulen, F.; Spreij, P.

    2015-01-01

    Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density r0 and intensity λ0. We take a nonparametric Bayesian approach to the problem and determine posterior contraction rates in this context,

  15. Bayesian recovery of the initial condition for the heat equation

    NARCIS (Netherlands)

    Knapik, B.T.; Vaart, van der A.W.; Zanten, van J.H.

    2011-01-01

    We study a Bayesian approach to recovering the initial condition for the heat equation from noisy observations of the solution at a later time. We consider a class of prior distributions indexed by a parameter quantifying "smoothness" and show that the corresponding posterior distributions contract

  16. Polynomial Chaos Surrogates for Bayesian Inference

    KAUST Repository

    Le Maitre, Olivier

    2016-01-06

    The Bayesian inference is a popular probabilistic method to solve inverse problems, such as the identification of field parameter in a PDE model. The inference rely on the Bayes rule to update the prior density of the sought field, from observations, and derive its posterior distribution. In most cases the posterior distribution has no explicit form and has to be sampled, for instance using a Markov-Chain Monte Carlo method. In practice the prior field parameter is decomposed and truncated (e.g. by means of Karhunen- Lo´eve decomposition) to recast the inference problem into the inference of a finite number of coordinates. Although proved effective in many situations, the Bayesian inference as sketched above faces several difficulties requiring improvements. First, sampling the posterior can be a extremely costly task as it requires multiple resolutions of the PDE model for different values of the field parameter. Second, when the observations are not very much informative, the inferred parameter field can highly depends on its prior which can be somehow arbitrary. These issues have motivated the introduction of reduced modeling or surrogates for the (approximate) determination of the parametrized PDE solution and hyperparameters in the description of the prior field. Our contribution focuses on recent developments in these two directions: the acceleration of the posterior sampling by means of Polynomial Chaos expansions and the efficient treatment of parametrized covariance functions for the prior field. We also discuss the possibility of making such approach adaptive to further improve its efficiency.

  17. Bayesian NL interpretation and learning

    NARCIS (Netherlands)

    Zeevat, H.

    2011-01-01

    Everyday natural language communication is normally successful, even though contemporary computational linguistics has shown that NL is characterised by very high degree of ambiguity and the results of stochastic methods are not good enough to explain the high success rate. Bayesian natural language

  18. Bayesian image restoration, using configurations

    DEFF Research Database (Denmark)

    Thorarinsdottir, Thordis

    configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for salt and pepper noise. The inference in the model is discussed...

  19. Bayesian image restoration, using configurations

    DEFF Research Database (Denmark)

    Thorarinsdottir, Thordis Linda

    2006-01-01

    configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for the salt and pepper noise. The inference in the model is discussed...

  20. Differentiated Bayesian Conjoint Choice Designs

    NARCIS (Netherlands)

    Z. Sándor (Zsolt); M. Wedel (Michel)

    2003-01-01

    textabstractPrevious conjoint choice design construction procedures have produced a single design that is administered to all subjects. This paper proposes to construct a limited set of different designs. The designs are constructed in a Bayesian fashion, taking into account prior uncertainty about

  1. Bayesian Networks and Influence Diagrams

    DEFF Research Database (Denmark)

    Kjærulff, Uffe Bro; Madsen, Anders Læsø

    Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis, Second Edition, provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. This new edition contains six new...

  2. Bayesian Sampling using Condition Indicators

    DEFF Research Database (Denmark)

    Faber, Michael H.; Sørensen, John Dalsgaard

    2002-01-01

    of condition indicators introduced by Benjamin and Cornell (1970) a Bayesian approach to quality control is formulated. The formulation is then extended to the case where the quality control is based on sampling of indirect information about the condition of the components, i.e. condition indicators...

  3. Bayesian Classification of Image Structures

    DEFF Research Database (Denmark)

    Goswami, Dibyendu; Kalkan, Sinan; Krüger, Norbert

    2009-01-01

    In this paper, we describe work on Bayesian classi ers for distinguishing between homogeneous structures, textures, edges and junctions. We build semi-local classiers from hand-labeled images to distinguish between these four different kinds of structures based on the concept of intrinsic dimensi...

  4. Bayesian estimates of linkage disequilibrium

    Directory of Open Access Journals (Sweden)

    Abad-Grau María M

    2007-06-01

    Full Text Available Abstract Background The maximum likelihood estimator of D' – a standard measure of linkage disequilibrium – is biased toward disequilibrium, and the bias is particularly evident in small samples and rare haplotypes. Results This paper proposes a Bayesian estimation of D' to address this problem. The reduction of the bias is achieved by using a prior distribution on the pair-wise associations between single nucleotide polymorphisms (SNPs that increases the likelihood of equilibrium with increasing physical distances between pairs of SNPs. We show how to compute the Bayesian estimate using a stochastic estimation based on MCMC methods, and also propose a numerical approximation to the Bayesian estimates that can be used to estimate patterns of LD in large datasets of SNPs. Conclusion Our Bayesian estimator of D' corrects the bias toward disequilibrium that affects the maximum likelihood estimator. A consequence of this feature is a more objective view about the extent of linkage disequilibrium in the human genome, and a more realistic number of tagging SNPs to fully exploit the power of genome wide association studies.

  5. 3-D contextual Bayesian classifiers

    DEFF Research Database (Denmark)

    Larsen, Rasmus

    In this paper we will consider extensions of a series of Bayesian 2-D contextual classification pocedures proposed by Owen (1984) Hjort & Mohn (1984) and Welch & Salter (1971) and Haslett (1985) to 3 spatial dimensions. It is evident that compared to classical pixelwise classification further...

  6. Bayesian Alternation During Tactile Augmentation

    Directory of Open Access Journals (Sweden)

    Caspar Mathias Goeke

    2016-10-01

    Full Text Available A large number of studies suggest that the integration of multisensory signals by humans is well described by Bayesian principles. However, there are very few reports about cue combination between a native and an augmented sense. In particular, we asked the question whether adult participants are able to integrate an augmented sensory cue with existing native sensory information. Hence for the purpose of this study we build a tactile augmentation device. Consequently, we compared different hypotheses of how untrained adult participants combine information from a native and an augmented sense. In a two-interval forced choice (2 IFC task, while subjects were blindfolded and seated on a rotating platform, our sensory augmentation device translated information on whole body yaw rotation to tactile stimulation. Three conditions were realized: tactile stimulation only (augmented condition, rotation only (native condition, and both augmented and native information (bimodal condition. Participants had to choose one out of two consecutive rotations with higher angular rotation. For the analysis, we fitted the participants’ responses with a probit model and calculated the just notable difference (JND. Then we compared several models for predicting bimodal from unimodal responses. An objective Bayesian alternation model yielded a better prediction (χred2 = 1.67 than the Bayesian integration model (χred2= 4.34. Slightly higher accuracy showed a non-Bayesian winner takes all model (χred2= 1.64, which either used only native or only augmented values per subject for prediction. However the performance of the Bayesian alternation model could be substantially improved (χred2= 1.09 utilizing subjective weights obtained by a questionnaire. As a result, the subjective Bayesian alternation model predicted bimodal performance most accurately among all tested models. These results suggest that information from augmented and existing sensory modalities in

  7. Topics in Bayesian statistics and maximum entropy

    International Nuclear Information System (INIS)

    Mutihac, R.; Cicuttin, A.; Cerdeira, A.; Stanciulescu, C.

    1998-12-01

    Notions of Bayesian decision theory and maximum entropy methods are reviewed with particular emphasis on probabilistic inference and Bayesian modeling. The axiomatic approach is considered as the best justification of Bayesian analysis and maximum entropy principle applied in natural sciences. Particular emphasis is put on solving the inverse problem in digital image restoration and Bayesian modeling of neural networks. Further topics addressed briefly include language modeling, neutron scattering, multiuser detection and channel equalization in digital communications, genetic information, and Bayesian court decision-making. (author)

  8. Development and comparison in uncertainty assessment based Bayesian modularization method in hydrological modeling

    Science.gov (United States)

    Li, Lu; Xu, Chong-Yu; Engeland, Kolbjørn

    2013-04-01

    SummaryWith respect to model calibration, parameter estimation and analysis of uncertainty sources, various regression and probabilistic approaches are used in hydrological modeling. A family of Bayesian methods, which incorporates different sources of information into a single analysis through Bayes' theorem, is widely used for uncertainty assessment. However, none of these approaches can well treat the impact of high flows in hydrological modeling. This study proposes a Bayesian modularization uncertainty assessment approach in which the highest streamflow observations are treated as suspect information that should not influence the inference of the main bulk of the model parameters. This study includes a comprehensive comparison and evaluation of uncertainty assessments by our new Bayesian modularization method and standard Bayesian methods using the Metropolis-Hastings (MH) algorithm with the daily hydrological model WASMOD. Three likelihood functions were used in combination with standard Bayesian method: the AR(1) plus Normal model independent of time (Model 1), the AR(1) plus Normal model dependent on time (Model 2) and the AR(1) plus Multi-normal model (Model 3). The results reveal that the Bayesian modularization method provides the most accurate streamflow estimates measured by the Nash-Sutcliffe efficiency and provide the best in uncertainty estimates for low, medium and entire flows compared to standard Bayesian methods. The study thus provides a new approach for reducing the impact of high flows on the discharge uncertainty assessment of hydrological models via Bayesian method.

  9. Adaptive Naive Bayesian Anti-Spam Engine

    CERN Document Server

    Gajewski, W P

    2006-01-01

    The problem of spam has been seriously troubling the Internet community during the last few years and currently reached an alarming scale. Observations made at CERN (European Organization for Nuclear Research located in Geneva, Switzerland) show that spam mails can constitute up to 75% of daily SMTP traffic. A naïve Bayesian classifier based on a Bag of Words representation of an email is widely used to stop this unwanted flood as it combines good performance with simplicity of the training and classification processes. However, facing the constantly changing patterns of spam, it is necessary to assure online adaptability of the classifier. This work proposes combining such a classifier with another NBC (naïve Bayesian classifier) based on pairs of adjacent words. Only the latter will be retrained with examples of spam reported by users. Tests are performed on considerable sets of mails both from public spam archives and CERN mailboxes. They suggest that this architecture can increase spam recall without af...

  10. A Bayesian approach to person perception.

    Science.gov (United States)

    Clifford, C W G; Mareschal, I; Otsuka, Y; Watson, T L

    2015-11-01

    Here we propose a Bayesian approach to person perception, outlining the theoretical position and a methodological framework for testing the predictions experimentally. We use the term person perception to refer not only to the perception of others' personal attributes such as age and sex but also to the perception of social signals such as direction of gaze and emotional expression. The Bayesian approach provides a formal description of the way in which our perception combines current sensory evidence with prior expectations about the structure of the environment. Such expectations can lead to unconscious biases in our perception that are particularly evident when sensory evidence is uncertain. We illustrate the ideas with reference to our recent studies on gaze perception which show that people have a bias to perceive the gaze of others as directed towards themselves. We also describe a potential application to the study of the perception of a person's sex, in which a bias towards perceiving males is typically observed. Copyright © 2015 Elsevier Inc. All rights reserved.

  11. Discovering Alzheimer Genetic Biomarkers Using Bayesian Networks

    Directory of Open Access Journals (Sweden)

    Fayroz F. Sherif

    2015-01-01

    Full Text Available Single nucleotide polymorphisms (SNPs contribute most of the genetic variation to the human genome. SNPs associate with many complex and common diseases like Alzheimer’s disease (AD. Discovering SNP biomarkers at different loci can improve early diagnosis and treatment of these diseases. Bayesian network provides a comprehensible and modular framework for representing interactions between genes or single SNPs. Here, different Bayesian network structure learning algorithms have been applied in whole genome sequencing (WGS data for detecting the causal AD SNPs and gene-SNP interactions. We focused on polymorphisms in the top ten genes associated with AD and identified by genome-wide association (GWA studies. New SNP biomarkers were observed to be significantly associated with Alzheimer’s disease. These SNPs are rs7530069, rs113464261, rs114506298, rs73504429, rs7929589, rs76306710, and rs668134. The obtained results demonstrated the effectiveness of using BN for identifying AD causal SNPs with acceptable accuracy. The results guarantee that the SNP set detected by Markov blanket based methods has a strong association with AD disease and achieves better performance than both naïve Bayes and tree augmented naïve Bayes. Minimal augmented Markov blanket reaches accuracy of 66.13% and sensitivity of 88.87% versus 61.58% and 59.43% in naïve Bayes, respectively.

  12. Bayesian reasoning in HEP principles and applications

    CERN Document Server

    D'Agostini, Giulio

    1998-01-01

    Bayesian statistics associate the idea of probability-the measure of the degree of belief that an event will occur - to the lack of knowledge, as it is commonly perceived intuitively. The Bayes' theorem becomes then the basic tool to evaluate the probability, combining (a priori) judgement and experimental information. This approach allows to treat in a logically consistent way all kinds of uncertainty. The lessons will deal with uncertainty arising from measurements: inference on the value of a physics quantity from experimental observations (examining in depth the cases of observations following Gaussian, binomialand poisson distributions); combinations of results; upper/lower limits and their combination; hypothesis tests versus probabilities of the hypotheses; systematic errors and the correlations they induce; simplified methods for routine applications (by-passing the explicit use of Bayes' theorem); type A and type B uncertainties (according to BIPM/ISO recovery of many standard methods, but deeping th...

  13. The Bayesian Approach to Association

    Science.gov (United States)

    Arora, N. S.

    2017-12-01

    The Bayesian approach to Association focuses mainly on quantifying the physics of the domain. In the case of seismic association for instance let X be the set of all significant events (above some threshold) and their attributes, such as location, time, and magnitude, Y1 be the set of detections that are caused by significant events and their attributes such as seismic phase, arrival time, amplitude etc., Y2 be the set of detections that are not caused by significant events, and finally Y be the set of observed detections We would now define the joint distribution P(X, Y1, Y2, Y) = P(X) P(Y1 | X) P(Y2) I(Y = Y1 + Y2) ; where the last term simply states that Y1 and Y2 are a partitioning of Y. Given the above joint distribution the inference problem is simply to find the X, Y1, and Y2 that maximizes posterior probability P(X, Y1, Y2| Y) which reduces to maximizing P(X) P(Y1 | X) P(Y2) I(Y = Y1 + Y2). In this expression P(X) captures our prior belief about event locations. P(Y1 | X) captures notions of travel time, residual error distributions as well as detection and mis-detection probabilities. While P(Y2) captures the false detection rate of our seismic network. The elegance of this approach is that all of the assumptions are stated clearly in the model for P(X), P(Y1|X) and P(Y2). The implementation of the inference is merely a by-product of this model. In contrast some of the other methods such as GA hide a number of assumptions in the implementation details of the inference - such as the so called "driver cells." The other important aspect of this approach is that all seismic knowledge including knowledge from other domains such as infrasound and hydroacoustic can be included in the same model. So, we don't need to separately account for misdetections or merge seismic and infrasound events as a separate step. Finally, it should be noted that the objective of automatic association is to simplify the job of humans who are publishing seismic bulletins based on this

  14. Bayesian statistics in radionuclide metrology: measurement of a decaying source

    International Nuclear Information System (INIS)

    Bochud, F. O.; Bailat, C.J.; Laedermann, J.P.

    2007-01-01

    The most intuitive way of defining a probability is perhaps through the frequency at which it appears when a large number of trials are realized in identical conditions. The probability derived from the obtained histogram characterizes the so-called frequentist or conventional statistical approach. In this sense, probability is defined as a physical property of the observed system. By contrast, in Bayesian statistics, a probability is not a physical property or a directly observable quantity, but a degree of belief or an element of inference. The goal of this paper is to show how Bayesian statistics can be used in radionuclide metrology and what its advantages and disadvantages are compared with conventional statistics. This is performed through the example of an yttrium-90 source typically encountered in environmental surveillance measurement. Because of the very low activity of this kind of source and the small half-life of the radionuclide, this measurement takes several days, during which the source decays significantly. Several methods are proposed to compute simultaneously the number of unstable nuclei at a given reference time, the decay constant and the background. Asymptotically, all approaches give the same result. However, Bayesian statistics produces coherent estimates and confidence intervals in a much smaller number of measurements. Apart from the conceptual understanding of statistics, the main difficulty that could deter radionuclide metrologists from using Bayesian statistics is the complexity of the computation. (authors)

  15. Bayesian estimation methods in metrology

    International Nuclear Information System (INIS)

    Cox, M.G.; Forbes, A.B.; Harris, P.M.

    2004-01-01

    In metrology -- the science of measurement -- a measurement result must be accompanied by a statement of its associated uncertainty. The degree of validity of a measurement result is determined by the validity of the uncertainty statement. In recognition of the importance of uncertainty evaluation, the International Standardization Organization in 1995 published the Guide to the Expression of Uncertainty in Measurement and the Guide has been widely adopted. The validity of uncertainty statements is tested in interlaboratory comparisons in which an artefact is measured by a number of laboratories and their measurement results compared. Since the introduction of the Mutual Recognition Arrangement, key comparisons are being undertaken to determine the degree of equivalence of laboratories for particular measurement tasks. In this paper, we discuss the possible development of the Guide to reflect Bayesian approaches and the evaluation of key comparison data using Bayesian estimation methods

  16. Deep Learning and Bayesian Methods

    Directory of Open Access Journals (Sweden)

    Prosper Harrison B.

    2017-01-01

    Full Text Available A revolution is underway in which deep neural networks are routinely used to solve diffcult problems such as face recognition and natural language understanding. Particle physicists have taken notice and have started to deploy these methods, achieving results that suggest a potentially significant shift in how data might be analyzed in the not too distant future. We discuss a few recent developments in the application of deep neural networks and then indulge in speculation about how such methods might be used to automate certain aspects of data analysis in particle physics. Next, the connection to Bayesian methods is discussed and the paper ends with thoughts on a significant practical issue, namely, how, from a Bayesian perspective, one might optimize the construction of deep neural networks.

  17. Bayesian inference on proportional elections.

    Directory of Open Access Journals (Sweden)

    Gabriel Hideki Vatanabe Brunello

    Full Text Available Polls for majoritarian voting systems usually show estimates of the percentage of votes for each candidate. However, proportional vote systems do not necessarily guarantee the candidate with the most percentage of votes will be elected. Thus, traditional methods used in majoritarian elections cannot be applied on proportional elections. In this context, the purpose of this paper was to perform a Bayesian inference on proportional elections considering the Brazilian system of seats distribution. More specifically, a methodology to answer the probability that a given party will have representation on the chamber of deputies was developed. Inferences were made on a Bayesian scenario using the Monte Carlo simulation technique, and the developed methodology was applied on data from the Brazilian elections for Members of the Legislative Assembly and Federal Chamber of Deputies in 2010. A performance rate was also presented to evaluate the efficiency of the methodology. Calculations and simulations were carried out using the free R statistical software.

  18. Space Shuttle RTOS Bayesian Network

    Science.gov (United States)

    Morris, A. Terry; Beling, Peter A.

    2001-01-01

    With shrinking budgets and the requirements to increase reliability and operational life of the existing orbiter fleet, NASA has proposed various upgrades for the Space Shuttle that are consistent with national space policy. The cockpit avionics upgrade (CAU), a high priority item, has been selected as the next major upgrade. The primary functions of cockpit avionics include flight control, guidance and navigation, communication, and orbiter landing support. Secondary functions include the provision of operational services for non-avionics systems such as data handling for the payloads and caution and warning alerts to the crew. Recently, a process to selection the optimal commercial-off-the-shelf (COTS) real-time operating system (RTOS) for the CAU was conducted by United Space Alliance (USA) Corporation, which is a joint venture between Boeing and Lockheed Martin, the prime contractor for space shuttle operations. In order to independently assess the RTOS selection, NASA has used the Bayesian network-based scoring methodology described in this paper. Our two-stage methodology addresses the issue of RTOS acceptability by incorporating functional, performance and non-functional software measures related to reliability, interoperability, certifiability, efficiency, correctness, business, legal, product history, cost and life cycle. The first stage of the methodology involves obtaining scores for the various measures using a Bayesian network. The Bayesian network incorporates the causal relationships between the various and often competing measures of interest while also assisting the inherently complex decision analysis process with its ability to reason under uncertainty. The structure and selection of prior probabilities for the network is extracted from experts in the field of real-time operating systems. Scores for the various measures are computed using Bayesian probability. In the second stage, multi-criteria trade-off analyses are performed between the scores

  19. Multiview Bayesian Correlated Component Analysis

    DEFF Research Database (Denmark)

    Kamronn, Simon Due; Poulsen, Andreas Trier; Hansen, Lars Kai

    2015-01-01

    are identical. Here we propose a hierarchical probabilistic model that can infer the level of universality in such multiview data, from completely unrelated representations, corresponding to canonical correlation analysis, to identical representations as in correlated component analysis. This new model, which...... we denote Bayesian correlated component analysis, evaluates favorably against three relevant algorithms in simulated data. A well-established benchmark EEG data set is used to further validate the new model and infer the variability of spatial representations across multiple subjects....

  20. 12th Brazilian Meeting on Bayesian Statistics

    CERN Document Server

    Louzada, Francisco; Rifo, Laura; Stern, Julio; Lauretto, Marcelo

    2015-01-01

    Through refereed papers, this volume focuses on the foundations of the Bayesian paradigm; their comparison to objectivistic or frequentist Statistics counterparts; and the appropriate application of Bayesian foundations. This research in Bayesian Statistics is applicable to data analysis in biostatistics, clinical trials, law, engineering, and the social sciences. EBEB, the Brazilian Meeting on Bayesian Statistics, is held every two years by the ISBrA, the International Society for Bayesian Analysis, one of the most active chapters of the ISBA. The 12th meeting took place March 10-14, 2014 in Atibaia. Interest in foundations of inductive Statistics has grown recently in accordance with the increasing availability of Bayesian methodological alternatives. Scientists need to deal with the ever more difficult choice of the optimal method to apply to their problem. This volume shows how Bayes can be the answer. The examination and discussion on the foundations work towards the goal of proper application of Bayesia...

  1. Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes.

    Science.gov (United States)

    Yang, Jingjing; Cox, Dennis D; Lee, Jong Soo; Ren, Peng; Choi, Taeryon

    2017-12-01

    Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected on discretized grids with measurement errors. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo methods. Compared to the standard Bayesian inference that suffers serious computational burden and instability in analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results to those obtainable by the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids when the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes. © 2017, The International Biometric Society.

  2. Minimum mean square error estimation and approximation of the Bayesian update

    KAUST Repository

    Litvinenko, Alexander; Matthies, Hermann G.; Zander, Elmar

    2015-01-01

    Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(w), a measurement operator Y (u(q); q), where u(q; w) uncertain solution. Aim: to identify q(w). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(w) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a functional approximation, e.g. polynomial chaos expansion (PCE). New: We derive linear, quadratic etc approximation of full Bayesian update.

  3. Minimum mean square error estimation and approximation of the Bayesian update

    KAUST Repository

    Litvinenko, Alexander

    2015-01-07

    Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(w), a measurement operator Y (u(q); q), where u(q; w) uncertain solution. Aim: to identify q(w). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(w) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a functional approximation, e.g. polynomial chaos expansion (PCE). New: We derive linear, quadratic etc approximation of full Bayesian update.

  4. Hierarchical Bayesian sparse image reconstruction with application to MRFM.

    Science.gov (United States)

    Dobigeon, Nicolas; Hero, Alfred O; Tourneret, Jean-Yves

    2009-09-01

    This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g., by maximizing the estimated posterior distribution. In our fully Bayesian approach, the posteriors of all the parameters are available. Thus, our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of the proposed hierarchical Bayesian sparse reconstruction method is illustrated on synthetic data and real data collected from a tobacco virus sample using a prototype MRFM instrument.

  5. A Bayesian Model of the Memory Colour Effect.

    Science.gov (United States)

    Witzel, Christoph; Olkkonen, Maria; Gegenfurtner, Karl R

    2018-01-01

    According to the memory colour effect, the colour of a colour-diagnostic object is not perceived independently of the object itself. Instead, it has been shown through an achromatic adjustment method that colour-diagnostic objects still appear slightly in their typical colour, even when they are colourimetrically grey. Bayesian models provide a promising approach to capture the effect of prior knowledge on colour perception and to link these effects to more general effects of cue integration. Here, we model memory colour effects using prior knowledge about typical colours as priors for the grey adjustments in a Bayesian model. This simple model does not involve any fitting of free parameters. The Bayesian model roughly captured the magnitude of the measured memory colour effect for photographs of objects. To some extent, the model predicted observed differences in memory colour effects across objects. The model could not account for the differences in memory colour effects across different levels of realism in the object images. The Bayesian model provides a particularly simple account of memory colour effects, capturing some of the multiple sources of variation of these effects.

  6. A Predictive Likelihood Approach to Bayesian Averaging

    Directory of Open Access Journals (Sweden)

    Tomáš Jeřábek

    2015-01-01

    Full Text Available Multivariate time series forecasting is applied in a wide range of economic activities related to regional competitiveness and is the basis of almost all macroeconomic analysis. In this paper we combine multivariate density forecasts of GDP growth, inflation and real interest rates from four various models, two type of Bayesian vector autoregression (BVAR models, a New Keynesian dynamic stochastic general equilibrium (DSGE model of small open economy and DSGE-VAR model. The performance of models is identified using historical dates including domestic economy and foreign economy, which is represented by countries of the Eurozone. Because forecast accuracy of observed models are different, the weighting scheme based on the predictive likelihood, the trace of past MSE matrix, model ranks are used to combine the models. The equal-weight scheme is used as a simple combination scheme. The results show that optimally combined densities are comparable to the best individual models.

  7. Efficient Bayesian network modeling of systems

    International Nuclear Information System (INIS)

    Bensi, Michelle; Kiureghian, Armen Der; Straub, Daniel

    2013-01-01

    The Bayesian network (BN) is a convenient tool for probabilistic modeling of system performance, particularly when it is of interest to update the reliability of the system or its components in light of observed information. In this paper, BN structures for modeling the performance of systems that are defined in terms of their minimum link or cut sets are investigated. Standard BN structures that define the system node as a child of its constituent components or its minimum link/cut sets lead to converging structures, which are computationally disadvantageous and could severely hamper application of the BN to real systems. A systematic approach to defining an alternative formulation is developed that creates chain-like BN structures that are orders of magnitude more efficient, particularly in terms of computational memory demand. The formulation uses an integer optimization algorithm to identify the most efficient BN structure. Example applications demonstrate the proposed methodology and quantify the gained computational advantage

  8. 3rd Bayesian Young Statisticians Meeting

    CERN Document Server

    Lanzarone, Ettore; Villalobos, Isadora; Mattei, Alessandra

    2017-01-01

    This book is a selection of peer-reviewed contributions presented at the third Bayesian Young Statisticians Meeting, BAYSM 2016, Florence, Italy, June 19-21. The meeting provided a unique opportunity for young researchers, M.S. students, Ph.D. students, and postdocs dealing with Bayesian statistics to connect with the Bayesian community at large, to exchange ideas, and to network with others working in the same field. The contributions develop and apply Bayesian methods in a variety of fields, ranging from the traditional (e.g., biostatistics and reliability) to the most innovative ones (e.g., big data and networks).

  9. Bayesian Methods and Universal Darwinism

    Science.gov (United States)

    Campbell, John

    2009-12-01

    Bayesian methods since the time of Laplace have been understood by their practitioners as closely aligned to the scientific method. Indeed a recent Champion of Bayesian methods, E. T. Jaynes, titled his textbook on the subject Probability Theory: the Logic of Science. Many philosophers of science including Karl Popper and Donald Campbell have interpreted the evolution of Science as a Darwinian process consisting of a `copy with selective retention' algorithm abstracted from Darwin's theory of Natural Selection. Arguments are presented for an isomorphism between Bayesian Methods and Darwinian processes. Universal Darwinism, as the term has been developed by Richard Dawkins, Daniel Dennett and Susan Blackmore, is the collection of scientific theories which explain the creation and evolution of their subject matter as due to the Operation of Darwinian processes. These subject matters span the fields of atomic physics, chemistry, biology and the social sciences. The principle of Maximum Entropy states that Systems will evolve to states of highest entropy subject to the constraints of scientific law. This principle may be inverted to provide illumination as to the nature of scientific law. Our best cosmological theories suggest the universe contained much less complexity during the period shortly after the Big Bang than it does at present. The scientific subject matter of atomic physics, chemistry, biology and the social sciences has been created since that time. An explanation is proposed for the existence of this subject matter as due to the evolution of constraints in the form of adaptations imposed on Maximum Entropy. It is argued these adaptations were discovered and instantiated through the Operations of a succession of Darwinian processes.

  10. Bayesian phylogeography finds its roots.

    Directory of Open Access Journals (Sweden)

    Philippe Lemey

    2009-09-01

    Full Text Available As a key factor in endemic and epidemic dynamics, the geographical distribution of viruses has been frequently interpreted in the light of their genetic histories. Unfortunately, inference of historical dispersal or migration patterns of viruses has mainly been restricted to model-free heuristic approaches that provide little insight into the temporal setting of the spatial dynamics. The introduction of probabilistic models of evolution, however, offers unique opportunities to engage in this statistical endeavor. Here we introduce a Bayesian framework for inference, visualization and hypothesis testing of phylogeographic history. By implementing character mapping in a Bayesian software that samples time-scaled phylogenies, we enable the reconstruction of timed viral dispersal patterns while accommodating phylogenetic uncertainty. Standard Markov model inference is extended with a stochastic search variable selection procedure that identifies the parsimonious descriptions of the diffusion process. In addition, we propose priors that can incorporate geographical sampling distributions or characterize alternative hypotheses about the spatial dynamics. To visualize the spatial and temporal information, we summarize inferences using virtual globe software. We describe how Bayesian phylogeography compares with previous parsimony analysis in the investigation of the influenza A H5N1 origin and H5N1 epidemiological linkage among sampling localities. Analysis of rabies in West African dog populations reveals how virus diffusion may enable endemic maintenance through continuous epidemic cycles. From these analyses, we conclude that our phylogeographic framework will make an important asset in molecular epidemiology that can be easily generalized to infer biogeogeography from genetic data for many organisms.

  11. Bayesian flood forecasting methods: A review

    Science.gov (United States)

    Han, Shasha; Coulibaly, Paulin

    2017-08-01

    Over the past few decades, floods have been seen as one of the most common and largely distributed natural disasters in the world. If floods could be accurately forecasted in advance, then their negative impacts could be greatly minimized. It is widely recognized that quantification and reduction of uncertainty associated with the hydrologic forecast is of great importance for flood estimation and rational decision making. Bayesian forecasting system (BFS) offers an ideal theoretic framework for uncertainty quantification that can be developed for probabilistic flood forecasting via any deterministic hydrologic model. It provides suitable theoretical structure, empirically validated models and reasonable analytic-numerical computation method, and can be developed into various Bayesian forecasting approaches. This paper presents a comprehensive review on Bayesian forecasting approaches applied in flood forecasting from 1999 till now. The review starts with an overview of fundamentals of BFS and recent advances in BFS, followed with BFS application in river stage forecasting and real-time flood forecasting, then move to a critical analysis by evaluating advantages and limitations of Bayesian forecasting methods and other predictive uncertainty assessment approaches in flood forecasting, and finally discusses the future research direction in Bayesian flood forecasting. Results show that the Bayesian flood forecasting approach is an effective and advanced way for flood estimation, it considers all sources of uncertainties and produces a predictive distribution of the river stage, river discharge or runoff, thus gives more accurate and reliable flood forecasts. Some emerging Bayesian forecasting methods (e.g. ensemble Bayesian forecasting system, Bayesian multi-model combination) were shown to overcome limitations of single model or fixed model weight and effectively reduce predictive uncertainty. In recent years, various Bayesian flood forecasting approaches have been

  12. Bayesian accounts of covert selective attention: A tutorial review.

    Science.gov (United States)

    Vincent, Benjamin T

    2015-05-01

    Decision making and optimal observer models offer an important theoretical approach to the study of covert selective attention. While their probabilistic formulation allows quantitative comparison to human performance, the models can be complex and their insights are not always immediately apparent. Part 1 establishes the theoretical appeal of the Bayesian approach, and introduces the way in which probabilistic approaches can be applied to covert search paradigms. Part 2 presents novel formulations of Bayesian models of 4 important covert attention paradigms, illustrating optimal observer predictions over a range of experimental manipulations. Graphical model notation is used to present models in an accessible way and Supplementary Code is provided to help bridge the gap between model theory and practical implementation. Part 3 reviews a large body of empirical and modelling evidence showing that many experimental phenomena in the domain of covert selective attention are a set of by-products. These effects emerge as the result of observers conducting Bayesian inference with noisy sensory observations, prior expectations, and knowledge of the generative structure of the stimulus environment.

  13. Bayesian inference for Hawkes processes

    DEFF Research Database (Denmark)

    Rasmussen, Jakob Gulddahl

    The Hawkes process is a practically and theoretically important class of point processes, but parameter-estimation for such a process can pose various problems. In this paper we explore and compare two approaches to Bayesian inference. The first approach is based on the so-called conditional...... intensity function, while the second approach is based on an underlying clustering and branching structure in the Hawkes process. For practical use, MCMC (Markov chain Monte Carlo) methods are employed. The two approaches are compared numerically using three examples of the Hawkes process....

  14. Bayesian inference for Hawkes processes

    DEFF Research Database (Denmark)

    Rasmussen, Jakob Gulddahl

    2013-01-01

    The Hawkes process is a practically and theoretically important class of point processes, but parameter-estimation for such a process can pose various problems. In this paper we explore and compare two approaches to Bayesian inference. The first approach is based on the so-called conditional...... intensity function, while the second approach is based on an underlying clustering and branching structure in the Hawkes process. For practical use, MCMC (Markov chain Monte Carlo) methods are employed. The two approaches are compared numerically using three examples of the Hawkes process....

  15. Numeracy, frequency, and Bayesian reasoning

    Directory of Open Access Journals (Sweden)

    Gretchen B. Chapman

    2009-02-01

    Full Text Available Previous research has demonstrated that Bayesian reasoning performance is improved if uncertainty information is presented as natural frequencies rather than single-event probabilities. A questionnaire study of 342 college students replicated this effect but also found that the performance-boosting benefits of the natural frequency presentation occurred primarily for participants who scored high in numeracy. This finding suggests that even comprehension and manipulation of natural frequencies requires a certain threshold of numeracy abilities, and that the beneficial effects of natural frequency presentation may not be as general as previously believed.

  16. Bayesian calibration of simultaneity in audiovisual temporal order judgments.

    Directory of Open Access Journals (Sweden)

    Shinya Yamamoto

    Full Text Available After repeated exposures to two successive audiovisual stimuli presented in one frequent order, participants eventually perceive a pair separated by some lag time in the same order as occurring simultaneously (lag adaptation. In contrast, we previously found that perceptual changes occurred in the opposite direction in response to tactile stimuli, conforming to bayesian integration theory (bayesian calibration. We further showed, in theory, that the effect of bayesian calibration cannot be observed when the lag adaptation was fully operational. This led to the hypothesis that bayesian calibration affects judgments regarding the order of audiovisual stimuli, but that this effect is concealed behind the lag adaptation mechanism. In the present study, we showed that lag adaptation is pitch-insensitive using two sounds at 1046 and 1480 Hz. This enabled us to cancel lag adaptation by associating one pitch with sound-first stimuli and the other with light-first stimuli. When we presented each type of stimulus (high- or low-tone in a different block, the point of simultaneity shifted to "sound-first" for the pitch associated with sound-first stimuli, and to "light-first" for the pitch associated with light-first stimuli. These results are consistent with lag adaptation. In contrast, when we delivered each type of stimulus in a randomized order, the point of simultaneity shifted to "light-first" for the pitch associated with sound-first stimuli, and to "sound-first" for the pitch associated with light-first stimuli. The results clearly show that bayesian calibration is pitch-specific and is at work behind pitch-insensitive lag adaptation during temporal order judgment of audiovisual stimuli.

  17. Bayesian image restoration for medical images using radon transform

    International Nuclear Information System (INIS)

    Shouno, Hayaru; Okada, Masato

    2010-01-01

    We propose an image reconstruction algorithm using Bayesian inference for Radon transformed observation data, which often appears in the field of medical image reconstruction known as computed tomography (CT). In order to apply our Bayesian reconstruction method, we introduced several hyper-parameters that control the ratio between prior information and the fidelity of the observation process. Since the quality of the reconstructed image is influenced by the estimation accuracy of these hyper-parameters, we propose an inference method for them based on the marginal likelihood maximization principle as well as the image reconstruction method. We are able to demonstrate a reconstruction result superior to that obtained using the conventional filtered back projection method. (author)

  18. A BAYESIAN ESTIMATE OF THE CMB–LARGE-SCALE STRUCTURE CROSS-CORRELATION

    Energy Technology Data Exchange (ETDEWEB)

    Moura-Santos, E. [Instituto de Física, Universidade de São Paulo, Rua do Matão trav. R 187, 05508-090, São Paulo—SP (Brazil); Carvalho, F. C. [Departamento de Física, Universidade do Estado do Rio Grande do Norte, 59610-210, Mossoró-RN (Brazil); Penna-Lima, M. [APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cité, 10, rue Alice Domon et Léonie Duquet, F-75205 Paris Cedex 13 (France); Novaes, C. P.; Wuensche, C. A., E-mail: emoura@if.usp.br, E-mail: fabiocabral@uern.br, E-mail: pennal@apc.in2p3.fr, E-mail: cawuenschel@das.inpe.br, E-mail: camilanovaes@on.br [Observatório Nacional, Rua General José Cristino 77, São Cristóvão, 20921-400, Rio de Janeiro, RJ (Brazil)

    2016-08-01

    Evidences for late-time acceleration of the universe are provided by multiple probes, such as Type Ia supernovae, the cosmic microwave background (CMB), and large-scale structure (LSS). In this work, we focus on the integrated Sachs–Wolfe (ISW) effect, i.e., secondary CMB fluctuations generated by evolving gravitational potentials due to the transition between, e.g., the matter and dark energy (DE) dominated phases. Therefore, assuming a flat universe, DE properties can be inferred from ISW detections. We present a Bayesian approach to compute the CMB–LSS cross-correlation signal. The method is based on the estimate of the likelihood for measuring a combined set consisting of a CMB temperature and galaxy contrast maps, provided that we have some information on the statistical properties of the fluctuations affecting these maps. The likelihood is estimated by a sampling algorithm, therefore avoiding the computationally demanding techniques of direct evaluation in either pixel or harmonic space. As local tracers of the matter distribution at large scales, we used the Two Micron All Sky Survey galaxy catalog and, for the CMB temperature fluctuations, the ninth-year data release of the Wilkinson Microwave Anisotropy Probe ( WMAP 9). The results show a dominance of cosmic variance over the weak recovered signal, due mainly to the shallowness of the catalog used, with systematics associated with the sampling algorithm playing a secondary role as sources of uncertainty. When combined with other complementary probes, the method presented in this paper is expected to be a useful tool to late-time acceleration studies in cosmology.

  19. Bayesian analysis of magnetic island dynamics

    International Nuclear Information System (INIS)

    Preuss, R.; Maraschek, M.; Zohm, H.; Dose, V.

    2003-01-01

    We examine a first order differential equation with respect to time used to describe magnetic islands in magnetically confined plasmas. The free parameters of this equation are obtained by employing Bayesian probability theory. Additionally, a typical Bayesian change point is solved in the process of obtaining the data

  20. Learning dynamic Bayesian networks with mixed variables

    DEFF Research Database (Denmark)

    Bøttcher, Susanne Gammelgaard

    This paper considers dynamic Bayesian networks for discrete and continuous variables. We only treat the case, where the distribution of the variables is conditional Gaussian. We show how to learn the parameters and structure of a dynamic Bayesian network and also how the Markov order can be learned...

  1. Using Bayesian Networks to Improve Knowledge Assessment

    Science.gov (United States)

    Millan, Eva; Descalco, Luis; Castillo, Gladys; Oliveira, Paula; Diogo, Sandra

    2013-01-01

    In this paper, we describe the integration and evaluation of an existing generic Bayesian student model (GBSM) into an existing computerized testing system within the Mathematics Education Project (PmatE--Projecto Matematica Ensino) of the University of Aveiro. This generic Bayesian student model had been previously evaluated with simulated…

  2. Using Bayesian belief networks in adaptive management.

    Science.gov (United States)

    J.B. Nyberg; B.G. Marcot; R. Sulyma

    2006-01-01

    Bayesian belief and decision networks are relatively new modeling methods that are especially well suited to adaptive-management applications, but they appear not to have been widely used in adaptive management to date. Bayesian belief networks (BBNs) can serve many purposes for practioners of adaptive management, from illustrating system relations conceptually to...

  3. Bayesian Decision Theoretical Framework for Clustering

    Science.gov (United States)

    Chen, Mo

    2011-01-01

    In this thesis, we establish a novel probabilistic framework for the data clustering problem from the perspective of Bayesian decision theory. The Bayesian decision theory view justifies the important questions: what is a cluster and what a clustering algorithm should optimize. We prove that the spectral clustering (to be specific, the…

  4. Robust Bayesian detection of unmodelled bursts

    International Nuclear Information System (INIS)

    Searle, Antony C; Sutton, Patrick J; Tinto, Massimo; Woan, Graham

    2008-01-01

    We develop a Bayesian treatment of the problem of detecting unmodelled gravitational wave bursts using the new global network of interferometric detectors. We also compare this Bayesian treatment with existing coherent methods, and demonstrate that the existing methods make implicit assumptions on the distribution of signals that make them sub-optimal for realistic signal populations

  5. Bayesian models: A statistical primer for ecologists

    Science.gov (United States)

    Hobbs, N. Thompson; Hooten, Mevin B.

    2015-01-01

    Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods—in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach.Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probability and develops a step-by-step sequence of connected ideas, including basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and inference from single and multiple models. This unique book places less emphasis on computer coding, favoring instead a concise presentation of the mathematical statistics needed to understand how and why Bayesian analysis works. It also explains how to write out properly formulated hierarchical Bayesian models and use them in computing, research papers, and proposals.This primer enables ecologists to understand the statistical principles behind Bayesian modeling and apply them to research, teaching, policy, and management.Presents the mathematical and statistical foundations of Bayesian modeling in language accessible to non-statisticiansCovers basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and moreDeemphasizes computer coding in favor of basic principlesExplains how to write out properly factored statistical expressions representing Bayesian models

  6. Particle identification in ALICE: a Bayesian approach

    NARCIS (Netherlands)

    Adam, J.; Adamova, D.; Aggarwal, M. M.; Rinella, G. Aglieri; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahn, S. U.; Aiola, S.; Akindinov, A.; Alam, S. N.; Albuquerque, D. S. D.; Aleksandrov, D.; Alessandro, B.; Alexandre, D.; Alfaro Molina, R.; Alici, A.; Alkin, A.; Almaraz, J. R. M.; Alme, J.; Alt, T.; Altinpinar, S.; Altsybeev, I.; Alves Garcia Prado, C.; Andrei, C.; Andronic, A.; Anguelov, V.; Anticic, T.; Antinori, F.; Antonioli, P.; Aphecetche, L.; Appelshaeuser, H.; Arcelli, S.; Arnaldi, R.; Arnold, O. W.; Arsene, I. C.; Arslandok, M.; Audurier, B.; Augustinus, A.; Averbeck, R.; Azmi, M. D.; Badala, A.; Baek, Y. W.; Bagnasco, S.; Bailhache, R.; Bala, R.; Balasubramanian, S.; Baldisseri, A.; Baral, R. C.; Barbano, A. M.; Barbera, R.; Barile, F.; Barnafoeldi, G. G.; Barnby, L. S.; Barret, V.; Bartalini, P.; Barth, K.; Bartke, J.; Bartsch, E.; Basile, M.; Bastid, N.; Bathen, B.; Batigne, G.; Camejo, A. Batista; Batyunya, B.; Batzing, P. C.; Bearden, I. G.; Beck, H.; Bedda, C.; Behera, N. K.; Belikov, I.; Bellini, F.; Bello Martinez, H.; Bellwied, R.; Belmont, R.; Belmont-Moreno, E.; Belyaev, V.; Benacek, P.; Bencedi, G.; Beole, S.; Berceanu, I.; Bercuci, A.; Berdnikov, Y.; Berenyi, D.; Bertens, R. A.; Berzano, D.; Betev, L.; Bhasin, A.; Bhat, I. R.; Bhati, A. K.; Bhattacharjee, B.; Bhom, J.; Bianchi, L.; Bianchi, N.; Bianchin, C.; Bielcik, J.; Bielcikova, J.; Bilandzic, A.; Biro, G.; Biswas, R.; Biswas, S.; Bjelogrlic, S.; Blair, J. T.; Blau, D.; Blume, C.; Bock, F.; Bogdanov, A.; Boggild, H.; Boldizsar, L.; Bombara, M.; Book, J.; Borel, H.; Borissov, A.; Borri, M.; Bossu, F.; Botta, E.; Bourjau, C.; Braun-Munzinger, P.; Bregant, M.; Breitner, T.; Broker, T. A.; Browning, T. A.; Broz, M.; Brucken, E. J.; Bruna, E.; Bruno, G. E.; Budnikov, D.; Buesching, H.; Bufalino, S.; Buncic, P.; Busch, O.; Buthelezi, Z.; Butt, J. B.; Buxton, J. T.; Cabala, J.; Caffarri, D.; Cai, X.; Caines, H.; Diaz, L. Calero; Caliva, A.; Calvo Villar, E.; Camerini, P.; Carena, F.; Carena, W.; Carnesecchi, F.; Castellanos, J. Castillo; Castro, A. J.; Casula, E. A. R.; Sanchez, C. Ceballos; Cepila, J.; Cerello, P.; Cerkala, J.; Chang, B.; Chapeland, S.; Chartier, M.; Charvet, J. L.; Chattopadhyay, S.; Chattopadhyay, S.; Chauvin, A.; Chelnokov, V.; Cherney, M.; Cheshkov, C.; Cheynis, B.; Barroso, V. Chibante; Chinellato, D. D.; Cho, S.; Chochula, P.; Choi, K.; Chojnacki, M.; Choudhury, S.; Christakoglou, P.; Christensen, C. H.; Christiansen, P.; Chujo, T.; Cicalo, C.; Cifarelli, L.; Cindolo, F.; Cleymans, J.; Colamaria, F.; Colella, D.; Collu, A.; Colocci, M.; Balbastre, G. Conesa; del Valle, Z. Conesa; Connors, M. E.; Contreras, J. G.; Cormier, T. M.; Morales, Y. Corrales; Cortes Maldonado, I.; Cortese, P.; Cosentino, M. R.; Costa, F.; Crochet, P.; Cruz Albino, R.; Cuautle, E.; Cunqueiro, L.; Dahms, T.; Dainese, A.; Danisch, M. C.; Danu, A.; Das, I.; Das, S.; Dash, A.; Dash, S.; De, S.; De Caro, A.; de Cataldo, G.; de Conti, C.; de Cuveland, J.; De Falco, A.; De Gruttola, D.; De Marco, N.; De Pasquale, S.; Deisting, A.; Deloff, A.; Denes, E.; Deplano, C.; Dhankher, P.; Di Bari, D.; Di Mauro, A.; Di Nezza, P.; Corchero, M. A. Diaz; Dietel, T.; Dillenseger, P.; Divia, R.; Djuvsland, O.; Dobrin, A.; Gimenez, D. Domenicis; Doenigus, B.; Dordic, O.; Drozhzhova, T.; Dubey, A. K.; Dubla, A.; Ducroux, L.; Dupieux, P.; Ehlers, R. J.; Elia, D.; Endress, E.; Engel, H.; Epple, E.; Erazmus, B.; Erdemir, I.; Erhardt, F.; Espagnon, B.; Estienne, M.; Esumi, S.; Eum, J.; Evans, D.; Evdokimov, S.; Eyyubova, G.; Fabbietti, L.; Fabris, D.; Faivre, J.; Fantoni, A.; Fasel, M.; Feldkamp, L.; Feliciello, A.; Feofilov, G.; Ferencei, J.; Fernandez Tellez, A.; Ferreiro, E. G.; Ferretti, A.; Festanti, A.; Feuillard, V. J. G.; Figiel, J.; Figueredo, M. A. S.; Filchagin, S.; Finogeev, D.; Fionda, F. M.; Fiore, E. M.; Fleck, M. G.; Floris, M.; Foertsch, S.; Foka, P.; Fokin, S.; Fragiacomo, E.; Francescon, A.; Frankenfeld, U.; Fronze, G. G.; Fuchs, U.; Furget, C.; Furs, A.; Girard, M. Fusco; Gaardhoje, J. J.; Gagliardi, M.; Gago, A. M.; Gallio, M.; Gangadharan, D. R.; Ganoti, P.; Gao, C.; Garabatos, C.; Garcia-Solis, E.; Gargiulo, C.; Gasik, P.; Gauger, E. F.; Germain, M.; Gheata, A.; Gheata, M.; Gianotti, P.; Giubellino, P.; Giubilato, P.; Gladysz-Dziadus, E.; Glaessel, P.; Gomez Coral, D. M.; Ramirez, A. Gomez; Gonzalez, A. S.; Gonzalez, V.; Gonzalez-Zamora, P.; Gorbunov, S.; Goerlich, L.; Gotovac, S.; Grabski, V.; Grachov, O. A.; Graczykowski, L. K.; Graham, K. L.; Grelli, A.; Grigoras, A.; Grigoras, C.; Grigoriev, V.; Grigoryan, A.; Grigoryan, S.; Grinyov, B.; Grion, N.; Gronefeld, J. M.; Grosse-Oetringhaus, J. F.; Grosso, R.; Guber, F.; Guernane, R.; Guerzoni, B.; Gulbrandsen, K.; Gunji, T.; Gupta, A.; Haake, R.; Haaland, O.; Hadjidakis, C.; Haiduc, M.; Hamagaki, H.; Hamar, G.; Hamon, J. C.; Harris, J. W.; Harton, A.; Hatzifotiadou, D.; Hayashi, S.; Heckel, S. T.; Hellbaer, E.; Helstrup, H.; Herghelegiu, A.; Herrera Corral, G.; Hess, B. A.; Hetland, K. F.; Hillemanns, H.; Hippolyte, B.; Horak, D.; Hosokawa, R.; Hristov, P.; Humanic, T. J.; Hussain, N.; Hussain, T.; Hutter, D.; Hwang, D. S.; Ilkaev, R.; Inaba, M.; Incani, E.; Ippolitov, M.; Irfan, M.; Ivanov, M.; Ivanov, V.; Izucheev, V.; Jacazio, N.; Jadhav, M. B.; Jadlovska, S.; Jadlovsky, J.; Jahnke, C.; Jakubowska, M. J.; Jang, H. J.; Janik, M. A.; Jayarathna, P. H. S. Y.; Jena, C.; Jena, S.; Bustamante, R. T. Jimenez; Jones, P. G.; Jusko, A.; Kalinak, P.; Kalweit, A.; Kamin, J.; Kaplin, V.; Kar, S.; Uysal, A. Karasu; Karavichev, O.; Karavicheva, T.; Karayan, L.; Karpechev, E.; Kebschull, U.; Keidel, R.; Keijdener, D. L. D.; Keil, M.; Khan, M. Mohisin; Khan, P.; Khan, S. A.; Khanzadeev, A.; Kharlov, Y.; Kileng, B.; Kim, D. W.; Kim, D. J.; Kim, D.; Kim, J. S.; Kim, M.; Kim, T.; Kirsch, S.; Kisel, I.; Kiselev, S.; Kisiel, A.; Kiss, G.; Klay, J. L.; Klein, C.; Klein-Boesing, C.; Klewin, S.; Kluge, A.; Knichel, M. L.; Knospe, A. G.; Kobdaj, C.; Kofarago, M.; Kollegger, T.; Kolojvari, A.; Kondratiev, V.; Kondratyeva, N.; Kondratyuk, E.; Konevskikh, A.; Kopcik, M.; Kostarakis, P.; Kour, M.; Kouzinopoulos, C.; Kovalenko, O.; Kovalenko, V.; Kowalski, M.; Meethaleveedu, G. Koyithatta; Kralik, I.; Kravcakova, A.; Krivda, M.; Krizek, F.; Kryshen, E.; Krzewicki, M.; Kubera, A. M.; Kucera, V.; Kuijer, P. G.; Kumar, J.; Kumar, L.; Kumar, S.; Kurashvili, P.; Kurepin, A.; Kurepin, A. B.; Kuryakin, A.; Kweon, M. J.; Kwon, Y.; La Pointe, S. L.; La Rocca, P.; Ladron de Guevara, P.; Lagana Fernandes, C.; Lakomov, I.; Langoy, R.; Lara, C.; Lardeux, A.; Lattuca, A.; Laudi, E.; Lea, R.; Leardini, L.; Lee, G. R.; Lee, S.; Lehas, F.; Lemmon, R. C.; Lenti, V.; Leogrande, E.; Monzon, I. Leon; Leon Vargas, H.; Leoncino, M.; Levai, P.; Lien, J.; Lietava, R.; Lindal, S.; Lindenstruth, V.; Lippmann, C.; Lisa, M. A.; Ljunggren, H. M.; Lodato, D. F.; Loenne, P. I.; Loginov, V.; Loizides, C.; Lopez, X.; Torres, E. Lopez; Lowe, A.; Luettig, P.; Lunardon, M.; Luparello, G.; Lutz, T. H.; Maevskaya, A.; Mager, M.; Mahajan, S.; Mahmood, S. M.; Maire, A.; Majka, R. D.; Malaev, M.; Maldonado Cervantes, I.; Malinina, L.; Mal'Kevich, D.; Malzacher, P.; Mamonov, A.; Manko, V.; Manso, F.; Manzari, V.; Marchisone, M.; Mares, J.; Margagliotti, G. V.; Margotti, A.; Margutti, J.; Marin, A.; Markert, C.; Marquard, M.; Martin, N. A.; Blanco, J. Martin; Martinengo, P.; Martinez, M. I.; Garcia, G. Martinez; Pedreira, M. Martinez; Mas, A.; Masciocchi, S.; Masera, M.; Masoni, A.; Mastroserio, A.; Matyja, A.; Mayer, C.; Mazer, J.; Mazzoni, M. A.; Mcdonald, D.; Meddi, F.; Melikyan, Y.; Menchaca-Rocha, A.; Meninno, E.; Perez, J. Mercado; Meres, M.; Miake, Y.; Mieskolainen, M. M.; Mikhaylov, K.; Milano, L.; Milosevic, J.; Mischke, A.; Mishra, A. N.; Miskowiec, D.; Mitra, J.; Mitu, C. M.; Mohammadi, N.; Mohanty, B.; Molnar, L.; Montano Zetina, L.; Montes, E.; De Godoy, D. A. Moreira; Moreno, L. A. P.; Moretto, S.; Morreale, A.; Morsch, A.; Muccifora, V.; Mudnic, E.; Muehlheim, D.; Muhuri, S.; Mukherjee, M.; Mulligan, J. D.; Munhoz, M. G.; Munzer, R. H.; Murakami, H.; Murray, S.; Musa, L.; Musinsky, J.; Naik, B.; Nair, R.; Nandi, B. K.; Nania, R.; Nappi, E.; Naru, M. U.; Natal da Luz, H.; Nattrass, C.; Navarro, S. R.; Nayak, K.; Nayak, R.; Nayak, T. K.; Nazarenko, S.; Nedosekin, A.; Nellen, L.; Ng, F.; Nicassio, M.; Niculescu, M.; Niedziela, J.; Nielsen, B. S.; Nikolaev, S.; Nikulin, S.; Nikulin, V.; Noferini, F.; Nomokonov, P.; Nooren, G.; Noris, J. C. C.; Norman, J.; Nyanin, A.; Nystrand, J.; Oeschler, H.; Oh, S.; Oh, S. K.; Ohlson, A.; Okatan, A.; Okubo, T.; Olah, L.; Oleniacz, J.; Oliveira Da Silva, A. C.; Oliver, M. H.; Onderwaater, J.; Oppedisano, C.; Orava, R.; Oravec, M.; Ortiz Velasquez, A.; Oskarsson, A.; Otwinowski, J.; Oyama, K.; Ozdemir, M.; Pachmayer, Y.; Pagano, D.; Pagano, P.; Paic, G.; Pal, S. K.; Pan, J.; Papikyan, V.; Pappalardo, G. S.; Pareek, P.; Park, W. J.; Parmar, S.; Passfeld, A.; Paticchio, V.; Patra, R. N.; Paul, B.; Pei, H.; Peitzmann, T.; Da Costa, H. Pereira; Peresunko, D.; Lara, C. E. Perez; Lezama, E. Perez; Peskov, V.; Pestov, Y.; Petracek, V.; Petrov, V.; Petrovici, M.; Petta, C.; Piano, S.; Pikna, M.; Pillot, P.; Pimentel, L. O. D. L.; Pinazza, O.; Pinsky, L.; Piyarathna, D. B.; Ploskon, M.; Planinic, M.; Pluta, J.; Pochybova, S.; Podesta-Lerma, P. L. M.; Poghosyan, M. G.; Polichtchouk, B.; Poljak, N.; Poonsawat, W.; Pop, A.; Porteboeuf-Houssais, S.; Porter, J.; Pospisil, J.; Prasad, S. K.; Preghenella, R.; Prino, F.; Pruneau, C. A.; Pshenichnov, I.; Puccio, M.; Puddu, G.; Pujahari, P.; Punin, V.; Putschke, J.; Qvigstad, H.; Rachevski, A.; Raha, S.; Rajput, S.; Rak, J.; Rakotozafindrabe, A.; Ramello, L.; Rami, F.; Raniwala, R.; Raniwala, S.; Raesaenen, S. S.; Rascanu, B. T.; Rathee, D.; Read, K. F.; Redlich, K.; Reed, R. J.; Reichelt, P.; Reidt, F.; Ren, X.; Renfordt, R.; Reolon, A. R.; Reshetin, A.; Reygers, K.; Riabov, V.; Ricci, R. A.; Richert, T.; Richter, M.; Riedler, P.; Riegler, W.; Riggi, F.; Ristea, C.; Rocco, E.; Rodriguez Cahuantzi, M.; Manso, A. Rodriguez; Roed, K.; Rogochaya, E.; Rohr, D.; Roehrich, D.; Ronchetti, F.; Ronflette, L.; Rosnet, P.; Rossi, A.; Roukoutakis, F.; Roy, A.; Roy, C.; Roy, P.; Montero, A. J. Rubio; Rui, R.; Russo, R.; Ryabinkin, E.; Ryabov, Y.; Rybicki, A.; Saarinen, S.; Sadhu, S.; Sadovsky, S.; Safarik, K.; Sahlmuller, B.; Sahoo, P.; Sahoo, R.; Sahoo, S.; Sahu, P. K.; Saini, J.; Sakai, S.; Saleh, M. A.; Salzwedel, J.; Sambyal, S.; Samsonov, V.; Sandor, L.; Sandoval, A.; Sano, M.; Sarkar, D.; Sarkar, N.; Sarma, P.; Scapparone, E.; Scarlassara, F.; Schiaua, C.; Schicker, R.; Schmidt, C.; Schmidt, H. R.; Schuchmann, S.; Schukraft, J.; Schulc, M.; Schutz, Y.; Schwarz, K.; Schweda, K.; Scioli, G.; Scomparin, E.; Scott, R.; Sefcik, M.; Seger, J. E.; Sekiguchi, Y.; Sekihata, D.; Selyuzhenkov, I.; Senosi, K.; Senyukov, S.; Serradilla, E.; Sevcenco, A.; Shabanov, A.; Shabetai, A.; Shadura, O.; Shahoyan, R.; Shahzad, M. I.; Shangaraev, A.; Sharma, M.; Sharma, M.; Sharma, N.; Sheikh, A. I.; Shigaki, K.; Shou, Q.; Shtejer, K.; Sibiriak, Y.; Siddhanta, S.; Sielewicz, K. M.; Siemiarczuk, T.; Silvermyr, D.; Silvestre, C.; Simatovic, G.; Simonetti, G.; Singaraju, R.; Singh, R.; Singha, S.; Singhal, V.; Sinha, B. C.; Sinha, T.; Sitar, B.; Sitta, M.; Skaali, T. B.; Slupecki, M.; Smirnov, N.; Snellings, R. J. M.; Snellman, T. W.; Song, J.; Song, M.; Song, Z.; Soramel, F.; Sorensen, S.; de Souza, R. D.; Sozzi, F.; Spacek, M.; Spiriti, E.; Sputowska, I.; Spyropoulou-Stassinaki, M.; Stachel, J.; Stan, I.; Stankus, P.; Stenlund, E.; Steyn, G.; Stiller, J. H.; Stocco, D.; Strmen, P.; Suaide, A. A. P.; Sugitate, T.; Suire, C.; Suleymanov, M.; Suljic, M.; Sultanov, R.; Sumbera, M.; Sumowidagdo, S.; Szabo, A.; Szanto de Toledo, A.; Szarka, I.; Szczepankiewicz, A.; Szymanski, M.; Tabassam, U.; Takahashi, J.; Tambave, G. J.; Tanaka, N.; Tarhini, M.; Tariq, M.; Tarzila, M. G.; Tauro, A.; Tejeda Munoz, G.; Telesca, A.; Terasaki, K.; Terrevoli, C.; Teyssier, B.; Thaeder, J.; Thakur, D.; Thomas, D.; Tieulent, R.; Timmins, A. R.; Toia, A.; Trogolo, S.; Trombetta, G.; Trubnikov, V.; Trzaska, W. H.; Tsuji, T.; Tumkin, A.; Turrisi, R.; Tveter, T. S.; Ullaland, K.; Uras, A.; Usai, G. L.; Utrobicic, A.; Vala, M.; Palomo, L. Valencia; Vallero, S.; Van Der Maarel, J.; Van Hoorne, J. W.; van Leeuwen, M.; Vanat, T.; Vyvre, P. Vande; Varga, D.; Vargas, A.; Vargyas, M.; Varma, R.; Vasileiou, M.; Vasiliev, A.; Vauthier, A.; Vechernin, V.; Veen, A. M.; Veldhoen, M.; Velure, A.; Vercellin, E.; Vergara Limon, S.; Vernet, R.; Verweij, M.; Vickovic, L.; Viesti, G.; Viinikainen, J.; Vilakazi, Z.; Baillie, O. Villalobos; Villatoro Tello, A.; Vinogradov, A.; Vinogradov, L.; Vinogradov, Y.; Virgili, T.; Vislavicius, V.; Viyogi, Y. P.; Vodopyanov, A.; Voelkl, M. A.; Voloshin, K.; Voloshin, S. A.; Volpe, G.; von Haller, B.; Vorobyev, I.; Vranic, D.; Vrlakova, J.; Vulpescu, B.; Wagner, B.; Wagner, J.; Wang, H.; Watanabe, D.; Watanabe, Y.; Weiser, D. F.; Westerhoff, U.; Whitehead, A. M.; Wiechula, J.; Wikne, J.; Wilk, G.; Wilkinson, J.; Williams, M. C. S.; Windelband, B.; Winn, M.; Yang, H.; Yano, S.; Yasin, Z.; Yokoyama, H.; Yoo, I. -K.; Yoon, J. H.; Yurchenko, V.; Yushmanov, I.; Zaborowska, A.; Zaccolo, V.; Zaman, A.; Zampolli, C.; Zanoli, H. J. C.; Zaporozhets, S.; Zardoshti, N.; Zarochentsev, A.; Zavada, P.; Zaviyalov, N.; Zbroszczyk, H.; Zgura, I. S.; Zhalov, M.; Zhang, C.; Zhao, C.; Zhigareva, N.; Zhou, Y.; Zhou, Z.; Zhu, H.; Zichichi, A.; Zimmermann, A.; Zimmermann, M. B.; Zinovjev, G.; Zyzak, M.

    2016-01-01

    We present a Bayesian approach to particle identification (PID) within the ALICE experiment. The aim is to more effectively combine the particle identification capabilities of its various detectors. After a brief explanation of the adopted methodology and formalism, the performance of the Bayesian

  7. Advances in Bayesian Modeling in Educational Research

    Science.gov (United States)

    Levy, Roy

    2016-01-01

    In this article, I provide a conceptually oriented overview of Bayesian approaches to statistical inference and contrast them with frequentist approaches that currently dominate conventional practice in educational research. The features and advantages of Bayesian approaches are illustrated with examples spanning several statistical modeling…

  8. Compiling Relational Bayesian Networks for Exact Inference

    DEFF Research Database (Denmark)

    Jaeger, Manfred; Darwiche, Adnan; Chavira, Mark

    2006-01-01

    We describe in this paper a system for exact inference with relational Bayesian networks as defined in the publicly available PRIMULA tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference...

  9. Compiling Relational Bayesian Networks for Exact Inference

    DEFF Research Database (Denmark)

    Jaeger, Manfred; Chavira, Mark; Darwiche, Adnan

    2004-01-01

    We describe a system for exact inference with relational Bayesian networks as defined in the publicly available \\primula\\ tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by evaluating...

  10. Optimal soil venting design using Bayesian Decision analysis

    OpenAIRE

    Kaluarachchi, J. J.; Wijedasa, A. H.

    1994-01-01

    Remediation of hydrocarbon-contaminated sites can be costly and the design process becomes complex in the presence of parameter uncertainty. Classical decision theory related to remediation design requires the parameter uncertainties to be stipulated in terms of statistical estimates based on site observations. In the absence of detailed data on parameter uncertainty, classical decision theory provides little contribution in designing a risk-based optimal design strategy. Bayesian decision th...

  11. Robust Learning of Fixed-Structure Bayesian Networks

    OpenAIRE

    Diakonikolas, Ilias; Kane, Daniel; Stewart, Alistair

    2016-01-01

    We investigate the problem of learning Bayesian networks in an agnostic model where an $\\epsilon$-fraction of the samples are adversarially corrupted. Our agnostic learning model is similar to -- in fact, stronger than -- Huber's contamination model in robust statistics. In this work, we study the fully observable Bernoulli case where the structure of the network is given. Even in this basic setting, previous learning algorithms either run in exponential time or lose dimension-dependent facto...

  12. BELM: Bayesian extreme learning machine.

    Science.gov (United States)

    Soria-Olivas, Emilio; Gómez-Sanchis, Juan; Martín, José D; Vila-Francés, Joan; Martínez, Marcelino; Magdalena, José R; Serrano, Antonio J

    2011-03-01

    The theory of extreme learning machine (ELM) has become very popular on the last few years. ELM is a new approach for learning the parameters of the hidden layers of a multilayer neural network (as the multilayer perceptron or the radial basis function neural network). Its main advantage is the lower computational cost, which is especially relevant when dealing with many patterns defined in a high-dimensional space. This brief proposes a bayesian approach to ELM, which presents some advantages over other approaches: it allows the introduction of a priori knowledge; obtains the confidence intervals (CIs) without the need of applying methods that are computationally intensive, e.g., bootstrap; and presents high generalization capabilities. Bayesian ELM is benchmarked against classical ELM in several artificial and real datasets that are widely used for the evaluation of machine learning algorithms. Achieved results show that the proposed approach produces a competitive accuracy with some additional advantages, namely, automatic production of CIs, reduction of probability of model overfitting, and use of a priori knowledge.

  13. BAYESIAN BICLUSTERING FOR PATIENT STRATIFICATION.

    Science.gov (United States)

    Khakabimamaghani, Sahand; Ester, Martin

    2016-01-01

    The move from Empirical Medicine towards Personalized Medicine has attracted attention to Stratified Medicine (SM). Some methods are provided in the literature for patient stratification, which is the central task of SM, however, there are still significant open issues. First, it is still unclear if integrating different datatypes will help in detecting disease subtypes more accurately, and, if not, which datatype(s) are most useful for this task. Second, it is not clear how we can compare different methods of patient stratification. Third, as most of the proposed stratification methods are deterministic, there is a need for investigating the potential benefits of applying probabilistic methods. To address these issues, we introduce a novel integrative Bayesian biclustering method, called B2PS, for patient stratification and propose methods for evaluating the results. Our experimental results demonstrate the superiority of B2PS over a popular state-of-the-art method and the benefits of Bayesian approaches. Our results agree with the intuition that transcriptomic data forms a better basis for patient stratification than genomic data.

  14. 2nd Bayesian Young Statisticians Meeting

    CERN Document Server

    Bitto, Angela; Kastner, Gregor; Posekany, Alexandra

    2015-01-01

    The Second Bayesian Young Statisticians Meeting (BAYSM 2014) and the research presented here facilitate connections among researchers using Bayesian Statistics by providing a forum for the development and exchange of ideas. WU Vienna University of Business and Economics hosted BAYSM 2014 from September 18th to 19th. The guidance of renowned plenary lecturers and senior discussants is a critical part of the meeting and this volume, which follows publication of contributions from BAYSM 2013. The meeting's scientific program reflected the variety of fields in which Bayesian methods are currently employed or could be introduced in the future. Three brilliant keynote lectures by Chris Holmes (University of Oxford), Christian Robert (Université Paris-Dauphine), and Mike West (Duke University), were complemented by 24 plenary talks covering the major topics Dynamic Models, Applications, Bayesian Nonparametrics, Biostatistics, Bayesian Methods in Economics, and Models and Methods, as well as a lively poster session ...

  15. Bayesian natural language semantics and pragmatics

    CERN Document Server

    Zeevat, Henk

    2015-01-01

    The contributions in this volume focus on the Bayesian interpretation of natural languages, which is widely used in areas of artificial intelligence, cognitive science, and computational linguistics. This is the first volume to take up topics in Bayesian Natural Language Interpretation and make proposals based on information theory, probability theory, and related fields. The methodologies offered here extend to the target semantic and pragmatic analyses of computational natural language interpretation. Bayesian approaches to natural language semantics and pragmatics are based on methods from signal processing and the causal Bayesian models pioneered by especially Pearl. In signal processing, the Bayesian method finds the most probable interpretation by finding the one that maximizes the product of the prior probability and the likelihood of the interpretation. It thus stresses the importance of a production model for interpretation as in Grice's contributions to pragmatics or in interpretation by abduction.

  16. A Bayesian hierarchical approach to comparative audit for carotid surgery.

    Science.gov (United States)

    Kuhan, G; Marshall, E C; Abidia, A F; Chetter, I C; McCollum, P T

    2002-12-01

    the aim of this study was to illustrate how a Bayesian hierarchical modelling approach can aid the reliable comparison of outcome rates between surgeons. retrospective analysis of prospective and retrospective data. binary outcome data (death/stroke within 30 days), together with information on 15 possible risk factors specific for CEA were available on 836 CEAs performed by four vascular surgeons from 1992-99. The median patient age was 68 (range 38-86) years and 60% were men. the model was developed using the WinBUGS software. After adjusting for patient-level risk factors, a cross-validatory approach was adopted to identify "divergent" performance. A ranking exercise was also carried out. the overall observed 30-day stroke/death rate was 3.9% (33/836). The model found diabetes, stroke and heart disease to be significant risk factors. There was no significant difference between the predicted and observed outcome rates for any surgeon (Bayesian p -value>0.05). Each surgeon had a median rank of 3 with associated 95% CI 1.0-5.0, despite the variability of observed stroke/death rate from 2.9-4.4%. After risk adjustment, there was very little residual between-surgeon variability in outcome rate. Bayesian hierarchical models can help to accurately quantify the uncertainty associated with surgeons' performance and rank.

  17. Kinematic Sunyaev-Zel'dovich Effect with Projected Fields: A Novel Probe of the Baryon Distribution with Planck, WMAP, and WISE Data.

    Science.gov (United States)

    Hill, J Colin; Ferraro, Simone; Battaglia, Nick; Liu, Jia; Spergel, David N

    2016-07-29

    The kinematic Sunyaev-Zel'dovich (KSZ) effect-the Doppler boosting of cosmic microwave background (CMB) photons due to Compton scattering off free electrons with nonzero bulk velocity-probes the abundance and the distribution of baryons in the Universe. All KSZ measurements to date have explicitly required spectroscopic redshifts. Here, we implement a novel estimator for the KSZ-large-scale structure cross-correlation based on projected fields: it does not require redshift estimates for individual objects, allowing KSZ measurements from large-scale imaging surveys. We apply this estimator to cleaned CMB temperature maps constructed from Planck and WMAP data and a galaxy sample from the Wide-field Infrared Survey Explorer (WISE). We measure the KSZ effect at 3.8σ-4.5σ significance, depending on the use of additional WISE galaxy bias constraints. We verify that our measurements are robust to possible dust emission from the WISE galaxies. Assuming the standard Λ cold dark matter cosmology, we directly constrain (f_{b}/0.158)(f_{free}/1.0)=1.48±0.19 (statistical error only) at redshift z≈0.4, where f_{b} is the fraction of matter in baryonic form and f_{free} is the free electron fraction. This is the tightest KSZ-derived constraint reported to date on these parameters. Astronomers have long known that baryons do not trace dark matter on ∼ kiloparsec scales and there has been strong evidence that galaxies are baryon poor. The consistency between the f_{b} value found here and the values inferred from analyses of the primordial CMB and big bang nucleosynthesis verifies that baryons approximately trace the dark matter distribution down to ∼ megaparsec scales. While our projected-field estimator is already competitive with other KSZ approaches when applied to current data sets (because we are able to use the full-sky WISE photometric survey), it will yield enormous signal-to-noise ratios when applied to upcoming high-resolution, multifrequency CMB surveys.

  18. Bayesian estimation of parameters in a regional hydrological model

    Directory of Open Access Journals (Sweden)

    K. Engeland

    2002-01-01

    Full Text Available This study evaluates the applicability of the distributed, process-oriented Ecomag model for prediction of daily streamflow in ungauged basins. The Ecomag model is applied as a regional model to nine catchments in the NOPEX area, using Bayesian statistics to estimate the posterior distribution of the model parameters conditioned on the observed streamflow. The distribution is calculated by Markov Chain Monte Carlo (MCMC analysis. The Bayesian method requires formulation of a likelihood function for the parameters and three alternative formulations are used. The first is a subjectively chosen objective function that describes the goodness of fit between the simulated and observed streamflow, as defined in the GLUE framework. The second and third formulations are more statistically correct likelihood models that describe the simulation errors. The full statistical likelihood model describes the simulation errors as an AR(1 process, whereas the simple model excludes the auto-regressive part. The statistical parameters depend on the catchments and the hydrological processes and the statistical and the hydrological parameters are estimated simultaneously. The results show that the simple likelihood model gives the most robust parameter estimates. The simulation error may be explained to a large extent by the catchment characteristics and climatic conditions, so it is possible to transfer knowledge about them to ungauged catchments. The statistical models for the simulation errors indicate that structural errors in the model are more important than parameter uncertainties. Keywords: regional hydrological model, model uncertainty, Bayesian analysis, Markov Chain Monte Carlo analysis

  19. Bayesian Inversion for Large Scale Antarctic Ice Sheet Flow

    KAUST Repository

    Ghattas, Omar

    2015-01-07

    The flow of ice from the interior of polar ice sheets is the primary contributor to projected sea level rise. One of the main difficulties faced in modeling ice sheet flow is the uncertain spatially-varying Robin boundary condition that describes the resistance to sliding at the base of the ice. Satellite observations of the surface ice flow velocity, along with a model of ice as a creeping incompressible shear-thinning fluid, can be used to infer this uncertain basal boundary condition. We cast this ill-posed inverse problem in the framework of Bayesian inference, which allows us to infer not only the basal sliding parameters, but also the associated uncertainty. To overcome the prohibitive nature of Bayesian methods for large-scale inverse problems, we exploit the fact that, despite the large size of observational data, they typically provide only sparse information on model parameters. We show results for Bayesian inversion of the basal sliding parameter field for the full Antarctic continent, and demonstrate that the work required to solve the inverse problem, measured in number of forward (and adjoint) ice sheet model solves, is independent of the parameter and data dimensions

  20. Bayesian Inversion for Large Scale Antarctic Ice Sheet Flow

    KAUST Repository

    Ghattas, Omar

    2015-01-01

    The flow of ice from the interior of polar ice sheets is the primary contributor to projected sea level rise. One of the main difficulties faced in modeling ice sheet flow is the uncertain spatially-varying Robin boundary condition that describes the resistance to sliding at the base of the ice. Satellite observations of the surface ice flow velocity, along with a model of ice as a creeping incompressible shear-thinning fluid, can be used to infer this uncertain basal boundary condition. We cast this ill-posed inverse problem in the framework of Bayesian inference, which allows us to infer not only the basal sliding parameters, but also the associated uncertainty. To overcome the prohibitive nature of Bayesian methods for large-scale inverse problems, we exploit the fact that, despite the large size of observational data, they typically provide only sparse information on model parameters. We show results for Bayesian inversion of the basal sliding parameter field for the full Antarctic continent, and demonstrate that the work required to solve the inverse problem, measured in number of forward (and adjoint) ice sheet model solves, is independent of the parameter and data dimensions

  1. A Bayesian Reflection on Surfaces

    Directory of Open Access Journals (Sweden)

    David R. Wolf

    1999-10-01

    Full Text Available Abstract: The topic of this paper is a novel Bayesian continuous-basis field representation and inference framework. Within this paper several problems are solved: The maximally informative inference of continuous-basis fields, that is where the basis for the field is itself a continuous object and not representable in a finite manner; the tradeoff between accuracy of representation in terms of information learned, and memory or storage capacity in bits; the approximation of probability distributions so that a maximal amount of information about the object being inferred is preserved; an information theoretic justification for multigrid methodology. The maximally informative field inference framework is described in full generality and denoted the Generalized Kalman Filter. The Generalized Kalman Filter allows the update of field knowledge from previous knowledge at any scale, and new data, to new knowledge at any other scale. An application example instance, the inference of continuous surfaces from measurements (for example, camera image data, is presented.

  2. Attention in a bayesian framework

    DEFF Research Database (Denmark)

    Whiteley, Louise Emma; Sahani, Maneesh

    2012-01-01

    , and include both selective phenomena, where attention is invoked by cues that point to particular stimuli, and integrative phenomena, where attention is invoked dynamically by endogenous processing. However, most previous Bayesian accounts of attention have focused on describing relatively simple experimental...... selective and integrative roles, and thus cannot be easily extended to complex environments. We suggest that the resource bottleneck stems from the computational intractability of exact perceptual inference in complex settings, and that attention reflects an evolved mechanism for approximate inference which...... can be shaped to refine the local accuracy of perception. We show that this approach extends the simple picture of attention as prior, so as to provide a unified and computationally driven account of both selective and integrative attentional phenomena....

  3. On Bayesian System Reliability Analysis

    Energy Technology Data Exchange (ETDEWEB)

    Soerensen Ringi, M

    1995-05-01

    The view taken in this thesis is that reliability, the probability that a system will perform a required function for a stated period of time, depends on a person`s state of knowledge. Reliability changes as this state of knowledge changes, i.e. when new relevant information becomes available. Most existing models for system reliability prediction are developed in a classical framework of probability theory and they overlook some information that is always present. Probability is just an analytical tool to handle uncertainty, based on judgement and subjective opinions. It is argued that the Bayesian approach gives a much more comprehensive understanding of the foundations of probability than the so called frequentistic school. A new model for system reliability prediction is given in two papers. The model encloses the fact that component failures are dependent because of a shared operational environment. The suggested model also naturally permits learning from failure data of similar components in non identical environments. 85 refs.

  4. Nonparametric Bayesian inference in biostatistics

    CERN Document Server

    Müller, Peter

    2015-01-01

    As chapters in this book demonstrate, BNP has important uses in clinical sciences and inference for issues like unknown partitions in genomics. Nonparametric Bayesian approaches (BNP) play an ever expanding role in biostatistical inference from use in proteomics to clinical trials. Many research problems involve an abundance of data and require flexible and complex probability models beyond the traditional parametric approaches. As this book's expert contributors show, BNP approaches can be the answer. Survival Analysis, in particular survival regression, has traditionally used BNP, but BNP's potential is now very broad. This applies to important tasks like arrangement of patients into clinically meaningful subpopulations and segmenting the genome into functionally distinct regions. This book is designed to both review and introduce application areas for BNP. While existing books provide theoretical foundations, this book connects theory to practice through engaging examples and research questions. Chapters c...

  5. On Bayesian System Reliability Analysis

    International Nuclear Information System (INIS)

    Soerensen Ringi, M.

    1995-01-01

    The view taken in this thesis is that reliability, the probability that a system will perform a required function for a stated period of time, depends on a person's state of knowledge. Reliability changes as this state of knowledge changes, i.e. when new relevant information becomes available. Most existing models for system reliability prediction are developed in a classical framework of probability theory and they overlook some information that is always present. Probability is just an analytical tool to handle uncertainty, based on judgement and subjective opinions. It is argued that the Bayesian approach gives a much more comprehensive understanding of the foundations of probability than the so called frequentistic school. A new model for system reliability prediction is given in two papers. The model encloses the fact that component failures are dependent because of a shared operational environment. The suggested model also naturally permits learning from failure data of similar components in non identical environments. 85 refs

  6. Bayesian estimation in homodyne interferometry

    International Nuclear Information System (INIS)

    Olivares, Stefano; Paris, Matteo G A

    2009-01-01

    We address phase-shift estimation by means of squeezed vacuum probe and homodyne detection. We analyse Bayesian estimator, which is known to asymptotically saturate the classical Cramer-Rao bound to the variance, and discuss convergence looking at the a posteriori distribution as the number of measurements increases. We also suggest two feasible adaptive methods, acting on the squeezing parameter and/or the homodyne local oscillator phase, which allow us to optimize homodyne detection and approach the ultimate bound to precision imposed by the quantum Cramer-Rao theorem. The performances of our two-step methods are investigated by means of Monte Carlo simulated experiments with a small number of homodyne data, thus giving a quantitative meaning to the notion of asymptotic optimality.

  7. Bayesian Kernel Mixtures for Counts.

    Science.gov (United States)

    Canale, Antonio; Dunson, David B

    2011-12-01

    Although Bayesian nonparametric mixture models for continuous data are well developed, there is a limited literature on related approaches for count data. A common strategy is to use a mixture of Poissons, which unfortunately is quite restrictive in not accounting for distributions having variance less than the mean. Other approaches include mixing multinomials, which requires finite support, and using a Dirichlet process prior with a Poisson base measure, which does not allow smooth deviations from the Poisson. As a broad class of alternative models, we propose to use nonparametric mixtures of rounded continuous kernels. An efficient Gibbs sampler is developed for posterior computation, and a simulation study is performed to assess performance. Focusing on the rounded Gaussian case, we generalize the modeling framework to account for multivariate count data, joint modeling with continuous and categorical variables, and other complications. The methods are illustrated through applications to a developmental toxicity study and marketing data. This article has supplementary material online.

  8. Bayesian networks in educational assessment

    CERN Document Server

    Almond, Russell G; Steinberg, Linda S; Yan, Duanli; Williamson, David M

    2015-01-01

    Bayesian inference networks, a synthesis of statistics and expert systems, have advanced reasoning under uncertainty in medicine, business, and social sciences. This innovative volume is the first comprehensive treatment exploring how they can be applied to design and analyze innovative educational assessments. Part I develops Bayes nets’ foundations in assessment, statistics, and graph theory, and works through the real-time updating algorithm. Part II addresses parametric forms for use with assessment, model-checking techniques, and estimation with the EM algorithm and Markov chain Monte Carlo (MCMC). A unique feature is the volume’s grounding in Evidence-Centered Design (ECD) framework for assessment design. This “design forward” approach enables designers to take full advantage of Bayes nets’ modularity and ability to model complex evidentiary relationships that arise from performance in interactive, technology-rich assessments such as simulations. Part III describes ECD, situates Bayes nets as ...

  9. Deconvolution map-making for cosmic microwave background observations

    International Nuclear Information System (INIS)

    Armitage, Charmaine; Wandelt, Benjamin D.

    2004-01-01

    We describe a new map-making code for cosmic microwave background observations. It implements fast algorithms for convolution and transpose convolution of two functions on the sphere [B. Wandelt and K. Gorski, Phys. Rev. D 63, 123002 (2001)]. Our code can account for arbitrary beam asymmetries and can be applied to any scanning strategy. We demonstrate the method using simulated time-ordered data for three beam models and two scanning patterns, including a coarsened version of the WMAP strategy. We quantitatively compare our results with a standard map-making method and demonstrate that the true sky is recovered with high accuracy using deconvolution map-making

  10. Robust bayesian analysis of an autoregressive model with ...

    African Journals Online (AJOL)

    In this work, robust Bayesian analysis of the Bayesian estimation of an autoregressive model with exponential innovations is performed. Using a Bayesian robustness methodology, we show that, using a suitable generalized quadratic loss, we obtain optimal Bayesian estimators of the parameters corresponding to the ...

  11. Bayesian models a statistical primer for ecologists

    CERN Document Server

    Hobbs, N Thompson

    2015-01-01

    Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods-in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach. Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probabili

  12. Bayesian data assimilation in shape registration

    KAUST Repository

    Cotter, C J

    2013-03-28

    In this paper we apply a Bayesian framework to the problem of geodesic curve matching. Given a template curve, the geodesic equations provide a mapping from initial conditions for the conjugate momentum onto topologically equivalent shapes. Here, we aim to recover the well-defined posterior distribution on the initial momentum which gives rise to observed points on the target curve; this is achieved by explicitly including a reparameterization in the formulation. Appropriate priors are chosen for the functions which together determine this field and the positions of the observation points, the initial momentum p0 and the reparameterization vector field ν, informed by regularity results about the forward model. Having done this, we illustrate how maximum likelihood estimators can be used to find regions of high posterior density, but also how we can apply recently developed Markov chain Monte Carlo methods on function spaces to characterize the whole of the posterior density. These illustrative examples also include scenarios where the posterior distribution is multimodal and irregular, leading us to the conclusion that knowledge of a state of global maximal posterior density does not always give us the whole picture, and full posterior sampling can give better quantification of likely states and the overall uncertainty inherent in the problem. © 2013 IOP Publishing Ltd.

  13. Orbits for 18 Visual Binaries and Two Double-line Spectroscopic Binaries Observed with HRCAM on the CTIO SOAR 4 m Telescope, Using a New Bayesian Orbit Code Based on Markov Chain Monte Carlo

    Science.gov (United States)

    Mendez, Rene A.; Claveria, Ruben M.; Orchard, Marcos E.; Silva, Jorge F.

    2017-11-01

    We present orbital elements and mass sums for 18 visual binary stars of spectral types B to K (five of which are new orbits) with periods ranging from 20 to more than 500 yr. For two double-line spectroscopic binaries with no previous orbits, the individual component masses, using combined astrometric and radial velocity data, have a formal uncertainty of ˜ 0.1 {M}⊙ . Adopting published photometry and trigonometric parallaxes, plus our own measurements, we place these objects on an H-R diagram and discuss their evolutionary status. These objects are part of a survey to characterize the binary population of stars in the Southern Hemisphere using the SOAR 4 m telescope+HRCAM at CTIO. Orbital elements are computed using a newly developed Markov chain Monte Carlo (MCMC) algorithm that delivers maximum-likelihood estimates of the parameters, as well as posterior probability density functions that allow us to evaluate the uncertainty of our derived parameters in a robust way. For spectroscopic binaries, using our approach, it is possible to derive a self-consistent parallax for the system from the combined astrometric and radial velocity data (“orbital parallax”), which compares well with the trigonometric parallaxes. We also present a mathematical formalism that allows a dimensionality reduction of the feature space from seven to three search parameters (or from 10 to seven dimensions—including parallax—in the case of spectroscopic binaries with astrometric data), which makes it possible to explore a smaller number of parameters in each case, improving the computational efficiency of our MCMC code. Based on observations obtained at the Southern Astrophysical Research (SOAR) telescope, which is a joint project of the Ministério da Ciência, Tecnologia, e Inovação (MCTI) da República Federativa do Brasil, the U.S. National Optical Astronomy Observatory (NOAO), the University of North Carolina at Chapel Hill (UNC), and Michigan State University (MSU).

  14. Prediction of Individual Serum Infliximab Concentrations in Inflammatory Bowel Disease by a Bayesian Dashboard System.

    Science.gov (United States)

    Eser, Alexander; Primas, Christian; Reinisch, Sieglinde; Vogelsang, Harald; Novacek, Gottfried; Mould, Diane R; Reinisch, Walter

    2018-01-30

    Despite a robust exposure-response relationship of infliximab in inflammatory bowel disease (IBD), attempts to adjust dosing to individually predicted serum concentrations of infliximab (SICs) are lacking. Compared with labor-intensive conventional software for pharmacokinetic (PK) modeling (eg, NONMEM) dashboards are easy-to-use programs incorporating complex Bayesian statistics to determine individual pharmacokinetics. We evaluated various infliximab detection assays and the number of samples needed to precisely forecast individual SICs using a Bayesian dashboard. We assessed long-term infliximab retention in patients being dosed concordantly versus discordantly with Bayesian dashboard recommendations. Three hundred eighty-two serum samples from 117 adult IBD patients on infliximab maintenance therapy were analyzed by 3 commercially available assays. Data from each assay was modeled using NONMEM and a Bayesian dashboard. PK parameter precision and residual variability were assessed. Forecast concentrations from both systems were compared with observed concentrations. Infliximab retention was assessed by prediction for dose intensification via Bayesian dashboard versus real-life practice. Forecast precision of SICs varied between detection assays. At least 3 SICs from a reliable assay are needed for an accurate forecast. The Bayesian dashboard performed similarly to NONMEM to predict SICs. Patients dosed concordantly with Bayesian dashboard recommendations had a significantly longer median drug survival than those dosed discordantly (51.5 versus 4.6 months, P dashboard helps to assess the diagnostic performance of infliximab detection assays. Three, not single, SICs provide sufficient information for individualized dose adjustment when incorporated into the Bayesian dashboard. Treatment adjusted to forecasted SICs is associated with longer drug retention of infliximab. © 2018, The American College of Clinical Pharmacology.

  15. Bayesian estimation of a proportion under an asymmetric observation error Estimación bayesiana de una proporción bajo error de estimación asimétrico

    Directory of Open Access Journals (Sweden)

    Juan Carlos Correa Morales

    2012-06-01

    Full Text Available The process of estimating a proportion that is associated with a sensitive question can yield responses that are not necessarily according to the reality.To reduce the probability o false response to this kind of sensitive questions some authors have proposed techniques of randomized response assuming asymmetric observation error. In this paper we present a generalization of the case where a symmetric error is assumed since this assumption could be unrealistic in practice. Under the assumption of an assymetric error the likelihood function is built. By doing this we intend that in practice the final user hasan alternative method to reduce the probability of false response. Assuming informative a priori distributions an expresion for the posterior distribution is found. Since this posterior distribution does not have a closed mathematical expression, it is neccesary to use the Gibbs sampler to carry out the estimation process. This technique is illustrated using real data about drug consumptions that were collected by the Oficina de Bienestar from the Universidad Nacional de Colombia at Medellín.El proceso de estimación de una proporción relacionada con una pregunta que puede ser altamente sensible para el encuestado, puede generar respuestas que no necesariamente coinciden con la realidad. Para reducir la probabilidad de respuestas falsas a este tipo de preguntas algunos autores han propuesto técnicas de respuesta aleatorizada asumiendo un error de observación asimétrico. En este artículo se presenta una generalización al caso donde se asume un error simétrico lo cual puede ser un supuesto poco realista en la práctica. Se deduce la función de verosimilitud bajo el supuesto de error de estimación asimétrico.Con esto se pretende que en la práctica se cuente con un método alternativo para reducir la probabilidad de respuestas falsas. Asumiendo distribuciones a priori informativas se encuentra una expresión para la distribuci

  16. Bayesian adaptive methods for clinical trials

    National Research Council Canada - National Science Library

    Berry, Scott M

    2011-01-01

    .... One is that Bayesian approaches implemented with the majority of their informative content coming from the current data, and not any external prior informa- tion, typically have good frequentist properties (e.g...

  17. A Bayesian approach to model uncertainty

    International Nuclear Information System (INIS)

    Buslik, A.

    1994-01-01

    A Bayesian approach to model uncertainty is taken. For the case of a finite number of alternative models, the model uncertainty is equivalent to parameter uncertainty. A derivation based on Savage's partition problem is given

  18. Structure-based bayesian sparse reconstruction

    KAUST Repository

    Quadeer, Ahmed Abdul; Al-Naffouri, Tareq Y.

    2012-01-01

    Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical

  19. An Intuitive Dashboard for Bayesian Network Inference

    International Nuclear Information System (INIS)

    Reddy, Vikas; Farr, Anna Charisse; Wu, Paul; Mengersen, Kerrie; Yarlagadda, Prasad K D V

    2014-01-01

    Current Bayesian network software packages provide good graphical interface for users who design and develop Bayesian networks for various applications. However, the intended end-users of these networks may not necessarily find such an interface appealing and at times it could be overwhelming, particularly when the number of nodes in the network is large. To circumvent this problem, this paper presents an intuitive dashboard, which provides an additional layer of abstraction, enabling the end-users to easily perform inferences over the Bayesian networks. Unlike most software packages, which display the nodes and arcs of the network, the developed tool organises the nodes based on the cause-and-effect relationship, making the user-interaction more intuitive and friendly. In addition to performing various types of inferences, the users can conveniently use the tool to verify the behaviour of the developed Bayesian network. The tool has been developed using QT and SMILE libraries in C++

  20. Learning Bayesian networks for discrete data

    KAUST Repository

    Liang, Faming

    2009-02-01

    Bayesian networks have received much attention in the recent literature. In this article, we propose an approach to learn Bayesian networks using the stochastic approximation Monte Carlo (SAMC) algorithm. Our approach has two nice features. Firstly, it possesses the self-adjusting mechanism and thus avoids essentially the local-trap problem suffered by conventional MCMC simulation-based approaches in learning Bayesian networks. Secondly, it falls into the class of dynamic importance sampling algorithms; the network features can be inferred by dynamically weighted averaging the samples generated in the learning process, and the resulting estimates can have much lower variation than the single model-based estimates. The numerical results indicate that our approach can mix much faster over the space of Bayesian networks than the conventional MCMC simulation-based approaches. © 2008 Elsevier B.V. All rights reserved.

  1. An Intuitive Dashboard for Bayesian Network Inference

    Science.gov (United States)

    Reddy, Vikas; Charisse Farr, Anna; Wu, Paul; Mengersen, Kerrie; Yarlagadda, Prasad K. D. V.

    2014-03-01

    Current Bayesian network software packages provide good graphical interface for users who design and develop Bayesian networks for various applications. However, the intended end-users of these networks may not necessarily find such an interface appealing and at times it could be overwhelming, particularly when the number of nodes in the network is large. To circumvent this problem, this paper presents an intuitive dashboard, which provides an additional layer of abstraction, enabling the end-users to easily perform inferences over the Bayesian networks. Unlike most software packages, which display the nodes and arcs of the network, the developed tool organises the nodes based on the cause-and-effect relationship, making the user-interaction more intuitive and friendly. In addition to performing various types of inferences, the users can conveniently use the tool to verify the behaviour of the developed Bayesian network. The tool has been developed using QT and SMILE libraries in C++.

  2. Bayesian optimization for computationally extensive probability distributions.

    Science.gov (United States)

    Tamura, Ryo; Hukushima, Koji

    2018-01-01

    An efficient method for finding a better maximizer of computationally extensive probability distributions is proposed on the basis of a Bayesian optimization technique. A key idea of the proposed method is to use extreme values of acquisition functions by Gaussian processes for the next training phase, which should be located near a local maximum or a global maximum of the probability distribution. Our Bayesian optimization technique is applied to the posterior distribution in the effective physical model estimation, which is a computationally extensive probability distribution. Even when the number of sampling points on the posterior distributions is fixed to be small, the Bayesian optimization provides a better maximizer of the posterior distributions in comparison to those by the random search method, the steepest descent method, or the Monte Carlo method. Furthermore, the Bayesian optimization improves the results efficiently by combining the steepest descent method and thus it is a powerful tool to search for a better maximizer of computationally extensive probability distributions.

  3. Correct Bayesian and frequentist intervals are similar

    International Nuclear Information System (INIS)

    Atwood, C.L.

    1986-01-01

    This paper argues that Bayesians and frequentists will normally reach numerically similar conclusions, when dealing with vague data or sparse data. It is shown that both statistical methodologies can deal reasonably with vague data. With sparse data, in many important practical cases Bayesian interval estimates and frequentist confidence intervals are approximately equal, although with discrete data the frequentist intervals are somewhat longer. This is not to say that the two methodologies are equally easy to use: The construction of a frequentist confidence interval may require new theoretical development. Bayesians methods typically require numerical integration, perhaps over many variables. Also, Bayesian can easily fall into the trap of over-optimism about their amount of prior knowledge. But in cases where both intervals are found correctly, the two intervals are usually not very different. (orig.)

  4. Implementing the Bayesian paradigm in risk analysis

    International Nuclear Information System (INIS)

    Aven, T.; Kvaloey, J.T.

    2002-01-01

    The Bayesian paradigm comprises a unified and consistent framework for analyzing and expressing risk. Yet, we see rather few examples of applications where the full Bayesian setting has been adopted with specifications of priors of unknown parameters. In this paper, we discuss some of the practical challenges of implementing Bayesian thinking and methods in risk analysis, emphasizing the introduction of probability models and parameters and associated uncertainty assessments. We conclude that there is a need for a pragmatic view in order to 'successfully' apply the Bayesian approach, such that we can do the assignments of some of the probabilities without adopting the somewhat sophisticated procedure of specifying prior distributions of parameters. A simple risk analysis example is presented to illustrate ideas

  5. An overview on Approximate Bayesian computation*

    Directory of Open Access Journals (Sweden)

    Baragatti Meïli

    2014-01-01

    Full Text Available Approximate Bayesian computation techniques, also called likelihood-free methods, are one of the most satisfactory approach to intractable likelihood problems. This overview presents recent results since its introduction about ten years ago in population genetics.

  6. Bayesian experts in exploring reaction kinetics of transcription circuits.

    Science.gov (United States)

    Yoshida, Ryo; Saito, Masaya M; Nagao, Hiromichi; Higuchi, Tomoyuki

    2010-09-15

    Biochemical reactions in cells are made of several types of biological circuits. In current systems biology, making differential equation (DE) models simulatable in silico has been an appealing, general approach to uncover a complex world of biochemical reaction dynamics. Despite of a need for simulation-aided studies, our research field has yet provided no clear answers: how to specify kinetic values in models that are difficult to measure from experimental/theoretical analyses on biochemical kinetics. We present a novel non-parametric Bayesian approach to this problem. The key idea lies in the development of a Dirichlet process (DP) prior distribution, called Bayesian experts, which reflects substantive knowledge on reaction mechanisms inherent in given models and experimentally observable kinetic evidences to the subsequent parameter search. The DP prior identifies significant local regions of unknown parameter space before proceeding to the posterior analyses. This article reports that a Bayesian expert-inducing stochastic search can effectively explore unknown parameters of in silico transcription circuits such that solutions of DEs reproduce transcriptomic time course profiles. A sample source code is available at the URL http://daweb.ism.ac.jp/~yoshidar/lisdas/.

  7. Bayesian Inference of High-Dimensional Dynamical Ocean Models

    Science.gov (United States)

    Lin, J.; Lermusiaux, P. F. J.; Lolla, S. V. T.; Gupta, A.; Haley, P. J., Jr.

    2015-12-01

    This presentation addresses a holistic set of challenges in high-dimension ocean Bayesian nonlinear estimation: i) predict the probability distribution functions (pdfs) of large nonlinear dynamical systems using stochastic partial differential equations (PDEs); ii) assimilate data using Bayes' law with these pdfs; iii) predict the future data that optimally reduce uncertainties; and (iv) rank the known and learn the new model formulations themselves. Overall, we allow the joint inference of the state, equations, geometry, boundary conditions and initial conditions of dynamical models. Examples are provided for time-dependent fluid and ocean flows, including cavity, double-gyre and Strait flows with jets and eddies. The Bayesian model inference, based on limited observations, is illustrated first by the estimation of obstacle shapes and positions in fluid flows. Next, the Bayesian inference of biogeochemical reaction equations and of their states and parameters is presented, illustrating how PDE-based machine learning can rigorously guide the selection and discovery of complex ecosystem models. Finally, the inference of multiscale bottom gravity current dynamics is illustrated, motivated in part by classic overflows and dense water formation sites and their relevance to climate monitoring and dynamics. This is joint work with our MSEAS group at MIT.

  8. On Bayesian reliability analysis with informative priors and censoring

    International Nuclear Information System (INIS)

    Coolen, F.P.A.

    1996-01-01

    In the statistical literature many methods have been presented to deal with censored observations, both within the Bayesian and non-Bayesian frameworks, and such methods have been successfully applied to, e.g., reliability problems. Also, in reliability theory it is often emphasized that, through shortage of statistical data and possibilities for experiments, one often needs to rely heavily on judgements of engineers, or other experts, for which means Bayesian methods are attractive. It is therefore important that such judgements can be elicited easily to provide informative prior distributions that reflect the knowledge of the engineers well. In this paper we focus on this aspect, especially on the situation that the judgements of the consulted engineers are based on experiences in environments where censoring has also been present previously. We suggest the use of the attractive interpretation of hyperparameters of conjugate prior distributions when these are available for assumed parametric models for lifetimes, and we show how one may go beyond the standard conjugate priors, using similar interpretations of hyper-parameters, to enable easier elicitation when censoring has been present in the past. This may even lead to more flexibility for modelling prior knowledge than when using standard conjugate priors, whereas the disadvantage of more complicated calculations that may be needed to determine posterior distributions play a minor role due to the advanced mathematical and statistical software that is widely available these days

  9. Bayesian statistical evaluation of peak area measurements in gamma spectrometry

    International Nuclear Information System (INIS)

    Silva, L.; Turkman, A.; Paulino, C.D.

    2010-01-01

    We analyze results from determinations of peak areas for a radioactive source containing several radionuclides. The statistical analysis was performed using Bayesian methods based on the usual Poisson model for observed counts. This model does not appear to be a very good assumption for the counting system under investigation, even though it is not questioned as a whole by the inferential procedures adopted. We conclude that, in order to avoid incorrect inferences on relevant quantities, one must proceed to a further study that allows us to include missing influence parameters and to select a model explaining the observed data much better.

  10. Bayesian probability theory and inverse problems

    International Nuclear Information System (INIS)

    Kopec, S.

    1994-01-01

    Bayesian probability theory is applied to approximate solving of the inverse problems. In order to solve the moment problem with the noisy data, the entropic prior is used. The expressions for the solution and its error bounds are presented. When the noise level tends to zero, the Bayesian solution tends to the classic maximum entropy solution in the L 2 norm. The way of using spline prior is also shown. (author)

  11. A Bayesian classifier for symbol recognition

    OpenAIRE

    Barrat , Sabine; Tabbone , Salvatore; Nourrissier , Patrick

    2007-01-01

    URL : http://www.buyans.com/POL/UploadedFile/134_9977.pdf; International audience; We present in this paper an original adaptation of Bayesian networks to symbol recognition problem. More precisely, a descriptor combination method, which enables to improve significantly the recognition rate compared to the recognition rates obtained by each descriptor, is presented. In this perspective, we use a simple Bayesian classifier, called naive Bayes. In fact, probabilistic graphical models, more spec...

  12. Bayesian Modeling of a Human MMORPG Player

    Science.gov (United States)

    Synnaeve, Gabriel; Bessière, Pierre

    2011-03-01

    This paper describes an application of Bayesian programming to the control of an autonomous avatar in a multiplayer role-playing game (the example is based on World of Warcraft). We model a particular task, which consists of choosing what to do and to select which target in a situation where allies and foes are present. We explain the model in Bayesian programming and show how we could learn the conditional probabilities from data gathered during human-played sessions.

  13. Variations on Bayesian Prediction and Inference

    Science.gov (United States)

    2016-05-09

    inference 2.2.1 Background There are a number of statistical inference problems that are not generally formulated via a full probability model...problem of inference about an unknown parameter, the Bayesian approach requires a full probability 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...the problem of inference about an unknown parameter, the Bayesian approach requires a full probability model/likelihood which can be an obstacle

  14. Bayesian target tracking based on particle filter

    Institute of Scientific and Technical Information of China (English)

    2005-01-01

    For being able to deal with the nonlinear or non-Gaussian problems, particle filters have been studied by many researchers. Based on particle filter, the extended Kalman filter (EKF) proposal function is applied to Bayesian target tracking. Markov chain Monte Carlo (MCMC) method, the resampling step, etc novel techniques are also introduced into Bayesian target tracking. And the simulation results confirm the improved particle filter with these techniques outperforms the basic one.

  15. MCMC for parameters estimation by bayesian approach

    International Nuclear Information System (INIS)

    Ait Saadi, H.; Ykhlef, F.; Guessoum, A.

    2011-01-01

    This article discusses the parameter estimation for dynamic system by a Bayesian approach associated with Markov Chain Monte Carlo methods (MCMC). The MCMC methods are powerful for approximating complex integrals, simulating joint distributions, and the estimation of marginal posterior distributions, or posterior means. The MetropolisHastings algorithm has been widely used in Bayesian inference to approximate posterior densities. Calibrating the proposal distribution is one of the main issues of MCMC simulation in order to accelerate the convergence.

  16. Bayesian Networks for Modeling Dredging Decisions

    Science.gov (United States)

    2011-10-01

    years, that algorithms have been developed to solve these problems efficiently. Most modern Bayesian network software uses junction tree (a.k.a. join... software was used to develop the network . This is by no means an exhaustive list of Bayesian network applications, but it is representative of recent...characteristic node (SCN), state- defining node ( SDN ), effect node (EFN), or value node. The five types of nodes can be described as follows: ERDC/EL TR-11

  17. Fully probabilistic design of hierarchical Bayesian models

    Czech Academy of Sciences Publication Activity Database

    Quinn, A.; Kárný, Miroslav; Guy, Tatiana Valentine

    2016-01-01

    Roč. 369, č. 1 (2016), s. 532-547 ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Fully probabilistic design * Ideal distribution * Minimum cross-entropy principle * Bayesian conditioning * Kullback-Leibler divergence * Bayesian nonparametric modelling Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.832, year: 2016 http://library.utia.cas.cz/separaty/2016/AS/karny-0463052.pdf

  18. A Bayesian Method for Weighted Sampling

    OpenAIRE

    Lo, Albert Y.

    1993-01-01

    Bayesian statistical inference for sampling from weighted distribution models is studied. Small-sample Bayesian bootstrap clone (BBC) approximations to the posterior distribution are discussed. A second-order property for the BBC in unweighted i.i.d. sampling is given. A consequence is that BBC approximations to a posterior distribution of the mean and to the sampling distribution of the sample average, can be made asymptotically accurate by a proper choice of the random variables that genera...

  19. Bayesian LASSO, scale space and decision making in association genetics.

    Science.gov (United States)

    Pasanen, Leena; Holmström, Lasse; Sillanpää, Mikko J

    2015-01-01

    LASSO is a penalized regression method that facilitates model fitting in situations where there are as many, or even more explanatory variables than observations, and only a few variables are relevant in explaining the data. We focus on the Bayesian version of LASSO and consider four problems that need special attention: (i) controlling false positives, (ii) multiple comparisons, (iii) collinearity among explanatory variables, and (iv) the choice of the tuning parameter that controls the amount of shrinkage and the sparsity of the estimates. The particular application considered is association genetics, where LASSO regression can be used to find links between chromosome locations and phenotypic traits in a biological organism. However, the proposed techniques are relevant also in other contexts where LASSO is used for variable selection. We separate the true associations from false positives using the posterior distribution of the effects (regression coefficients) provided by Bayesian LASSO. We propose to solve the multiple comparisons problem by using simultaneous inference based on the joint posterior distribution of the effects. Bayesian LASSO also tends to distribute an effect among collinear variables, making detection of an association difficult. We propose to solve this problem by considering not only individual effects but also their functionals (i.e. sums and differences). Finally, whereas in Bayesian LASSO the tuning parameter is often regarded as a random variable, we adopt a scale space view and consider a whole range of fixed tuning parameters, instead. The effect estimates and the associated inference are considered for all tuning parameters in the selected range and the results are visualized with color maps that provide useful insights into data and the association problem considered. The methods are illustrated using two sets of artificial data and one real data set, all representing typical settings in association genetics.

  20. Looking for Sustainable Urban Mobility through Bayesian Networks

    Directory of Open Access Journals (Sweden)

    Giovanni Fusco

    2004-11-01

    Full Text Available There is no formalised theory of sustainable urban mobility systems. Observed patterns of urban mobility are often considered unsustainable. But we don’t know what a city with sustainable mobility should look like. It is nevertheless increasingly apparent that the urban mobility system plays an important role in the achievement of the city’s wider sustainability objectives.In this paper we explore the characteristics of sustainable urban mobility systems through the technique of Bayesian networks. At the frontier between multivariate statistics and artificial intelligence, Bayesian networks provide powerful models of causal knowledge in an uncertain context. Using data on urban structure, transportation offer, mobility demand, resource consumption and environmental externalities from seventy-five world cities, we developed a systemic model of the city-transportation-environment interaction in the form of a Bayesian network. The network could then be used to infer the features of the city with sustainable mobility.The Bayesian model indicates that the city with sustainable mobility is most probably a dense city with highly efficient transit and multimodal mobility. It produces high levels of accessibility without relying on a fast road network. The achievement of sustainability objectives for urban mobility is probably compatible with all socioeconomic contexts.By measuring the distance of world cities from the inferred sustainability profile, we finally derive a geography of sustainability for mobility systems. The cities closest to the sustainability profile are in Central Europe as well as in affluent countries of the Far East. Car-dependent American cities are the farthest from the desired sustainability profile.

  1. Philosophy and the practice of Bayesian statistics.

    Science.gov (United States)

    Gelman, Andrew; Shalizi, Cosma Rohilla

    2013-02-01

    A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework. © 2012 The British Psychological Society.

  2. Sparse Bayesian Inference and the Temperature Structure of the Solar Corona

    Energy Technology Data Exchange (ETDEWEB)

    Warren, Harry P. [Space Science Division, Naval Research Laboratory, Washington, DC 20375 (United States); Byers, Jeff M. [Materials Science and Technology Division, Naval Research Laboratory, Washington, DC 20375 (United States); Crump, Nicholas A. [Naval Center for Space Technology, Naval Research Laboratory, Washington, DC 20375 (United States)

    2017-02-20

    Measuring the temperature structure of the solar atmosphere is critical to understanding how it is heated to high temperatures. Unfortunately, the temperature of the upper atmosphere cannot be observed directly, but must be inferred from spectrally resolved observations of individual emission lines that span a wide range of temperatures. Such observations are “inverted” to determine the distribution of plasma temperatures along the line of sight. This inversion is ill posed and, in the absence of regularization, tends to produce wildly oscillatory solutions. We introduce the application of sparse Bayesian inference to the problem of inferring the temperature structure of the solar corona. Within a Bayesian framework a preference for solutions that utilize a minimum number of basis functions can be encoded into the prior and many ad hoc assumptions can be avoided. We demonstrate the efficacy of the Bayesian approach by considering a test library of 40 assumed temperature distributions.

  3. Analysis of COSIMA spectra: Bayesian approach

    Directory of Open Access Journals (Sweden)

    H. J. Lehto

    2015-06-01

    secondary ion mass spectrometer (TOF-SIMS spectra. The method is applied to the COmetary Secondary Ion Mass Analyzer (COSIMA TOF-SIMS mass spectra where the analysis can be broken into subgroups of lines close to integer mass values. The effects of the instrumental dead time are discussed in a new way. The method finds the joint probability density functions of measured line parameters (number of lines, and their widths, peak amplitudes, integrated amplitudes and positions. In the case of two or more lines, these distributions can take complex forms. The derived line parameters can be used to further calibrate the mass scaling of TOF-SIMS and to feed the results into other analysis methods such as multivariate analyses of spectra. We intend to use the method, first as a comprehensive tool to perform quantitative analysis of spectra, and second as a fast tool for studying interesting targets for obtaining additional TOF-SIMS measurements of the sample, a property unique to COSIMA. Finally, we point out that the Bayesian method can be thought of as a means to solve inverse problems but with forward calculations, only with no iterative corrections or other manipulation of the observed data.

  4. Optimal Bayesian Experimental Design for Combustion Kinetics

    KAUST Repository

    Huan, Xun

    2011-01-04

    Experimental diagnostics play an essential role in the development and refinement of chemical kinetic models, whether for the combustion of common complex hydrocarbons or of emerging alternative fuels. Questions of experimental design—e.g., which variables or species to interrogate, at what resolution and under what conditions—are extremely important in this context, particularly when experimental resources are limited. This paper attempts to answer such questions in a rigorous and systematic way. We propose a Bayesian framework for optimal experimental design with nonlinear simulation-based models. While the framework is broadly applicable, we use it to infer rate parameters in a combustion system with detailed kinetics. The framework introduces a utility function that reflects the expected information gain from a particular experiment. Straightforward evaluation (and maximization) of this utility function requires Monte Carlo sampling, which is infeasible with computationally intensive models. Instead, we construct a polynomial surrogate for the dependence of experimental observables on model parameters and design conditions, with the help of dimension-adaptive sparse quadrature. Results demonstrate the efficiency and accuracy of the surrogate, as well as the considerable effectiveness of the experimental design framework in choosing informative experimental conditions.

  5. Varying prior information in Bayesian inversion

    International Nuclear Information System (INIS)

    Walker, Matthew; Curtis, Andrew

    2014-01-01

    Bayes' rule is used to combine likelihood and prior probability distributions. The former represents knowledge derived from new data, the latter represents pre-existing knowledge; the Bayesian combination is the so-called posterior distribution, representing the resultant new state of knowledge. While varying the likelihood due to differing data observations is common, there are also situations where the prior distribution must be changed or replaced repeatedly. For example, in mixture density neural network (MDN) inversion, using current methods the neural network employed for inversion needs to be retrained every time prior information changes. We develop a method of prior replacement to vary the prior without re-training the network. Thus the efficiency of MDN inversions can be increased, typically by orders of magnitude when applied to geophysical problems. We demonstrate this for the inversion of seismic attributes in a synthetic subsurface geological reservoir model. We also present results which suggest that prior replacement can be used to control the statistical properties (such as variance) of the final estimate of the posterior in more general (e.g., Monte Carlo based) inverse problem solutions. (paper)

  6. Bayesian estimation applied to multiple species

    International Nuclear Information System (INIS)

    Kunz, Martin; Bassett, Bruce A.; Hlozek, Renee A.

    2007-01-01

    Observed data are often contaminated by undiscovered interlopers, leading to biased parameter estimation. Here we present BEAMS (Bayesian estimation applied to multiple species) which significantly improves on the standard maximum likelihood approach in the case where the probability for each data point being ''pure'' is known. We discuss the application of BEAMS to future type-Ia supernovae (SNIa) surveys, such as LSST, which are projected to deliver over a million supernovae light curves without spectra. The multiband light curves for each candidate will provide a probability of being Ia (pure) but the full sample will be significantly contaminated with other types of supernovae and transients. Given a sample of N supernovae with mean probability, , of being Ia, BEAMS delivers parameter constraints equal to N spectroscopically confirmed SNIa. In addition BEAMS can be simultaneously used to tease apart different families of data and to recover properties of the underlying distributions of those families (e.g. the type-Ibc and II distributions). Hence BEAMS provides a unified classification and parameter estimation methodology which may be useful in a diverse range of problems such as photometric redshift estimation or, indeed, any parameter estimation problem where contamination is an issue

  7. EXONEST: The Bayesian Exoplanetary Explorer

    Directory of Open Access Journals (Sweden)

    Kevin H. Knuth

    2017-10-01

    Full Text Available The fields of astronomy and astrophysics are currently engaged in an unprecedented era of discovery as recent missions have revealed thousands of exoplanets orbiting other stars. While the Kepler Space Telescope mission has enabled most of these exoplanets to be detected by identifying transiting events, exoplanets often exhibit additional photometric effects that can be used to improve the characterization of exoplanets. The EXONEST Exoplanetary Explorer is a Bayesian exoplanet inference engine based on nested sampling and originally designed to analyze archived Kepler Space Telescope and CoRoT (Convection Rotation et Transits planétaires exoplanet mission data. We discuss the EXONEST software package and describe how it accommodates plug-and-play models of exoplanet-associated photometric effects for the purpose of exoplanet detection, characterization and scientific hypothesis testing. The current suite of models allows for both circular and eccentric orbits in conjunction with photometric effects, such as the primary transit and secondary eclipse, reflected light, thermal emissions, ellipsoidal variations, Doppler beaming and superrotation. We discuss our new efforts to expand the capabilities of the software to include more subtle photometric effects involving reflected and refracted light. We discuss the EXONEST inference engine design and introduce our plans to port the current MATLAB-based EXONEST software package over to the next generation Exoplanetary Explorer, which will be a Python-based open source project with the capability to employ third-party plug-and-play models of exoplanet-related photometric effects.

  8. Maximum entropy and Bayesian methods

    International Nuclear Information System (INIS)

    Smith, C.R.; Erickson, G.J.; Neudorfer, P.O.

    1992-01-01

    Bayesian probability theory and Maximum Entropy methods are at the core of a new view of scientific inference. These 'new' ideas, along with the revolution in computational methods afforded by modern computers allow astronomers, electrical engineers, image processors of any type, NMR chemists and physicists, and anyone at all who has to deal with incomplete and noisy data, to take advantage of methods that, in the past, have been applied only in some areas of theoretical physics. The title workshops have been the focus of a group of researchers from many different fields, and this diversity is evident in this book. There are tutorial and theoretical papers, and applications in a very wide variety of fields. Almost any instance of dealing with incomplete and noisy data can be usefully treated by these methods, and many areas of theoretical research are being enhanced by the thoughtful application of Bayes' theorem. Contributions contained in this volume present a state-of-the-art overview that will be influential and useful for many years to come

  9. Inverse problems in the Bayesian framework

    International Nuclear Information System (INIS)

    Calvetti, Daniela; Somersalo, Erkki; Kaipio, Jari P

    2014-01-01

    The history of Bayesian methods dates back to the original works of Reverend Thomas Bayes and Pierre-Simon Laplace: the former laid down some of the basic principles on inverse probability in his classic article ‘An essay towards solving a problem in the doctrine of chances’ that was read posthumously in the Royal Society in 1763. Laplace, on the other hand, in his ‘Memoirs on inverse probability’ of 1774 developed the idea of updating beliefs and wrote down the celebrated Bayes’ formula in the form we know today. Although not identified yet as a framework for investigating inverse problems, Laplace used the formalism very much in the spirit it is used today in the context of inverse problems, e.g., in his study of the distribution of comets. With the evolution of computational tools, Bayesian methods have become increasingly popular in all fields of human knowledge in which conclusions need to be drawn based on incomplete and noisy data. Needless to say, inverse problems, almost by definition, fall into this category. Systematic work for developing a Bayesian inverse problem framework can arguably be traced back to the 1980s, (the original first edition being published by Elsevier in 1987), although articles on Bayesian methodology applied to inverse problems, in particular in geophysics, had appeared much earlier. Today, as testified by the articles in this special issue, the Bayesian methodology as a framework for considering inverse problems has gained a lot of popularity, and it has integrated very successfully with many traditional inverse problems ideas and techniques, providing novel ways to interpret and implement traditional procedures in numerical analysis, computational statistics, signal analysis and data assimilation. The range of applications where the Bayesian framework has been fundamental goes from geophysics, engineering and imaging to astronomy, life sciences and economy, and continues to grow. There is no question that Bayesian

  10. Modelling of JET diagnostics using Bayesian Graphical Models

    Energy Technology Data Exchange (ETDEWEB)

    Svensson, J. [IPP Greifswald, Greifswald (Germany); Ford, O. [Imperial College, London (United Kingdom); McDonald, D.; Hole, M.; Nessi, G. von; Meakins, A.; Brix, M.; Thomsen, H.; Werner, A.; Sirinelli, A.

    2011-07-01

    The mapping between physics parameters (such as densities, currents, flows, temperatures etc) defining the plasma 'state' under a given model and the raw observations of each plasma diagnostic will 1) depend on the particular physics model used, 2) is inherently probabilistic, from uncertainties on both observations and instrumental aspects of the mapping, such as calibrations, instrument functions etc. A flexible and principled way of modelling such interconnected probabilistic systems is through so called Bayesian graphical models. Being an amalgam between graph theory and probability theory, Bayesian graphical models can simulate the complex interconnections between physics models and diagnostic observations from multiple heterogeneous diagnostic systems, making it relatively easy to optimally combine the observations from multiple diagnostics for joint inference on parameters of the underlying physics model, which in itself can be represented as part of the graph. At JET about 10 diagnostic systems have to date been modelled in this way, and has lead to a number of new results, including: the reconstruction of the flux surface topology and q-profiles without any specific equilibrium assumption, using information from a number of different diagnostic systems; profile inversions taking into account the uncertainties in the flux surface positions and a substantial increase in accuracy of JET electron density and temperature profiles, including improved pedestal resolution, through the joint analysis of three diagnostic systems. It is believed that the Bayesian graph approach could potentially be utilised for very large sets of diagnostics, providing a generic data analysis framework for nuclear fusion experiments, that would be able to optimally utilize the information from multiple diagnostics simultaneously, and where the explicit graph representation of the connections to underlying physics models could be used for sophisticated model testing. This

  11. Robust Bayesian Experimental Design for Conceptual Model Discrimination

    Science.gov (United States)

    Pham, H. V.; Tsai, F. T. C.

    2015-12-01

    A robust Bayesian optimal experimental design under uncertainty is presented to provide firm information for model discrimination, given the least number of pumping wells and observation wells. Firm information is the maximum information of a system can be guaranteed from an experimental design. The design is based on the Box-Hill expected entropy decrease (EED) before and after the experiment design and the Bayesian model averaging (BMA) framework. A max-min programming is introduced to choose the robust design that maximizes the minimal Box-Hill EED subject to that the highest expected posterior model probability satisfies a desired probability threshold. The EED is calculated by the Gauss-Hermite quadrature. The BMA method is used to predict future observations and to quantify future observation uncertainty arising from conceptual and parametric uncertainties in calculating EED. Monte Carlo approach is adopted to quantify the uncertainty in the posterior model probabilities. The optimal experimental design is tested by a synthetic 5-layer anisotropic confined aquifer. Nine conceptual groundwater models are constructed due to uncertain geological architecture and boundary condition. High-performance computing is used to enumerate all possible design solutions in order to identify the most plausible groundwater model. Results highlight the impacts of scedasticity in future observation data as well as uncertainty sources on potential pumping and observation locations.

  12. Use of Bayesian Estimates to determine the Volatility Parameter Input in the Black-Scholes and Binomial Option Pricing Models

    Directory of Open Access Journals (Sweden)

    Shu Wing Ho

    2011-12-01

    Full Text Available The valuation of options and many other derivative instruments requires an estimation of exante or forward looking volatility. This paper adopts a Bayesian approach to estimate stock price volatility. We find evidence that overall Bayesian volatility estimates more closely approximate the implied volatility of stocks derived from traded call and put options prices compared to historical volatility estimates sourced from IVolatility.com (“IVolatility”. Our evidence suggests use of the Bayesian approach to estimate volatility can provide a more accurate measure of ex-ante stock price volatility and will be useful in the pricing of derivative securities where the implied stock price volatility cannot be observed.

  13. Bayesian analogy with relational transformations.

    Science.gov (United States)

    Lu, Hongjing; Chen, Dawn; Holyoak, Keith J

    2012-07-01

    How can humans acquire relational representations that enable analogical inference and other forms of high-level reasoning? Using comparative relations as a model domain, we explore the possibility that bottom-up learning mechanisms applied to objects coded as feature vectors can yield representations of relations sufficient to solve analogy problems. We introduce Bayesian analogy with relational transformations (BART) and apply the model to the task of learning first-order comparative relations (e.g., larger, smaller, fiercer, meeker) from a set of animal pairs. Inputs are coded by vectors of continuous-valued features, based either on human magnitude ratings, normed feature ratings (De Deyne et al., 2008), or outputs of the topics model (Griffiths, Steyvers, & Tenenbaum, 2007). Bootstrapping from empirical priors, the model is able to induce first-order relations represented as probabilistic weight distributions, even when given positive examples only. These learned representations allow classification of novel instantiations of the relations and yield a symbolic distance effect of the sort obtained with both humans and other primates. BART then transforms its learned weight distributions by importance-guided mapping, thereby placing distinct dimensions into correspondence. These transformed representations allow BART to reliably solve 4-term analogies (e.g., larger:smaller::fiercer:meeker), a type of reasoning that is arguably specific to humans. Our results provide a proof-of-concept that structured analogies can be solved with representations induced from unstructured feature vectors by mechanisms that operate in a largely bottom-up fashion. We discuss potential implications for algorithmic and neural models of relational thinking, as well as for the evolution of abstract thought. Copyright 2012 APA, all rights reserved.

  14. Bayesian tomographic reconstruction of microsystems

    International Nuclear Information System (INIS)

    Salem, Sofia Fekih; Vabre, Alexandre; Mohammad-Djafari, Ali

    2007-01-01

    The microtomography by X ray transmission plays an increasingly dominating role in the study and the understanding of microsystems. Within this framework, an experimental setup of high resolution X ray microtomography was developed at CEA-List to quantify the physical parameters related to the fluids flow in microsystems. Several difficulties rise from the nature of experimental data collected on this setup: enhanced error measurements due to various physical phenomena occurring during the image formation (diffusion, beam hardening), and specificities of the setup (limited angle, partial view of the object, weak contrast).To reconstruct the object we must solve an inverse problem. This inverse problem is known to be ill-posed. It therefore needs to be regularized by introducing prior information. The main prior information we account for is that the object is composed of a finite known number of different materials distributed in compact regions. This a priori information is introduced via a Gauss-Markov field for the contrast distributions with a hidden Potts-Markov field for the class materials in the Bayesian estimation framework. The computations are done by using an appropriate Markov Chain Monte Carlo (MCMC) technique.In this paper, we present first the basic steps of the proposed algorithms. Then we focus on one of the main steps in any iterative reconstruction method which is the computation of forward and adjoint operators (projection and backprojection). A fast implementation of these two operators is crucial for the real application of the method. We give some details on the fast computation of these steps and show some preliminary results of simulations

  15. A Bayesian CUSUM plot: Diagnosing quality of treatment.

    Science.gov (United States)

    Rosthøj, Steen; Jacobsen, Rikke-Line

    2017-12-01

    To present a CUSUM plot based on Bayesian diagnostic reasoning displaying evidence in favour of "healthy" rather than "sick" quality of treatment (QOT), and to demonstrate a technique using Kaplan-Meier survival curves permitting application to case series with ongoing follow-up. For a case series with known final outcomes: Consider each case a diagnostic test of good versus poor QOT (expected vs. increased failure rates), determine the likelihood ratio (LR) of the observed outcome, convert LR to weight taking log to base 2, and add up weights sequentially in a plot showing how many times odds in favour of good QOT have been doubled. For a series with observed survival times and an expected survival curve: Divide the curve into time intervals, determine "healthy" and specify "sick" risks of failure in each interval, construct a "sick" survival curve, determine the LR of survival or failure at the given observation times, convert to weights, and add up. The Bayesian plot was applied retrospectively to 39 children with acute lymphoblastic leukaemia with completed follow-up, using Nordic collaborative results as reference, showing equal odds between good and poor QOT. In the ongoing treatment trial, with 22 of 37 children still at risk for event, QOT has been monitored with average survival curves as reference, odds so far favoring good QOT 2:1. QOT in small patient series can be assessed with a Bayesian CUSUM plot, retrospectively when all treatment outcomes are known, but also in ongoing series with unfinished follow-up. © 2017 John Wiley & Sons, Ltd.

  16. Collective animal behavior from Bayesian estimation and probability matching.

    Directory of Open Access Journals (Sweden)

    Alfonso Pérez-Escudero

    2011-11-01

    Full Text Available Animals living in groups make movement decisions that depend, among other factors, on social interactions with other group members. Our present understanding of social rules in animal collectives is mainly based on empirical fits to observations, with less emphasis in obtaining first-principles approaches that allow their derivation. Here we show that patterns of collective decisions can be derived from the basic ability of animals to make probabilistic estimations in the presence of uncertainty. We build a decision-making model with two stages: Bayesian estimation and probabilistic matching. In the first stage, each animal makes a Bayesian estimation of which behavior is best to perform taking into account personal information about the environment and social information collected by observing the behaviors of other animals. In the probability matching stage, each animal chooses a behavior with a probability equal to the Bayesian-estimated probability that this behavior is the most appropriate one. This model derives very simple rules of interaction in animal collectives that depend only on two types of reliability parameters, one that each animal assigns to the other animals and another given by the quality of the non-social information. We test our model by obtaining theoretically a rich set of observed collective patterns of decisions in three-spined sticklebacks, Gasterosteus aculeatus, a shoaling fish species. The quantitative link shown between probabilistic estimation and collective rules of behavior allows a better contact with other fields such as foraging, mate selection, neurobiology and psychology, and gives predictions for experiments directly testing the relationship between estimation and collective behavior.

  17. Bayesian hierarchical modelling of North Atlantic windiness

    Science.gov (United States)

    Vanem, E.; Breivik, O. N.

    2013-03-01

    Extreme weather conditions represent serious natural hazards to ship operations and may be the direct cause or contributing factor to maritime accidents. Such severe environmental conditions can be taken into account in ship design and operational windows can be defined that limits hazardous operations to less extreme conditions. Nevertheless, possible changes in the statistics of extreme weather conditions, possibly due to anthropogenic climate change, represent an additional hazard to ship operations that is less straightforward to account for in a consistent way. Obviously, there are large uncertainties as to how future climate change will affect the extreme weather conditions at sea and there is a need for stochastic models that can describe the variability in both space and time at various scales of the environmental conditions. Previously, Bayesian hierarchical space-time models have been developed to describe the variability and complex dependence structures of significant wave height in space and time. These models were found to perform reasonably well and provided some interesting results, in particular, pertaining to long-term trends in the wave climate. In this paper, a similar framework is applied to oceanic windiness and the spatial and temporal variability of the 10-m wind speed over an area in the North Atlantic ocean is investigated. When the results from the model for North Atlantic windiness is compared to the results for significant wave height over the same area, it is interesting to observe that whereas an increasing trend in significant wave height was identified, no statistically significant long-term trend was estimated in windiness. This may indicate that the increase in significant wave height is not due to an increase in locally generated wind waves, but rather to increased swell. This observation is also consistent with studies that have suggested a poleward shift of the main storm tracks.

  18. Bayesian hierarchical modelling of North Atlantic windiness

    Directory of Open Access Journals (Sweden)

    E. Vanem

    2013-03-01

    Full Text Available Extreme weather conditions represent serious natural hazards to ship operations and may be the direct cause or contributing factor to maritime accidents. Such severe environmental conditions can be taken into account in ship design and operational windows can be defined that limits hazardous operations to less extreme conditions. Nevertheless, possible changes in the statistics of extreme weather conditions, possibly due to anthropogenic climate change, represent an additional hazard to ship operations that is less straightforward to account for in a consistent way. Obviously, there are large uncertainties as to how future climate change will affect the extreme weather conditions at sea and there is a need for stochastic models that can describe the variability in both space and time at various scales of the environmental conditions. Previously, Bayesian hierarchical space-time models have been developed to describe the variability and complex dependence structures of significant wave height in space and time. These models were found to perform reasonably well and provided some interesting results, in particular, pertaining to long-term trends in the wave climate. In this paper, a similar framework is applied to oceanic windiness and the spatial and temporal variability of the 10-m wind speed over an area in the North Atlantic ocean is investigated. When the results from the model for North Atlantic windiness is compared to the results for significant wave height over the same area, it is interesting to observe that whereas an increasing trend in significant wave height was identified, no statistically significant long-term trend was estimated in windiness. This may indicate that the increase in significant wave height is not due to an increase in locally generated wind waves, but rather to increased swell. This observation is also consistent with studies that have suggested a poleward shift of the main storm tracks.

  19. Bayesian tomography by interacting Markov chains

    Science.gov (United States)

    Romary, T.

    2017-12-01

    In seismic tomography, we seek to determine the velocity of the undergound from noisy first arrival travel time observations. In most situations, this is an ill posed inverse problem that admits several unperfect solutions. Given an a priori distribution over the parameters of the velocity model, the Bayesian formulation allows to state this problem as a probabilistic one, with a solution under the form of a posterior distribution. The posterior distribution is generally high dimensional and may exhibit multimodality. Moreover, as it is known only up to a constant, the only sensible way to addressthis problem is to try to generate simulations from the posterior. The natural tools to perform these simulations are Monte Carlo Markov chains (MCMC). Classical implementations of MCMC algorithms generally suffer from slow mixing: the generated states are slow to enter the stationary regime, that is to fit the observations, and when one mode of the posterior is eventually identified, it may become difficult to visit others. Using a varying temperature parameter relaxing the constraint on the data may help to enter the stationary regime. Besides, the sequential nature of MCMC makes them ill fitted toparallel implementation. Running a large number of chains in parallel may be suboptimal as the information gathered by each chain is not mutualized. Parallel tempering (PT) can be seen as a first attempt to make parallel chains at different temperatures communicate but only exchange information between current states. In this talk, I will show that PT actually belongs to a general class of interacting Markov chains algorithm. I will also show that this class enables to design interacting schemes that can take advantage of the whole history of the chain, by authorizing exchanges toward already visited states. The algorithms will be illustrated with toy examples and an application to first arrival traveltime tomography.

  20. Bayesian inversion of refraction seismic traveltime data

    Science.gov (United States)

    Ryberg, T.; Haberland, Ch

    2018-03-01

    We apply a Bayesian Markov chain Monte Carlo (McMC) formalism to the inversion of refraction seismic, traveltime data sets to derive 2-D velocity models below linear arrays (i.e. profiles) of sources and seismic receivers. Typical refraction data sets, especially when using the far-offset observations, are known as having experimental geometries which are very poor, highly ill-posed and far from being ideal. As a consequence, the structural resolution quickly degrades with depth. Conventional inversion techniques, based on regularization, potentially suffer from the choice of appropriate inversion parameters (i.e. number and distribution of cells, starting velocity models, damping and smoothing constraints, data noise level, etc.) and only local model space exploration. McMC techniques are used for exhaustive sampling of the model space without the need of prior knowledge (or assumptions) of inversion parameters, resulting in a large number of models fitting the observations. Statistical analysis of these models allows to derive an average (reference) solution and its standard deviation, thus providing uncertainty estimates of the inversion result. The highly non-linear character of the inversion problem, mainly caused by the experiment geometry, does not allow to derive a reference solution and error map by a simply averaging procedure. We present a modified averaging technique, which excludes parts of the prior distribution in the posterior values due to poor ray coverage, thus providing reliable estimates of inversion model properties even in those parts of the models. The model is discretized by a set of Voronoi polygons (with constant slowness cells) or a triangulated mesh (with interpolation within the triangles). Forward traveltime calculations are performed by a fast, finite-difference-based eikonal solver. The method is applied to a data set from a refraction seismic survey from Northern Namibia and compared to conventional tomography. An inversion test

  1. Objective Bayesianism and the Maximum Entropy Principle

    Directory of Open Access Journals (Sweden)

    Jon Williamson

    2013-09-01

    Full Text Available Objective Bayesian epistemology invokes three norms: the strengths of our beliefs should be probabilities; they should be calibrated to our evidence of physical probabilities; and they should otherwise equivocate sufficiently between the basic propositions that we can express. The three norms are sometimes explicated by appealing to the maximum entropy principle, which says that a belief function should be a probability function, from all those that are calibrated to evidence, that has maximum entropy. However, the three norms of objective Bayesianism are usually justified in different ways. In this paper, we show that the three norms can all be subsumed under a single justification in terms of minimising worst-case expected loss. This, in turn, is equivalent to maximising a generalised notion of entropy. We suggest that requiring language invariance, in addition to minimising worst-case expected loss, motivates maximisation of standard entropy as opposed to maximisation of other instances of generalised entropy. Our argument also provides a qualified justification for updating degrees of belief by Bayesian conditionalisation. However, conditional probabilities play a less central part in the objective Bayesian account than they do under the subjective view of Bayesianism, leading to a reduced role for Bayes’ Theorem.

  2. A default Bayesian hypothesis test for mediation.

    Science.gov (United States)

    Nuijten, Michèle B; Wetzels, Ruud; Matzke, Dora; Dolan, Conor V; Wagenmakers, Eric-Jan

    2015-03-01

    In order to quantify the relationship between multiple variables, researchers often carry out a mediation analysis. In such an analysis, a mediator (e.g., knowledge of a healthy diet) transmits the effect from an independent variable (e.g., classroom instruction on a healthy diet) to a dependent variable (e.g., consumption of fruits and vegetables). Almost all mediation analyses in psychology use frequentist estimation and hypothesis-testing techniques. A recent exception is Yuan and MacKinnon (Psychological Methods, 14, 301-322, 2009), who outlined a Bayesian parameter estimation procedure for mediation analysis. Here we complete the Bayesian alternative to frequentist mediation analysis by specifying a default Bayesian hypothesis test based on the Jeffreys-Zellner-Siow approach. We further extend this default Bayesian test by allowing a comparison to directional or one-sided alternatives, using Markov chain Monte Carlo techniques implemented in JAGS. All Bayesian tests are implemented in the R package BayesMed (Nuijten, Wetzels, Matzke, Dolan, & Wagenmakers, 2014).

  3. Classifying emotion in Twitter using Bayesian network

    Science.gov (United States)

    Surya Asriadie, Muhammad; Syahrul Mubarok, Mohamad; Adiwijaya

    2018-03-01

    Language is used to express not only facts, but also emotions. Emotions are noticeable from behavior up to the social media statuses written by a person. Analysis of emotions in a text is done in a variety of media such as Twitter. This paper studies classification of emotions on twitter using Bayesian network because of its ability to model uncertainty and relationships between features. The result is two models based on Bayesian network which are Full Bayesian Network (FBN) and Bayesian Network with Mood Indicator (BNM). FBN is a massive Bayesian network where each word is treated as a node. The study shows the method used to train FBN is not very effective to create the best model and performs worse compared to Naive Bayes. F1-score for FBN is 53.71%, while for Naive Bayes is 54.07%. BNM is proposed as an alternative method which is based on the improvement of Multinomial Naive Bayes and has much lower computational complexity compared to FBN. Even though it’s not better compared to FBN, the resulting model successfully improves the performance of Multinomial Naive Bayes. F1-Score for Multinomial Naive Bayes model is 51.49%, while for BNM is 52.14%.

  4. Optimization of inspection and replacement period by using Bayesian statistics

    International Nuclear Information System (INIS)

    Kasai, Masao; Watanabe, Yasushi; Kusakari, Yoshiyuki; Notoya, Junichi

    2006-01-01

    This study describes the formulations to optimize the time interval of inspections and/or replacements of equipment/parts taking into account the probability density functions (PDF) for failure rates and parameters of failure distribution functions (FDF) and evaluates the optimized results of these time intervals using our formulations by comparing with those using only representative values of failure rates and the parameters of FDF instead of using these PDFs. The PDFs are obtained with Bayesian method and the representative values are obtained with likelihood estimation method. However, any significant difference is not observed between both optimized results within our preliminary calculations. (author)

  5. Bayesian conformational analysis of ring molecules through reversible jump MCMC

    DEFF Research Database (Denmark)

    Nolsøe, Kim; Kessler, Mathieu; Pérez, José

    2005-01-01

    In this paper we address the problem of classifying the conformations of mmembered rings using experimental observations obtained by crystal structure analysis. We formulate a model for the data generation mechanism that consists in a multidimensional mixture model. We perform inference for the p...... for the proportions and the components in a Bayesian framework, implementing an MCMC Reversible Jumps Algorithm to obtain samples of the posterior distributions. The method is illustrated on a simulated data set and on real data corresponding to cyclo-octane structures....

  6. Bayesian inference of substrate properties from film behavior

    International Nuclear Information System (INIS)

    Aggarwal, R; Demkowicz, M J; Marzouk, Y M

    2015-01-01

    We demonstrate that by observing the behavior of a film deposited on a substrate, certain features of the substrate may be inferred with quantified uncertainty using Bayesian methods. We carry out this demonstration on an illustrative film/substrate model where the substrate is a Gaussian random field and the film is a two-component mixture that obeys the Cahn–Hilliard equation. We construct a stochastic reduced order model to describe the film/substrate interaction and use it to infer substrate properties from film behavior. This quantitative inference strategy may be adapted to other film/substrate systems. (paper)

  7. Bayesian optimal experimental design for the Shock-tube experiment

    International Nuclear Information System (INIS)

    Terejanu, G; Bryant, C M; Miki, K

    2013-01-01

    The sequential optimal experimental design formulated as an information-theoretic sensitivity analysis is applied to the ignition delay problem using real experimental. The optimal design is obtained by maximizing the statistical dependence between the model parameters and observables, which is quantified in this study using mutual information. This is naturally posed in the Bayesian framework. The study shows that by monitoring the information gain after each measurement update, one can design a stopping criteria for the experimental process which gives a minimal set of experiments to efficiently learn the Arrhenius parameters.

  8. Bayesian Parameter Estimation via Filtering and Functional Approximations

    KAUST Repository

    Matthies, Hermann G.

    2016-11-25

    The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation and updating of parameters in a computational model. This is a filter acting on random variables, and while its Monte Carlo variant --- the Ensemble Kalman Filter (EnKF) --- is fairly straightforward, we subsequently only sketch its implementation with the help of functional representations.

  9. Bayesian Parameter Estimation via Filtering and Functional Approximations

    KAUST Repository

    Matthies, Hermann G.; Litvinenko, Alexander; Rosic, Bojana V.; Zander, Elmar

    2016-01-01

    The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation and updating of parameters in a computational model. This is a filter acting on random variables, and while its Monte Carlo variant --- the Ensemble Kalman Filter (EnKF) --- is fairly straightforward, we subsequently only sketch its implementation with the help of functional representations.

  10. Empirical Bayesian inference and model uncertainty

    International Nuclear Information System (INIS)

    Poern, K.

    1994-01-01

    This paper presents a hierarchical or multistage empirical Bayesian approach for the estimation of uncertainty concerning the intensity of a homogeneous Poisson process. A class of contaminated gamma distributions is considered to describe the uncertainty concerning the intensity. These distributions in turn are defined through a set of secondary parameters, the knowledge of which is also described and updated via Bayes formula. This two-stage Bayesian approach is an example where the modeling uncertainty is treated in a comprehensive way. Each contaminated gamma distributions, represented by a point in the 3D space of secondary parameters, can be considered as a specific model of the uncertainty about the Poisson intensity. Then, by the empirical Bayesian method each individual model is assigned a posterior probability

  11. Bayesian Inference Methods for Sparse Channel Estimation

    DEFF Research Database (Denmark)

    Pedersen, Niels Lovmand

    2013-01-01

    This thesis deals with sparse Bayesian learning (SBL) with application to radio channel estimation. As opposed to the classical approach for sparse signal representation, we focus on the problem of inferring complex signals. Our investigations within SBL constitute the basis for the development...... of Bayesian inference algorithms for sparse channel estimation. Sparse inference methods aim at finding the sparse representation of a signal given in some overcomplete dictionary of basis vectors. Within this context, one of our main contributions to the field of SBL is a hierarchical representation...... analysis of the complex prior representation, where we show that the ability to induce sparse estimates of a given prior heavily depends on the inference method used and, interestingly, whether real or complex variables are inferred. We also show that the Bayesian estimators derived from the proposed...

  12. Bayesian estimation of dose rate effectiveness

    International Nuclear Information System (INIS)

    Arnish, J.J.; Groer, P.G.

    2000-01-01

    A Bayesian statistical method was used to quantify the effectiveness of high dose rate 137 Cs gamma radiation at inducing fatal mammary tumours and increasing the overall mortality rate in BALB/c female mice. The Bayesian approach considers both the temporal and dose dependence of radiation carcinogenesis and total mortality. This paper provides the first direct estimation of dose rate effectiveness using Bayesian statistics. This statistical approach provides a quantitative description of the uncertainty of the factor characterising the dose rate in terms of a probability density function. The results show that a fixed dose from 137 Cs gamma radiation delivered at a high dose rate is more effective at inducing fatal mammary tumours and increasing the overall mortality rate in BALB/c female mice than the same dose delivered at a low dose rate. (author)

  13. A Bayesian Approach for Summarizing and Modeling Time-Series Exposure Data with Left Censoring.

    Science.gov (United States)

    Houseman, E Andres; Virji, M Abbas

    2017-08-01

    were significant in some frequentist models, but in the Bayesian model their credible intervals contained zero; such discrepancies were observed in multiple datasets. Variance components from the Bayesian model reflected substantial autocorrelation, consistent with the frequentist models, except for the auto-regressive moving average model. Plots of means from the Bayesian model showed good fit to the observed data. The proposed Bayesian model provides an approach for modeling non-stationary autocorrelation in a hierarchical modeling framework to estimate task means, standard deviations, quantiles, and parameter estimates for covariates that are less biased and have better performance characteristics than some of the contemporary methods. Published by Oxford University Press on behalf of the British Occupational Hygiene Society 2017.

  14. Variational Bayesian Learning for Wavelet Independent Component Analysis

    Science.gov (United States)

    Roussos, E.; Roberts, S.; Daubechies, I.

    2005-11-01

    In an exploratory approach to data analysis, it is often useful to consider the observations as generated from a set of latent generators or "sources" via a generally unknown mapping. For the noisy overcomplete case, where we have more sources than observations, the problem becomes extremely ill-posed. Solutions to such inverse problems can, in many cases, be achieved by incorporating prior knowledge about the problem, captured in the form of constraints. This setting is a natural candidate for the application of the Bayesian methodology, allowing us to incorporate "soft" constraints in a natural manner. The work described in this paper is mainly driven by problems in functional magnetic resonance imaging of the brain, for the neuro-scientific goal of extracting relevant "maps" from the data. This can be stated as a `blind' source separation problem. Recent experiments in the field of neuroscience show that these maps are sparse, in some appropriate sense. The separation problem can be solved by independent component analysis (ICA), viewed as a technique for seeking sparse components, assuming appropriate distributions for the sources. We derive a hybrid wavelet-ICA model, transforming the signals into a domain where the modeling assumption of sparsity of the coefficients with respect to a dictionary is natural. We follow a graphical modeling formalism, viewing ICA as a probabilistic generative model. We use hierarchical source and mixing models and apply Bayesian inference to the problem. This allows us to perform model selection in order to infer the complexity of the representation, as well as automatic denoising. Since exact inference and learning in such a model is intractable, we follow a variational Bayesian mean-field approach in the conjugate-exponential family of distributions, for efficient unsupervised learning in multi-dimensional settings. The performance of the proposed algorithm is demonstrated on some representative experiments.

  15. A Nonparametric Bayesian Approach For Emission Tomography Reconstruction

    International Nuclear Information System (INIS)

    Barat, Eric; Dautremer, Thomas

    2007-01-01

    We introduce a PET reconstruction algorithm following a nonparametric Bayesian (NPB) approach. In contrast with Expectation Maximization (EM), the proposed technique does not rely on any space discretization. Namely, the activity distribution--normalized emission intensity of the spatial poisson process--is considered as a spatial probability density and observations are the projections of random emissions whose distribution has to be estimated. This approach is nonparametric in the sense that the quantity of interest belongs to the set of probability measures on R k (for reconstruction in k-dimensions) and it is Bayesian in the sense that we define a prior directly on this spatial measure. In this context, we propose to model the nonparametric probability density as an infinite mixture of multivariate normal distributions. As a prior for this mixture we consider a Dirichlet Process Mixture (DPM) with a Normal-Inverse Wishart (NIW) model as base distribution of the Dirichlet Process. As in EM-family reconstruction, we use a data augmentation scheme where the set of hidden variables are the emission locations for each observed line of response in the continuous object space. Thanks to the data augmentation, we propose a Markov Chain Monte Carlo (MCMC) algorithm (Gibbs sampler) which is able to generate draws from the posterior distribution of the spatial intensity. A difference with EM is that one step of the Gibbs sampler corresponds to the generation of emission locations while only the expected number of emissions per pixel/voxel is used in EM. Another key difference is that the estimated spatial intensity is a continuous function such that there is no need to compute a projection matrix. Finally, draws from the intensity posterior distribution allow the estimation of posterior functionnals like the variance or confidence intervals. Results are presented for simulated data based on a 2D brain phantom and compared to Bayesian MAP-EM

  16. Prediction of road accidents: A Bayesian hierarchical approach.

    Science.gov (United States)

    Deublein, Markus; Schubert, Matthias; Adey, Bryan T; Köhler, Jochen; Faber, Michael H

    2013-03-01

    In this paper a novel methodology for the prediction of the occurrence of road accidents is presented. The methodology utilizes a combination of three statistical methods: (1) gamma-updating of the occurrence rates of injury accidents and injured road users, (2) hierarchical multivariate Poisson-lognormal regression analysis taking into account correlations amongst multiple dependent model response variables and effects of discrete accident count data e.g. over-dispersion, and (3) Bayesian inference algorithms, which are applied by means of data mining techniques supported by Bayesian Probabilistic Networks in order to represent non-linearity between risk indicating and model response variables, as well as different types of uncertainties which might be present in the development of the specific models. Prior Bayesian Probabilistic Networks are first established by means of multivariate regression analysis of the observed frequencies of the model response variables, e.g. the occurrence of an accident, and observed values of the risk indicating variables, e.g. degree of road curvature. Subsequently, parameter learning is done using updating algorithms, to determine the posterior predictive probability distributions of the model response variables, conditional on the values of the risk indicating variables. The methodology is illustrated through a case study using data of the Austrian rural motorway network. In the case study, on randomly selected road segments the methodology is used to produce a model to predict the expected number of accidents in which an injury has occurred and the expected number of light, severe and fatally injured road users. Additionally, the methodology is used for geo-referenced identification of road sections with increased occurrence probabilities of injury accident events on a road link between two Austrian cities. It is shown that the proposed methodology can be used to develop models to estimate the occurrence of road accidents for any

  17. A nonparametric Bayesian approach for genetic evaluation in ...

    African Journals Online (AJOL)

    South African Journal of Animal Science ... the Bayesian and Classical models, a Bayesian procedure is provided which allows these random ... data from the Elsenburg Dormer sheep stud and data from a simulation experiment are utilized. >

  18. Bayesian disease mapping: hierarchical modeling in spatial epidemiology

    National Research Council Canada - National Science Library

    Lawson, Andrew

    2013-01-01

    .... Exploring these new developments, Bayesian Disease Mapping: Hierarchical Modeling in Spatial Epidemiology, Second Edition provides an up-to-date, cohesive account of the full range of Bayesian disease mapping methods and applications...

  19. Sparse reconstruction using distribution agnostic bayesian matching pursuit

    KAUST Repository

    Masood, Mudassir; Al-Naffouri, Tareq Y.

    2013-01-01

    A fast matching pursuit method using a Bayesian approach is introduced for sparse signal recovery. This method performs Bayesian estimates of sparse signals even when the signal prior is non-Gaussian or unknown. It is agnostic on signal statistics

  20. Bayesian uncertainty analyses of probabilistic risk models

    International Nuclear Information System (INIS)

    Pulkkinen, U.

    1989-01-01

    Applications of Bayesian principles to the uncertainty analyses are discussed in the paper. A short review of the most important uncertainties and their causes is provided. An application of the principle of maximum entropy to the determination of Bayesian prior distributions is described. An approach based on so called probabilistic structures is presented in order to develop a method of quantitative evaluation of modelling uncertainties. The method is applied to a small example case. Ideas for application areas for the proposed method are discussed

  1. Justifying Objective Bayesianism on Predicate Languages

    Directory of Open Access Journals (Sweden)

    Jürgen Landes

    2015-04-01

    Full Text Available Objective Bayesianism says that the strengths of one’s beliefs ought to be probabilities, calibrated to physical probabilities insofar as one has evidence of them, and otherwise sufficiently equivocal. These norms of belief are often explicated using the maximum entropy principle. In this paper we investigate the extent to which one can provide a unified justification of the objective Bayesian norms in the case in which the background language is a first-order predicate language, with a view to applying the resulting formalism to inductive logic. We show that the maximum entropy principle can be motivated largely in terms of minimising worst-case expected loss.

  2. Motion Learning Based on Bayesian Program Learning

    Directory of Open Access Journals (Sweden)

    Cheng Meng-Zhen

    2017-01-01

    Full Text Available The concept of virtual human has been highly anticipated since the 1980s. By using computer technology, Human motion simulation could generate authentic visual effect, which could cheat human eyes visually. Bayesian Program Learning train one or few motion data, generate new motion data by decomposing and combining. And the generated motion will be more realistic and natural than the traditional one.In this paper, Motion learning based on Bayesian program learning allows us to quickly generate new motion data, reduce workload, improve work efficiency, reduce the cost of motion capture, and improve the reusability of data.

  3. Length Scales in Bayesian Automatic Adaptive Quadrature

    Directory of Open Access Journals (Sweden)

    Adam Gh.

    2016-01-01

    Full Text Available Two conceptual developments in the Bayesian automatic adaptive quadrature approach to the numerical solution of one-dimensional Riemann integrals [Gh. Adam, S. Adam, Springer LNCS 7125, 1–16 (2012] are reported. First, it is shown that the numerical quadrature which avoids the overcomputing and minimizes the hidden floating point loss of precision asks for the consideration of three classes of integration domain lengths endowed with specific quadrature sums: microscopic (trapezoidal rule, mesoscopic (Simpson rule, and macroscopic (quadrature sums of high algebraic degrees of precision. Second, sensitive diagnostic tools for the Bayesian inference on macroscopic ranges, coming from the use of Clenshaw-Curtis quadrature, are derived.

  4. Bayesian parameter estimation in probabilistic risk assessment

    International Nuclear Information System (INIS)

    Siu, Nathan O.; Kelly, Dana L.

    1998-01-01

    Bayesian statistical methods are widely used in probabilistic risk assessment (PRA) because of their ability to provide useful estimates of model parameters when data are sparse and because the subjective probability framework, from which these methods are derived, is a natural framework to address the decision problems motivating PRA. This paper presents a tutorial on Bayesian parameter estimation especially relevant to PRA. It summarizes the philosophy behind these methods, approaches for constructing likelihood functions and prior distributions, some simple but realistic examples, and a variety of cautions and lessons regarding practical applications. References are also provided for more in-depth coverage of various topics

  5. Bayesian estimation and tracking a practical guide

    CERN Document Server

    Haug, Anton J

    2012-01-01

    A practical approach to estimating and tracking dynamic systems in real-worl applications Much of the literature on performing estimation for non-Gaussian systems is short on practical methodology, while Gaussian methods often lack a cohesive derivation. Bayesian Estimation and Tracking addresses the gap in the field on both accounts, providing readers with a comprehensive overview of methods for estimating both linear and nonlinear dynamic systems driven by Gaussian and non-Gaussian noices. Featuring a unified approach to Bayesian estimation and tracking, the book emphasizes the derivation

  6. COBRA: a Bayesian approach to pulsar searching

    Science.gov (United States)

    Lentati, L.; Champion, D. J.; Kramer, M.; Barr, E.; Torne, P.

    2018-02-01

    We introduce COBRA, a GPU-accelerated Bayesian analysis package for performing pulsar searching, that uses candidates from traditional search techniques to set the prior used for the periodicity of the source, and performs a blind search in all remaining parameters. COBRA incorporates models for both isolated and accelerated systems, as well as both Keplerian and relativistic binaries, and exploits pulse phase information to combine search epochs coherently, over time, frequency or across multiple telescopes. We demonstrate the efficacy of our approach in a series of simulations that challenge typical search techniques, including highly aliased signals, and relativistic binary systems. In the most extreme case, we simulate an 8 h observation containing 24 orbits of a pulsar in a binary with a 30 M⊙ companion. Even in this scenario we show that we can build up from an initial low-significance candidate, to fully recovering the signal. We also apply the method to survey data of three pulsars from the globular cluster 47Tuc: PSRs J0024-7204D, J0023-7203J and J0024-7204R. This final pulsar is in a 1.6 h binary, the shortest of any pulsar in 47Tuc, and additionally shows significant scintillation. By allowing the amplitude of the source to vary as a function of time, however, we show that we are able to obtain optimal combinations of such noisy data. We also demonstrate the ability of COBRA to perform high-precision pulsar timing directly on the single pulse survey data, and obtain a 95 per cent upper limit on the eccentricity of PSR J0024-7204R of εb < 0.0007.

  7. Bayesian methods to estimate urban growth potential

    Science.gov (United States)

    Smith, Jordan W.; Smart, Lindsey S.; Dorning, Monica; Dupéy, Lauren Nicole; Méley, Andréanne; Meentemeyer, Ross K.

    2017-01-01

    Urban growth often influences the production of ecosystem services. The impacts of urbanization on landscapes can subsequently affect landowners’ perceptions, values and decisions regarding their land. Within land-use and land-change research, very few models of dynamic landscape-scale processes like urbanization incorporate empirically-grounded landowner decision-making processes. Very little attention has focused on the heterogeneous decision-making processes that aggregate to influence broader-scale patterns of urbanization. We examine the land-use tradeoffs faced by individual landowners in one of the United States’ most rapidly urbanizing regions − the urban area surrounding Charlotte, North Carolina. We focus on the land-use decisions of non-industrial private forest owners located across the region’s development gradient. A discrete choice experiment is used to determine the critical factors influencing individual forest owners’ intent to sell their undeveloped properties across a series of experimentally varied scenarios of urban growth. Data are analyzed using a hierarchical Bayesian approach. The estimates derived from the survey data are used to modify a spatially-explicit trend-based urban development potential model, derived from remotely-sensed imagery and observed changes in the region’s socioeconomic and infrastructural characteristics between 2000 and 2011. This modeling approach combines the theoretical underpinnings of behavioral economics with spatiotemporal data describing a region’s historical development patterns. By integrating empirical social preference data into spatially-explicit urban growth models, we begin to more realistically capture processes as well as patterns that drive the location, magnitude and rates of urban growth.

  8. Probabilistic Inference: Task Dependency and Individual Differences of Probability Weighting Revealed by Hierarchical Bayesian Modeling.

    Science.gov (United States)

    Boos, Moritz; Seer, Caroline; Lange, Florian; Kopp, Bruno

    2016-01-01

    Cognitive determinants of probabilistic inference were examined using hierarchical Bayesian modeling techniques. A classic urn-ball paradigm served as experimental strategy, involving a factorial two (prior probabilities) by two (likelihoods) design. Five computational models of cognitive processes were compared with the observed behavior. Parameter-free Bayesian posterior probabilities and parameter-free base rate neglect provided inadequate models of probabilistic inference. The introduction of distorted subjective probabilities yielded more robust and generalizable results. A general class of (inverted) S-shaped probability weighting functions had been proposed; however, the possibility of large differences in probability distortions not only across experimental conditions, but also across individuals, seems critical for the model's success. It also seems advantageous to consider individual differences in parameters of probability weighting as being sampled from weakly informative prior distributions of individual parameter values. Thus, the results from hierarchical Bayesian modeling converge with previous results in revealing that probability weighting parameters show considerable task dependency and individual differences. Methodologically, this work exemplifies the usefulness of hierarchical Bayesian modeling techniques for cognitive psychology. Theoretically, human probabilistic inference might be best described as the application of individualized strategic policies for Bayesian belief revision.

  9. Probabilistic inference: Task dependency and individual differences of probability weighting revealed by hierarchical Bayesian modelling

    Directory of Open Access Journals (Sweden)

    Moritz eBoos

    2016-05-01

    Full Text Available Cognitive determinants of probabilistic inference were examined using hierarchical Bayesian modelling techniques. A classic urn-ball paradigm served as experimental strategy, involving a factorial two (prior probabilities by two (likelihoods design. Five computational models of cognitive processes were compared with the observed behaviour. Parameter-free Bayesian posterior probabilities and parameter-free base rate neglect provided inadequate models of probabilistic inference. The introduction of distorted subjective probabilities yielded more robust and generalizable results. A general class of (inverted S-shaped probability weighting functions had been proposed; however, the possibility of large differences in probability distortions not only across experimental conditions, but also across individuals, seems critical for the model’s success. It also seems advantageous to consider individual differences in parameters of probability weighting as being sampled from weakly informative prior distributions of individual parameter values. Thus, the results from hierarchical Bayesian modelling converge with previous results in revealing that probability weighting parameters show considerable task dependency and individual differences. Methodologically, this work exemplifies the usefulness of hierarchical Bayesian modelling techniques for cognitive psychology. Theoretically, human probabilistic inference might be best described as the application of individualized strategic policies for Bayesian belief revision.

  10. A Fault Diagnosis Methodology for Gear Pump Based on EEMD and Bayesian Network.

    Science.gov (United States)

    Liu, Zengkai; Liu, Yonghong; Shan, Hongkai; Cai, Baoping; Huang, Qing

    2015-01-01

    This paper proposes a fault diagnosis methodology for a gear pump based on the ensemble empirical mode decomposition (EEMD) method and the Bayesian network. Essentially, the presented scheme is a multi-source information fusion based methodology. Compared with the conventional fault diagnosis with only EEMD, the proposed method is able to take advantage of all useful information besides sensor signals. The presented diagnostic Bayesian network consists of a fault layer, a fault feature layer and a multi-source information layer. Vibration signals from sensor measurement are decomposed by the EEMD method and the energy of intrinsic mode functions (IMFs) are calculated as fault features. These features are added into the fault feature layer in the Bayesian network. The other sources of useful information are added to the information layer. The generalized three-layer Bayesian network can be developed by fully incorporating faults and fault symptoms as well as other useful information such as naked eye inspection and maintenance records. Therefore, diagnostic accuracy and capacity can be improved. The proposed methodology is applied to the fault diagnosis of a gear pump and the structure and parameters of the Bayesian network is established. Compared with artificial neural network and support vector machine classification algorithms, the proposed model has the best diagnostic performance when sensor data is used only. A case study has demonstrated that some information from human observation or system repair records is very helpful to the fault diagnosis. It is effective and efficient in diagnosing faults based on uncertain, incomplete information.

  11. Bayesian conditional-independence modeling of the AIDS epidemic in England and Wales

    Science.gov (United States)

    Gilks, Walter R.; De Angelis, Daniela; Day, Nicholas E.

    We describe the use of conditional-independence modeling, Bayesian inference and Markov chain Monte Carlo, to model and project the HIV-AIDS epidemic in homosexual/bisexual males in England and Wales. Complexity in this analysis arises through selectively missing data, indirectly observed underlying processes, and measurement error. Our emphasis is on presentation and discussion of the concepts, not on the technicalities of this analysis, which can be found elsewhere [D. De Angelis, W.R. Gilks, N.E. Day, Bayesian projection of the the acquired immune deficiency syndrome epidemic (with discussion), Applied Statistics, in press].

  12. Basic and Advanced Bayesian Structural Equation Modeling With Applications in the Medical and Behavioral Sciences

    CERN Document Server

    Lee, Sik-Yum

    2012-01-01

    This book provides clear instructions to researchers on how to apply Structural Equation Models (SEMs) for analyzing the inter relationships between observed and latent variables. Basic and Advanced Bayesian Structural Equation Modeling introduces basic and advanced SEMs for analyzing various kinds of complex data, such as ordered and unordered categorical data, multilevel data, mixture data, longitudinal data, highly non-normal data, as well as some of their combinations. In addition, Bayesian semiparametric SEMs to capture the true distribution of explanatory latent variables are introduce

  13. A Fast Iterative Bayesian Inference Algorithm for Sparse Channel Estimation

    DEFF Research Database (Denmark)

    Pedersen, Niels Lovmand; Manchón, Carles Navarro; Fleury, Bernard Henri

    2013-01-01

    representation of the Bessel K probability density function; a highly efficient, fast iterative Bayesian inference method is then applied to the proposed model. The resulting estimator outperforms other state-of-the-art Bayesian and non-Bayesian estimators, either by yielding lower mean squared estimation error...

  14. A Gentle Introduction to Bayesian Analysis : Applications to Developmental Research

    NARCIS (Netherlands)

    Van de Schoot, Rens; Kaplan, David; Denissen, Jaap; Asendorpf, Jens B.; Neyer, Franz J.; van Aken, Marcel A G

    2014-01-01

    Bayesian statistical methods are becoming ever more popular in applied and fundamental research. In this study a gentle introduction to Bayesian analysis is provided. It is shown under what circumstances it is attractive to use Bayesian estimation, and how to interpret properly the results. First,

  15. A gentle introduction to Bayesian analysis : Applications to developmental research

    NARCIS (Netherlands)

    van de Schoot, R.; Kaplan, D.; Denissen, J.J.A.; Asendorpf, J.B.; Neyer, F.J.; van Aken, M.A.G.

    2014-01-01

    Bayesian statistical methods are becoming ever more popular in applied and fundamental research. In this study a gentle introduction to Bayesian analysis is provided. It is shown under what circumstances it is attractive to use Bayesian estimation, and how to interpret properly the results. First,

  16. A default Bayesian hypothesis test for ANOVA designs

    NARCIS (Netherlands)

    Wetzels, R.; Grasman, R.P.P.P.; Wagenmakers, E.J.

    2012-01-01

    This article presents a Bayesian hypothesis test for analysis of variance (ANOVA) designs. The test is an application of standard Bayesian methods for variable selection in regression models. We illustrate the effect of various g-priors on the ANOVA hypothesis test. The Bayesian test for ANOVA

  17. Prior approval: the growth of Bayesian methods in psychology.

    Science.gov (United States)

    Andrews, Mark; Baguley, Thom

    2013-02-01

    Within the last few years, Bayesian methods of data analysis in psychology have proliferated. In this paper, we briefly review the history or the Bayesian approach to statistics, and consider the implications that Bayesian methods have for the theory and practice of data analysis in psychology.

  18. Robust Learning of High-dimensional Biological Networks with Bayesian Networks

    Science.gov (United States)

    Nägele, Andreas; Dejori, Mathäus; Stetter, Martin

    Structure learning of Bayesian networks applied to gene expression data has become a potentially useful method to estimate interactions between genes. However, the NP-hardness of Bayesian network structure learning renders the reconstruction of the full genetic network with thousands of genes unfeasible. Consequently, the maximal network size is usually restricted dramatically to a small set of genes (corresponding with variables in the Bayesian network). Although this feature reduction step makes structure learning computationally tractable, on the downside, the learned structure might be adversely affected due to the introduction of missing genes. Additionally, gene expression data are usually very sparse with respect to the number of samples, i.e., the number of genes is much greater than the number of different observations. Given these problems, learning robust network features from microarray data is a challenging task. This chapter presents several approaches tackling the robustness issue in order to obtain a more reliable estimation of learned network features.

  19. Survival Bayesian Estimation of Exponential-Gamma Under Linex Loss Function

    Science.gov (United States)

    Rizki, S. W.; Mara, M. N.; Sulistianingsih, E.

    2017-06-01

    This paper elaborates a research of the cancer patients after receiving a treatment in cencored data using Bayesian estimation under Linex Loss function for Survival Model which is assumed as an exponential distribution. By giving Gamma distribution as prior and likelihood function produces a gamma distribution as posterior distribution. The posterior distribution is used to find estimatior {\\hat{λ }}BL by using Linex approximation. After getting {\\hat{λ }}BL, the estimators of hazard function {\\hat{h}}BL and survival function {\\hat{S}}BL can be found. Finally, we compare the result of Maximum Likelihood Estimation (MLE) and Linex approximation to find the best method for this observation by finding smaller MSE. The result shows that MSE of hazard and survival under MLE are 2.91728E-07 and 0.000309004 and by using Bayesian Linex worths 2.8727E-07 and 0.000304131, respectively. It concludes that the Bayesian Linex is better than MLE.

  20. Bayesian interpolation in a dynamic sinusoidal model with application to packet-loss concealment

    DEFF Research Database (Denmark)

    Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Cemgil, Ali Taylan

    2010-01-01

    a Bayesian inference scheme for the missing observations, hidden states and model parameters of the dynamic model. The inference scheme is based on a Markov chain Monte Carlo method known as Gibbs sampler. We illustrate the performance of the inference scheme to the application of packet-loss concealment...

  1. Bayesian Maximum Entropy prediction of soil categories using a traditional soil map as soft information.

    NARCIS (Netherlands)

    Brus, D.J.; Bogaert, P.; Heuvelink, G.B.M.

    2008-01-01

    Bayesian Maximum Entropy was used to estimate the probabilities of occurrence of soil categories in the Netherlands, and to simulate realizations from the associated multi-point pdf. Besides the hard observations (H) of the categories at 8369 locations, the soil map of the Netherlands 1:50 000 was

  2. A non-parametric Bayesian approach to decompounding from high frequency data

    NARCIS (Netherlands)

    Gugushvili, Shota; van der Meulen, F.H.; Spreij, Peter

    2016-01-01

    Given a sample from a discretely observed compound Poisson process, we consider non-parametric estimation of the density f0 of its jump sizes, as well as of its intensity λ0. We take a Bayesian approach to the problem and specify the prior on f0 as the Dirichlet location mixture of normal densities.

  3. Upper limit for Poisson variable incorporating systematic uncertainties by Bayesian approach

    International Nuclear Information System (INIS)

    Zhu, Yongsheng

    2007-01-01

    To calculate the upper limit for the Poisson observable at given confidence level with inclusion of systematic uncertainties in background expectation and signal efficiency, formulations have been established along the line of Bayesian approach. A FORTRAN program, BPULE, has been developed to implement the upper limit calculation

  4. Bayesian Sensitivity Analysis of Statistical Models with Missing Data.

    Science.gov (United States)

    Zhu, Hongtu; Ibrahim, Joseph G; Tang, Niansheng

    2014-04-01

    Methods for handling missing data depend strongly on the mechanism that generated the missing values, such as missing completely at random (MCAR) or missing at random (MAR), as well as other distributional and modeling assumptions at various stages. It is well known that the resulting estimates and tests may be sensitive to these assumptions as well as to outlying observations. In this paper, we introduce various perturbations to modeling assumptions and individual observations, and then develop a formal sensitivity analysis to assess these perturbations in the Bayesian analysis of statistical models with missing data. We develop a geometric framework, called the Bayesian perturbation manifold, to characterize the intrinsic structure of these perturbations. We propose several intrinsic influence measures to perform sensitivity analysis and quantify the effect of various perturbations to statistical models. We use the proposed sensitivity analysis procedure to systematically investigate the tenability of the non-ignorable missing at random (NMAR) assumption. Simulation studies are conducted to evaluate our methods, and a dataset is analyzed to illustrate the use of our diagnostic measures.

  5. MAP estimators and their consistency in Bayesian nonparametric inverse problems

    KAUST Repository

    Dashti, M.

    2013-09-01

    We consider the inverse problem of estimating an unknown function u from noisy measurements y of a known, possibly nonlinear, map applied to u. We adopt a Bayesian approach to the problem and work in a setting where the prior measure is specified as a Gaussian random field μ0. We work under a natural set of conditions on the likelihood which implies the existence of a well-posed posterior measure, μy. Under these conditions, we show that the maximum a posteriori (MAP) estimator is well defined as the minimizer of an Onsager-Machlup functional defined on the Cameron-Martin space of the prior; thus, we link a problem in probability with a problem in the calculus of variations. We then consider the case where the observational noise vanishes and establish a form of Bayesian posterior consistency for the MAP estimator. We also prove a similar result for the case where the observation of can be repeated as many times as desired with independent identically distributed noise. The theory is illustrated with examples from an inverse problem for the Navier-Stokes equation, motivated by problems arising in weather forecasting, and from the theory of conditioned diffusions, motivated by problems arising in molecular dynamics. © 2013 IOP Publishing Ltd.

  6. Approximate Bayesian computation for forward modeling in cosmology

    International Nuclear Information System (INIS)

    Akeret, Joël; Refregier, Alexandre; Amara, Adam; Seehars, Sebastian; Hasner, Caspar

    2015-01-01

    Bayesian inference is often used in cosmology and astrophysics to derive constraints on model parameters from observations. This approach relies on the ability to compute the likelihood of the data given a choice of model parameters. In many practical situations, the likelihood function may however be unavailable or intractable due to non-gaussian errors, non-linear measurements processes, or complex data formats such as catalogs and maps. In these cases, the simulation of mock data sets can often be made through forward modeling. We discuss how Approximate Bayesian Computation (ABC) can be used in these cases to derive an approximation to the posterior constraints using simulated data sets. This technique relies on the sampling of the parameter set, a distance metric to quantify the difference between the observation and the simulations and summary statistics to compress the information in the data. We first review the principles of ABC and discuss its implementation using a Population Monte-Carlo (PMC) algorithm and the Mahalanobis distance metric. We test the performance of the implementation using a Gaussian toy model. We then apply the ABC technique to the practical case of the calibration of image simulations for wide field cosmological surveys. We find that the ABC analysis is able to provide reliable parameter constraints for this problem and is therefore a promising technique for other applications in cosmology and astrophysics. Our implementation of the ABC PMC method is made available via a public code release

  7. MAP estimators and their consistency in Bayesian nonparametric inverse problems

    International Nuclear Information System (INIS)

    Dashti, M; Law, K J H; Stuart, A M; Voss, J

    2013-01-01

    We consider the inverse problem of estimating an unknown function u from noisy measurements y of a known, possibly nonlinear, map G applied to u. We adopt a Bayesian approach to the problem and work in a setting where the prior measure is specified as a Gaussian random field μ 0 . We work under a natural set of conditions on the likelihood which implies the existence of a well-posed posterior measure, μ y . Under these conditions, we show that the maximum a posteriori (MAP) estimator is well defined as the minimizer of an Onsager–Machlup functional defined on the Cameron–Martin space of the prior; thus, we link a problem in probability with a problem in the calculus of variations. We then consider the case where the observational noise vanishes and establish a form of Bayesian posterior consistency for the MAP estimator. We also prove a similar result for the case where the observation of G(u) can be repeated as many times as desired with independent identically distributed noise. The theory is illustrated with examples from an inverse problem for the Navier–Stokes equation, motivated by problems arising in weather forecasting, and from the theory of conditioned diffusions, motivated by problems arising in molecular dynamics. (paper)

  8. Identification of transmissivity fields using a Bayesian strategy and perturbative approach

    Science.gov (United States)

    Zanini, Andrea; Tanda, Maria Giovanna; Woodbury, Allan D.

    2017-10-01

    The paper deals with the crucial problem of the groundwater parameter estimation that is the basis for efficient modeling and reclamation activities. A hierarchical Bayesian approach is developed: it uses the Akaike's Bayesian Information Criteria in order to estimate the hyperparameters (related to the covariance model chosen) and to quantify the unknown noise variance. The transmissivity identification proceeds in two steps: the first, called empirical Bayesian interpolation, uses Y* (Y = lnT) observations to interpolate Y values on a specified grid; the second, called empirical Bayesian update, improve the previous Y estimate through the addition of hydraulic head observations. The relationship between the head and the lnT has been linearized through a perturbative solution of the flow equation. In order to test the proposed approach, synthetic aquifers from literature have been considered. The aquifers in question contain a variety of boundary conditions (both Dirichelet and Neuman type) and scales of heterogeneities (σY2 = 1.0 and σY2 = 5.3). The estimated transmissivity fields were compared to the true one. The joint use of Y* and head measurements improves the estimation of Y considering both degrees of heterogeneity. Even if the variance of the strong transmissivity field can be considered high for the application of the perturbative approach, the results show the same order of approximation of the non-linear methods proposed in literature. The procedure allows to compute the posterior probability distribution of the target quantities and to quantify the uncertainty in the model prediction. Bayesian updating has advantages related both to the Monte-Carlo (MC) and non-MC approaches. In fact, as the MC methods, Bayesian updating allows computing the direct posterior probability distribution of the target quantities and as non-MC methods it has computational times in the order of seconds.

  9. Bayesian Meta-Analysis of Coefficient Alpha

    Science.gov (United States)

    Brannick, Michael T.; Zhang, Nanhua

    2013-01-01

    The current paper describes and illustrates a Bayesian approach to the meta-analysis of coefficient alpha. Alpha is the most commonly used estimate of the reliability or consistency (freedom from measurement error) for educational and psychological measures. The conventional approach to meta-analysis uses inverse variance weights to combine…

  10. Bayesian decision theory : A simple toy problem

    NARCIS (Netherlands)

    van Erp, H.R.N.; Linger, R.O.; van Gelder, P.H.A.J.M.

    2016-01-01

    We give here a comparison of the expected outcome theory, the expected utility theory, and the Bayesian decision theory, by way of a simple numerical toy problem in which we look at the investment willingness to avert a high impact low probability event. It will be found that for this toy problem

  11. Optimal Detection under the Restricted Bayesian Criterion

    Directory of Open Access Journals (Sweden)

    Shujun Liu

    2017-07-01

    Full Text Available This paper aims to find a suitable decision rule for a binary composite hypothesis-testing problem with a partial or coarse prior distribution. To alleviate the negative impact of the information uncertainty, a constraint is considered that the maximum conditional risk cannot be greater than a predefined value. Therefore, the objective of this paper becomes to find the optimal decision rule to minimize the Bayes risk under the constraint. By applying the Lagrange duality, the constrained optimization problem is transformed to an unconstrained optimization problem. In doing so, the restricted Bayesian decision rule is obtained as a classical Bayesian decision rule corresponding to a modified prior distribution. Based on this transformation, the optimal restricted Bayesian decision rule is analyzed and the corresponding algorithm is developed. Furthermore, the relation between the Bayes risk and the predefined value of the constraint is also discussed. The Bayes risk obtained via the restricted Bayesian decision rule is a strictly decreasing and convex function of the constraint on the maximum conditional risk. Finally, the numerical results including a detection example are presented and agree with the theoretical results.

  12. Heuristics as Bayesian inference under extreme priors.

    Science.gov (United States)

    Parpart, Paula; Jones, Matt; Love, Bradley C

    2018-05-01

    Simple heuristics are often regarded as tractable decision strategies because they ignore a great deal of information in the input data. One puzzle is why heuristics can outperform full-information models, such as linear regression, which make full use of the available information. These "less-is-more" effects, in which a relatively simpler model outperforms a more complex model, are prevalent throughout cognitive science, and are frequently argued to demonstrate an inherent advantage of simplifying computation or ignoring information. In contrast, we show at the computational level (where algorithmic restrictions are set aside) that it is never optimal to discard information. Through a formal Bayesian analysis, we prove that popular heuristics, such as tallying and take-the-best, are formally equivalent to Bayesian inference under the limit of infinitely strong priors. Varying the strength of the prior yields a continuum of Bayesian models with the heuristics at one end and ordinary regression at the other. Critically, intermediate models perform better across all our simulations, suggesting that down-weighting information with the appropriate prior is preferable to entirely ignoring it. Rather than because of their simplicity, our analyses suggest heuristics perform well because they implement strong priors that approximate the actual structure of the environment. We end by considering how new heuristics could be derived by infinitely strengthening the priors of other Bayesian models. These formal results have implications for work in psychology, machine learning and economics. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

  13. A strongly quasiconvex PAC-Bayesian bound

    DEFF Research Database (Denmark)

    Thiemann, Niklas; Igel, Christian; Wintenberger, Olivier

    2017-01-01

    We propose a new PAC-Bayesian bound and a way of constructing a hypothesis space, so that the bound is convex in the posterior distribution and also convex in a trade-off parameter between empirical performance of the posterior distribution and its complexity. The complexity is measured by the Ku...

  14. Multisnapshot Sparse Bayesian Learning for DOA

    DEFF Research Database (Denmark)

    Gerstoft, Peter; Mecklenbrauker, Christoph F.; Xenaki, Angeliki

    2016-01-01

    The directions of arrival (DOA) of plane waves are estimated from multisnapshot sensor array data using sparse Bayesian learning (SBL). The prior for the source amplitudes is assumed independent zero-mean complex Gaussian distributed with hyperparameters, the unknown variances (i.e., the source...

  15. Approximate Bayesian evaluations of measurement uncertainty

    Science.gov (United States)

    Possolo, Antonio; Bodnar, Olha

    2018-04-01

    The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty. This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand. The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists. We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.

  16. Inverse Problems in a Bayesian Setting

    KAUST Repository

    Matthies, Hermann G.

    2016-02-13

    In a Bayesian setting, inverse problems and uncertainty quantification (UQ)—the propagation of uncertainty through a computational (forward) model—are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.

  17. Error probabilities in default Bayesian hypothesis testing

    NARCIS (Netherlands)

    Gu, Xin; Hoijtink, Herbert; Mulder, J,

    2016-01-01

    This paper investigates the classical type I and type II error probabilities of default Bayes factors for a Bayesian t test. Default Bayes factors quantify the relative evidence between the null hypothesis and the unrestricted alternative hypothesis without needing to specify prior distributions for

  18. Bayesian Averaging is Well-Temperated

    DEFF Research Database (Denmark)

    Hansen, Lars Kai

    2000-01-01

    Bayesian predictions are stochastic just like predictions of any other inference scheme that generalize from a finite sample. While a simple variational argument shows that Bayes averaging is generalization optimal given that the prior matches the teacher parameter distribution the situation is l...

  19. Robust bayesian inference of generalized Pareto distribution ...

    African Journals Online (AJOL)

    En utilisant une etude exhaustive de Monte Carlo, nous prouvons que, moyennant une fonction perte generalisee adequate, on peut construire un estimateur Bayesien robuste du modele. Key words: Bayesian estimation; Extreme value; Generalized Fisher information; Gener- alized Pareto distribution; Monte Carlo; ...

  20. Inverse Problems in a Bayesian Setting

    KAUST Repository

    Matthies, Hermann G.; Zander, Elmar; Rosić, Bojana V.; Litvinenko, Alexander; Pajonk, Oliver

    2016-01-01

    In a Bayesian setting, inverse problems and uncertainty quantification (UQ)—the propagation of uncertainty through a computational (forward) model—are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.

  1. A Bayesian perspective on some replacement strategies

    International Nuclear Information System (INIS)

    Mazzuchi, Thomas A.; Soyer, Refik

    1996-01-01

    In this paper we present a Bayesian decision theoretic approach for determining optimal replacement strategies. This approach enables us to formally incorporate, express, and update our uncertainty when determining optimal replacement strategies. We develop relevant expressions for both the block replacement protocol with minimal repair and the age replacement protocol and illustrate the use of our approach with real data

  2. Comparison between Fisherian and Bayesian approach to ...

    African Journals Online (AJOL)

    ... of its simplicity and optimality properties is normally used for two group cases. However, Bayesian approach is found to be better than Fisher's approach because of its low misclassification error rate. Keywords: variance-covariance matrices, centroids, prior probability, mahalanobis distance, probability of misclassification ...

  3. Non-Linear Approximation of Bayesian Update

    KAUST Repository

    Litvinenko, Alexander

    2016-01-01

    We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.

  4. Comprehension and computation in Bayesian problem solving

    Directory of Open Access Journals (Sweden)

    Eric D. Johnson

    2015-07-01

    Full Text Available Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian reasoning relative to normalized formats (e.g. probabilities, percentages, both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on transparent Bayesian problems varies widely, and generally remains rather unimpressive. We suggest there has been an over-focus on this representational facilitator (i.e. transparent problem structures at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct versus incorrect reasoners depart, and how individual difference might influence this time point.

  5. A Bayesian Approach to Interactive Retrieval

    Science.gov (United States)

    Tague, Jean M.

    1973-01-01

    A probabilistic model for interactive retrieval is presented. Bayesian statistical decision theory principles are applied: use of prior and sample information about the relationship of document descriptions to query relevance; maximization of expected value of a utility function, to the problem of optimally restructuring search strategies in an…

  6. Encoding dependence in Bayesian causal networks

    Science.gov (United States)

    Bayesian networks (BNs) represent complex, uncertain spatio-temporal dynamics by propagation of conditional probabilities between identifiable states with a testable causal interaction model. Typically, they assume random variables are discrete in time and space with a static network structure that ...

  7. Forecasting nuclear power supply with Bayesian autoregression

    International Nuclear Information System (INIS)

    Beck, R.; Solow, J.L.

    1994-01-01

    We explore the possibility of forecasting the quarterly US generation of electricity from nuclear power using a Bayesian autoregression model. In terms of forecasting accuracy, this approach compares favorably with both the Department of Energy's current forecasting methodology and their more recent efforts using ARIMA models, and it is extremely easy and inexpensive to implement. (author)

  8. A Bayesian Nonparametric Approach to Factor Analysis

    DEFF Research Database (Denmark)

    Piatek, Rémi; Papaspiliopoulos, Omiros

    2018-01-01

    This paper introduces a new approach for the inference of non-Gaussian factor models based on Bayesian nonparametric methods. It relaxes the usual normality assumption on the latent factors, widely used in practice, which is too restrictive in many settings. Our approach, on the contrary, does no...

  9. Hierarchical Bayesian Models of Subtask Learning

    Science.gov (United States)

    Anglim, Jeromy; Wynton, Sarah K. A.

    2015-01-01

    The current study used Bayesian hierarchical methods to challenge and extend previous work on subtask learning consistency. A general model of individual-level subtask learning was proposed focusing on power and exponential functions with constraints to test for inconsistency. To study subtask learning, we developed a novel computer-based booking…

  10. Non-Linear Approximation of Bayesian Update

    KAUST Repository

    Litvinenko, Alexander

    2016-06-23

    We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.

  11. Bayesian approach and application to operation safety

    International Nuclear Information System (INIS)

    Procaccia, H.; Suhner, M.Ch.

    2003-01-01

    The management of industrial risks requires the development of statistical and probabilistic analyses which use all the available convenient information in order to compensate the insufficient experience feedback in a domain where accidents and incidents remain too scarce to perform a classical statistical frequency analysis. The Bayesian decision approach is well adapted to this problem because it integrates both the expertise and the experience feedback. The domain of knowledge is widen, the forecasting study becomes possible and the decisions-remedial actions are strengthen thanks to risk-cost-benefit optimization analyzes. This book presents the bases of the Bayesian approach and its concrete applications in various industrial domains. After a mathematical presentation of the industrial operation safety concepts and of the Bayesian approach principles, this book treats of some of the problems that can be solved thanks to this approach: softwares reliability, controls linked with the equipments warranty, dynamical updating of databases, expertise modeling and weighting, Bayesian optimization in the domains of maintenance, quality control, tests and design of new equipments. A synthesis of the mathematical formulae used in this approach is given in conclusion. (J.S.)

  12. Advances in Applications of Hierarchical Bayesian Methods with Hydrological Models

    Science.gov (United States)

    Alexander, R. B.; Schwarz, G. E.; Boyer, E. W.

    2017-12-01

    Mechanistic and empirical watershed models are increasingly used to inform water resource decisions. Growing access to historical stream measurements and data from in-situ sensor technologies has increased the need for improved techniques for coupling models with hydrological measurements. Techniques that account for the intrinsic uncertainties of both models and measurements are especially needed. Hierarchical Bayesian methods provide an efficient modeling tool for quantifying model and prediction uncertainties, including those associated with measurements. Hierarchical methods can also be used to explore spatial and temporal variations in model parameters and uncertainties that are informed by hydrological measurements. We used hierarchical Bayesian methods to develop a hybrid (statistical-mechanistic) SPARROW (SPAtially Referenced Regression On Watershed attributes) model of long-term mean annual streamflow across diverse environmental and climatic drainages in 18 U.S. hydrological regions. Our application illustrates the use of a new generation of Bayesian methods that offer more advanced computational efficiencies than the prior generation. Evaluations of the effects of hierarchical (regional) variations in model coefficients and uncertainties on model accuracy indicates improved prediction accuracies (median of 10-50%) but primarily in humid eastern regions, where model uncertainties are one-third of those in arid western regions. Generally moderate regional variability is observed for most hierarchical coefficients. Accounting for measurement and structural uncertainties, using hierarchical state-space techniques, revealed the effects of spatially-heterogeneous, latent hydrological processes in the "localized" drainages between calibration sites; this improved model precision, with only minor changes in regional coefficients. Our study can inform advances in the use of hierarchical methods with hydrological models to improve their integration with stream

  13. Quantum Bayesian networks with application to games displaying Parrondo's paradox

    Science.gov (United States)

    Pejic, Michael

    Bayesian networks and their accompanying graphical models are widely used for prediction and analysis across many disciplines. We will reformulate these in terms of linear maps. This reformulation will suggest a natural extension, which we will show is equivalent to standard textbook quantum mechanics. Therefore, this extension will be termed quantum. However, the term quantum should not be taken to imply this extension is necessarily only of utility in situations traditionally thought of as in the domain of quantum mechanics. In principle, it may be employed in any modelling situation, say forecasting the weather or the stock market---it is up to experiment to determine if this extension is useful in practice. Even restricting to the domain of quantum mechanics, with this new formulation the advantages of Bayesian networks can be maintained for models incorporating quantum and mixed classical-quantum behavior. The use of these will be illustrated by various basic examples. Parrondo's paradox refers to the situation where two, multi-round games with a fixed winning criteria, both with probability greater than one-half for one player to win, are combined. Using a possibly biased coin to determine the rule to employ for each round, paradoxically, the previously losing player now wins the combined game with probabilitygreater than one-half. Using the extended Bayesian networks, we will formulate and analyze classical observed, classical hidden, and quantum versions of a game that displays this paradox, finding bounds for the discrepancy from naive expectations for the occurrence of the paradox. A quantum paradox inspired by Parrondo's paradox will also be analyzed. We will prove a bound for the discrepancy from naive expectations for this paradox as well. Games involving quantum walks that achieve this bound will be presented.

  14. Predicting coastal cliff erosion using a Bayesian probabilistic model

    Science.gov (United States)

    Hapke, Cheryl J.; Plant, Nathaniel G.

    2010-01-01

    Regional coastal cliff retreat is difficult to model due to the episodic nature of failures and the along-shore variability of retreat events. There is a growing demand, however, for predictive models that can be used to forecast areas vulnerable to coastal erosion hazards. Increasingly, probabilistic models are being employed that require data sets of high temporal density to define the joint probability density function that relates forcing variables (e.g. wave conditions) and initial conditions (e.g. cliff geometry) to erosion events. In this study we use a multi-parameter Bayesian network to investigate correlations between key variables that control and influence variations in cliff retreat processes. The network uses Bayesian statistical methods to estimate event probabilities using existing observations. Within this framework, we forecast the spatial distribution of cliff retreat along two stretches of cliffed coast in Southern California. The input parameters are the height and slope of the cliff, a descriptor of material strength based on the dominant cliff-forming lithology, and the long-term cliff erosion rate that represents prior behavior. The model is forced using predicted wave impact hours. Results demonstrate that the Bayesian approach is well-suited to the forward modeling of coastal cliff retreat, with the correct outcomes forecast in 70–90% of the modeled transects. The model also performs well in identifying specific locations of high cliff erosion, thus providing a foundation for hazard mapping. This approach can be employed to predict cliff erosion at time-scales ranging from storm events to the impacts of sea-level rise at the century-scale.

  15. Bayesian modeling of the mass and density of asteroids

    Science.gov (United States)

    Dotson, Jessie L.; Mathias, Donovan

    2017-10-01

    Mass and density are two of the fundamental properties of any object. In the case of near earth asteroids, knowledge about the mass of an asteroid is essential for estimating the risk due to (potential) impact and planning possible mitigation options. The density of an asteroid can illuminate the structure of the asteroid. A low density can be indicative of a rubble pile structure whereas a higher density can imply a monolith and/or higher metal content. The damage resulting from an impact of an asteroid with Earth depends on its interior structure in addition to its total mass, and as a result, density is a key parameter to understanding the risk of asteroid impact. Unfortunately, measuring the mass and density of asteroids is challenging and often results in measurements with large uncertainties. In the absence of mass / density measurements for a specific object, understanding the range and distribution of likely values can facilitate probabilistic assessments of structure and impact risk. Hierarchical Bayesian models have recently been developed to investigate the mass - radius relationship of exoplanets (Wolfgang, Rogers & Ford 2016) and to probabilistically forecast the mass of bodies large enough to establish hydrostatic equilibrium over a range of 9 orders of magnitude in mass (from planemos to main sequence stars; Chen & Kipping 2017). Here, we extend this approach to investigate the mass and densities of asteroids. Several candidate Bayesian models are presented, and their performance is assessed relative to a synthetic asteroid population. In addition, a preliminary Bayesian model for probablistically forecasting masses and densities of asteroids is presented. The forecasting model is conditioned on existing asteroid data and includes observational errors, hyper-parameter uncertainties and intrinsic scatter.

  16. Bayesian Fundamentalism or Enlightenment? On the explanatory status and theoretical contributions of Bayesian models of cognition.

    Science.gov (United States)

    Jones, Matt; Love, Bradley C

    2011-08-01

    The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology - namely, Behaviorism and evolutionary psychology - that set aside mechanistic explanations or make use of optimality assumptions. Through these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls

  17. Bayesian Correlation Analysis for Sequence Count Data.

    Directory of Open Access Journals (Sweden)

    Daniel Sánchez-Taltavull

    Full Text Available Evaluating the similarity of different measured variables is a fundamental task of statistics, and a key part of many bioinformatics algorithms. Here we propose a Bayesian scheme for estimating the correlation between different entities' measurements based on high-throughput sequencing data. These entities could be different genes or miRNAs whose expression is measured by RNA-seq, different transcription factors or histone marks whose expression is measured by ChIP-seq, or even combinations of different types of entities. Our Bayesian formulation accounts for both measured signal levels and uncertainty in those levels, due to varying sequencing depth in different experiments and to varying absolute levels of individual entities, both of which affect the precision of the measurements. In comparison with a traditional Pearson correlation analysis, we show that our Bayesian correlation analysis retains high correlations when measurement confidence is high, but suppresses correlations when measurement confidence is low-especially for entities with low signal levels. In addition, we consider the influence of priors on the Bayesian correlation estimate. Perhaps surprisingly, we show that naive, uniform priors on entities' signal levels can lead to highly biased correlation estimates, particularly when different experiments have widely varying sequencing depths. However, we propose two alternative priors that provably mitigate this problem. We also prove that, like traditional Pearson correlation, our Bayesian correlation calculation constitutes a kernel in the machine learning sense, and thus can be used as a similarity measure in any kernel-based machine learning algorithm. We demonstrate our approach on two RNA-seq datasets and one miRNA-seq dataset.

  18. Influence of Genotype on Warfarin Maintenance Dose Predictions Produced Using a Bayesian Dose Individualization Tool.

    Science.gov (United States)

    Saffian, Shamin M; Duffull, Stephen B; Roberts, Rebecca L; Tait, Robert C; Black, Leanne; Lund, Kirstin A; Thomson, Alison H; Wright, Daniel F B

    2016-12-01

    A previously established Bayesian dosing tool for warfarin was found to produce biased maintenance dose predictions. In this study, we aimed (1) to determine whether the biased warfarin dose predictions previously observed could be replicated in a new cohort of patients from 2 different clinical settings, (2) to explore the influence of CYP2C9 and VKORC1 genotype on predictive performance of the Bayesian dosing tool, and (3) to determine whether the previous population used to develop the kinetic-pharmacodynamic model underpinning the Bayesian dosing tool was sufficiently different from the test (posterior) population to account for the biased dose predictions. The warfarin maintenance doses for 140 patients were predicted using the dosing tool and compared with the observed maintenance dose. The impact of genotype was assessed by predicting maintenance doses with prior parameter values known to be altered by genetic variability (eg, EC50 for VKORC1 genotype). The prior population was evaluated by fitting the published kinetic-pharmacodynamic model, which underpins the Bayesian tool, to the observed data using NONMEM and comparing the model parameter estimates with published values. The Bayesian tool produced positively biased dose predictions in the new cohort of patients (mean prediction error [95% confidence interval]; 0.32 mg/d [0.14-0.5]). The bias was only observed in patients requiring ≥7 mg/d. The direction and magnitude of the observed bias was not influenced by genotype. The prior model provided a good fit to our data, which suggests that the bias was not caused by different prior and posterior populations. Maintenance doses for patients requiring ≥7 mg/d were overpredicted. The bias was not due to the influence of genotype nor was it related to differences between the prior and posterior populations. There is a need for a more mechanistic model that captures warfarin dose-response relationship at higher warfarin doses.

  19. Primordial helium abundance from CMB: A constraint from recent observations and a forecast

    International Nuclear Information System (INIS)

    Ichikawa, Kazuhide; Sekiguchi, Toyokazu; Takahashi, Tomo

    2008-01-01

    We studied a constraint on the primordial helium abundance Y p from current and future observations of CMB. Using the currently available data from WMAP, ACBAR, CBI, and BOOMERANG, we obtained the constraint as Y p =0.25 -0.07 +0.10 at 68% confidence level. We also provide a forecast for the Planck experiment using the Markov chain Monte Carlo approach. In addition to forecasting the constraint on Y p , we investigate how assumptions for Y p affect constraints on the other cosmological parameters.

  20. Quantum-Like Bayesian Networks for Modeling Decision Making

    Directory of Open Access Journals (Sweden)

    Catarina eMoreira

    2016-01-01

    Full Text Available In this work, we explore an alternative quantum structure to perform quantum probabilistic inferences to accommodate the paradoxical findings of the Sure Thing Principle. We propose a Quantum-Like Bayesian Network, which consists in replacing classical probabilities by quantum probability amplitudes. However, since this approach suffers from the problem of exponential growth of quantum parameters, we also propose a similarity heuristic that automatically fits quantum parameters through vector similarities. This makes the proposed model general and predictive in contrast to the current state of the art models, which cannot be generalized for more complex decision scenarios and that only provide an explanatory nature for the observed paradoxes. In the end, the model that we propose consists in a nonparametric method for estimating inference effects from a statistical point of view. It is a statistical model that is simpler than the previous quantum dynamic and quantum-like models proposed in the literature. We tested the proposed network with several empirical data from the literature, mainly from the Prisoner's Dilemma game and the Two Stage Gambling game. The results obtained show that the proposed quantum Bayesian Network is a general method that can accommodate violations of the laws of classical probability theory and make accurate predictions regarding human decision-making in these scenarios.

  1. Bayesian energy landscape tilting: towards concordant models of molecular ensembles.

    Science.gov (United States)

    Beauchamp, Kyle A; Pande, Vijay S; Das, Rhiju

    2014-03-18

    Predicting biological structure has remained challenging for systems such as disordered proteins that take on myriad conformations. Hybrid simulation/experiment strategies have been undermined by difficulties in evaluating errors from computational model inaccuracies and data uncertainties. Building on recent proposals from maximum entropy theory and nonequilibrium thermodynamics, we address these issues through a Bayesian energy landscape tilting (BELT) scheme for computing Bayesian hyperensembles over conformational ensembles. BELT uses Markov chain Monte Carlo to directly sample maximum-entropy conformational ensembles consistent with a set of input experimental observables. To test this framework, we apply BELT to model trialanine, starting from disagreeing simulations with the force fields ff96, ff99, ff99sbnmr-ildn, CHARMM27, and OPLS-AA. BELT incorporation of limited chemical shift and (3)J measurements gives convergent values of the peptide's α, β, and PPII conformational populations in all cases. As a test of predictive power, all five BELT hyperensembles recover set-aside measurements not used in the fitting and report accurate errors, even when starting from highly inaccurate simulations. BELT's principled framework thus enables practical predictions for complex biomolecular systems from discordant simulations and sparse data. Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.

  2. An Adaptively Accelerated Bayesian Deblurring Method with Entropy Prior

    Directory of Open Access Journals (Sweden)

    Yong-Hoon Kim

    2008-05-01

    Full Text Available The development of an efficient adaptively accelerated iterative deblurring algorithm based on Bayesian statistical concept has been reported. Entropy of an image has been used as a “prior” distribution and instead of additive form, used in conventional acceleration methods an exponent form of relaxation constant has been used for acceleration. Thus the proposed method is called hereafter as adaptively accelerated maximum a posteriori with entropy prior (AAMAPE. Based on empirical observations in different experiments, the exponent is computed adaptively using first-order derivatives of the deblurred image from previous two iterations. This exponent improves speed of the AAMAPE method in early stages and ensures stability at later stages of iteration. In AAMAPE method, we also consider the constraint of the nonnegativity and flux conservation. The paper discusses the fundamental idea of the Bayesian image deblurring with the use of entropy as prior, and the analytical analysis of superresolution and the noise amplification characteristics of the proposed method. The experimental results show that the proposed AAMAPE method gives lower RMSE and higher SNR in 44% lesser iterations as compared to nonaccelerated maximum a posteriori with entropy prior (MAPE method. Moreover, AAMAPE followed by wavelet wiener filtering gives better result than the state-of-the-art methods.

  3. AIC, BIC, Bayesian evidence against the interacting dark energy model

    Energy Technology Data Exchange (ETDEWEB)

    Szydlowski, Marek [Jagiellonian University, Astronomical Observatory, Krakow (Poland); Jagiellonian University, Mark Kac Complex Systems Research Centre, Krakow (Poland); Krawiec, Adam [Jagiellonian University, Institute of Economics, Finance and Management, Krakow (Poland); Jagiellonian University, Mark Kac Complex Systems Research Centre, Krakow (Poland); Kurek, Aleksandra [Jagiellonian University, Astronomical Observatory, Krakow (Poland); Kamionka, Michal [University of Wroclaw, Astronomical Institute, Wroclaw (Poland)

    2015-01-01

    Recent astronomical observations have indicated that the Universe is in a phase of accelerated expansion. While there are many cosmological models which try to explain this phenomenon, we focus on the interacting ΛCDM model where an interaction between the dark energy and dark matter sectors takes place. This model is compared to its simpler alternative - the ΛCDM model. To choose between these models the likelihood ratio test was applied as well as the model comparison methods (employing Occam's principle): the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the Bayesian evidence. Using the current astronomical data: type Ia supernova (Union2.1), h(z), baryon acoustic oscillation, the Alcock- Paczynski test, and the cosmic microwave background data, we evaluated both models. The analyses based on the AIC indicated that there is less support for the interacting ΛCDM model when compared to the ΛCDM model, while those based on the BIC indicated that there is strong evidence against it in favor of the ΛCDM model. Given the weak or almost non-existing support for the interacting ΛCDM model and bearing in mind Occam's razor we are inclined to reject this model. (orig.)

  4. AIC, BIC, Bayesian evidence against the interacting dark energy model

    Energy Technology Data Exchange (ETDEWEB)

    Szydłowski, Marek, E-mail: marek.szydlowski@uj.edu.pl [Astronomical Observatory, Jagiellonian University, Orla 171, 30-244, Kraków (Poland); Mark Kac Complex Systems Research Centre, Jagiellonian University, Reymonta 4, 30-059, Kraków (Poland); Krawiec, Adam, E-mail: adam.krawiec@uj.edu.pl [Institute of Economics, Finance and Management, Jagiellonian University, Łojasiewicza 4, 30-348, Kraków (Poland); Mark Kac Complex Systems Research Centre, Jagiellonian University, Reymonta 4, 30-059, Kraków (Poland); Kurek, Aleksandra, E-mail: alex@oa.uj.edu.pl [Astronomical Observatory, Jagiellonian University, Orla 171, 30-244, Kraków (Poland); Kamionka, Michał, E-mail: kamionka@astro.uni.wroc.pl [Astronomical Institute, University of Wrocław, ul. Kopernika 11, 51-622, Wrocław (Poland)

    2015-01-14

    Recent astronomical observations have indicated that the Universe is in a phase of accelerated expansion. While there are many cosmological models which try to explain this phenomenon, we focus on the interacting ΛCDM model where an interaction between the dark energy and dark matter sectors takes place. This model is compared to its simpler alternative—the ΛCDM model. To choose between these models the likelihood ratio test was applied as well as the model comparison methods (employing Occam’s principle): the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the Bayesian evidence. Using the current astronomical data: type Ia supernova (Union2.1), h(z), baryon acoustic oscillation, the Alcock–Paczynski test, and the cosmic microwave background data, we evaluated both models. The analyses based on the AIC indicated that there is less support for the interacting ΛCDM model when compared to the ΛCDM model, while those based on the BIC indicated that there is strong evidence against it in favor of the ΛCDM model. Given the weak or almost non-existing support for the interacting ΛCDM model and bearing in mind Occam’s razor we are inclined to reject this model.

  5. AIC, BIC, Bayesian evidence against the interacting dark energy model

    International Nuclear Information System (INIS)

    Szydlowski, Marek; Krawiec, Adam; Kurek, Aleksandra; Kamionka, Michal

    2015-01-01

    Recent astronomical observations have indicated that the Universe is in a phase of accelerated expansion. While there are many cosmological models which try to explain this phenomenon, we focus on the interacting ΛCDM model where an interaction between the dark energy and dark matter sectors takes place. This model is compared to its simpler alternative - the ΛCDM model. To choose between these models the likelihood ratio test was applied as well as the model comparison methods (employing Occam's principle): the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the Bayesian evidence. Using the current astronomical data: type Ia supernova (Union2.1), h(z), baryon acoustic oscillation, the Alcock- Paczynski test, and the cosmic microwave background data, we evaluated both models. The analyses based on the AIC indicated that there is less support for the interacting ΛCDM model when compared to the ΛCDM model, while those based on the BIC indicated that there is strong evidence against it in favor of the ΛCDM model. Given the weak or almost non-existing support for the interacting ΛCDM model and bearing in mind Occam's razor we are inclined to reject this model. (orig.)

  6. Mining data from hemodynamic simulations via Bayesian emulation

    Directory of Open Access Journals (Sweden)

    Nair Prasanth B

    2007-12-01

    Full Text Available Abstract Background: Arterial geometry variability is inevitable both within and across individuals. To ensure realistic prediction of cardiovascular flows, there is a need for efficient numerical methods that can systematically account for geometric uncertainty. Methods and results: A statistical framework based on Bayesian Gaussian process modeling was proposed for mining data generated from computer simulations. The proposed approach was applied to analyze the influence of geometric parameters on hemodynamics in the human carotid artery bifurcation. A parametric model in conjunction with a design of computer experiments strategy was used for generating a set of observational data that contains the maximum wall shear stress values for a range of probable arterial geometries. The dataset was mined via a Bayesian Gaussian process emulator to estimate: (a the influence of key parameters on the output via sensitivity analysis, (b uncertainty in output as a function of uncertainty in input, and (c which settings of the input parameters result in maximum and minimum values of the output. Finally, potential diagnostic indicators were proposed that can be used to aid the assessment of stroke risk for a given patient's geometry.

  7. Application of Bayesian Networks to hindcast barrier island morphodynamics

    Science.gov (United States)

    Wilson, Kathleen E.; Adams, Peter N.; Hapke, Cheryl J.; Lentz, Erika E.; Brenner, Owen T.

    2015-01-01

    Prediction of coastal vulnerability is of increasing concern to policy makers, coastal managers and other stakeholders. Coastal regions and barrier islands along the Atlantic and Gulf coasts are subject to frequent, large storms, whose waves and storm surge can dramatically alter beach morphology, threaten infrastructure, and impact local economies. Given that precise forecasts of regional hazards are challenging, because of the complex interactions between processes on many scales, a range of probable geomorphic change in response to storm conditions is often more helpful than deterministic predictions. Site-specific probabilistic models of coastal change are reliable because they are formulated with observations so that local factors, of potentially high influence, are inherent in the model. The development and use of predictive tools such as Bayesian Networks in response to future storms has the potential to better inform management decisions and hazard preparation in coastal communities. We present several Bayesian Networks designed to hindcast distinct morphologic changes attributable to the Nor'Ida storm of 2009, at Fire Island, New York. Model predictions are informed with historical system behavior, initial morphologic conditions, and a parameterized treatment of wave climate.

  8. Bayesian modeling of recombination events in bacterial populations

    Directory of Open Access Journals (Sweden)

    Dowson Chris

    2008-10-01

    Full Text Available Abstract Background We consider the discovery of recombinant segments jointly with their origins within multilocus DNA sequences from bacteria representing heterogeneous populations of fairly closely related species. The currently available methods for recombination detection capable of probabilistic characterization of uncertainty have a limited applicability in practice as the number of strains in a data set increases. Results We introduce a Bayesian spatial structural model representing the continuum of origins over sites within the observed sequences, including a probabilistic characterization of uncertainty related to the origin of any particular site. To enable a statistically accurate and practically feasible approach to the analysis of large-scale data sets representing a single genus, we have developed a novel software tool (BRAT, Bayesian Recombination Tracker implementing the model and the corresponding learning algorithm, which is capable of identifying the posterior optimal structure and to estimate the marginal posterior probabilities of putative origins over the sites. Conclusion A multitude of challenging simulation scenarios and an analysis of real data from seven housekeeping genes of 120 strains of genus Burkholderia are used to illustrate the possibilities offered by our approach. The software is freely available for download at URL http://web.abo.fi/fak/mnf//mate/jc/software/brat.html.

  9. Bayesian Travel Time Inversion adopting Gaussian Process Regression

    Science.gov (United States)

    Mauerberger, S.; Holschneider, M.

    2017-12-01

    A major application in seismology is the determination of seismic velocity models. Travel time measurements are putting an integral constraint on the velocity between source and receiver. We provide insight into travel time inversion from a correlation-based Bayesian point of view. Therefore, the concept of Gaussian process regression is adopted to estimate a velocity model. The non-linear travel time integral is approximated by a 1st order Taylor expansion. A heuristic covariance describes correlations amongst observations and a priori model. That approach enables us to assess a proxy of the Bayesian posterior distribution at ordinary computational costs. No multi dimensional numeric integration nor excessive sampling is necessary. Instead of stacking the data, we suggest to progressively build the posterior distribution. Incorporating only a single evidence at a time accounts for the deficit of linearization. As a result, the most probable model is given by the posterior mean whereas uncertainties are described by the posterior covariance.As a proof of concept, a synthetic purely 1d model is addressed. Therefore a single source accompanied by multiple receivers is considered on top of a model comprising a discontinuity. We consider travel times of both phases - direct and reflected wave - corrupted by noise. Left and right of the interface are assumed independent where the squared exponential kernel serves as covariance.

  10. Can natural selection encode Bayesian priors?

    Science.gov (United States)

    Ramírez, Juan Camilo; Marshall, James A R

    2017-08-07

    The evolutionary success of many organisms depends on their ability to make decisions based on estimates of the state of their environment (e.g., predation risk) from uncertain information. These decision problems have optimal solutions and individuals in nature are expected to evolve the behavioural mechanisms to make decisions as if using the optimal solutions. Bayesian inference is the optimal method to produce estimates from uncertain data, thus natural selection is expected to favour individuals with the behavioural mechanisms to make decisions as if they were computing Bayesian estimates in typically-experienced environments, although this does not necessarily imply that favoured decision-makers do perform Bayesian computations exactly. Each individual should evolve to behave as if updating a prior estimate of the unknown environment variable to a posterior estimate as it collects evidence. The prior estimate represents the decision-maker's default belief regarding the environment variable, i.e., the individual's default 'worldview' of the environment. This default belief has been hypothesised to be shaped by natural selection and represent the environment experienced by the individual's ancestors. We present an evolutionary model to explore how accurately Bayesian prior estimates can be encoded genetically and shaped by natural selection when decision-makers learn from uncertain information. The model simulates the evolution of a population of individuals that are required to estimate the probability of an event. Every individual has a prior estimate of this probability and collects noisy cues from the environment in order to update its prior belief to a Bayesian posterior estimate with the evidence gained. The prior is inherited and passed on to offspring. Fitness increases with the accuracy of the posterior estimates produced. Simulations show that prior estimates become accurate over evolutionary time. In addition to these 'Bayesian' individuals, we also

  11. Frequency offset estimation in OFDM systems using Bayesian filtering

    Science.gov (United States)

    Yu, Yihua

    2011-10-01

    Orthogonal frequency division multiplexing (OFDM) is sensitive to carrier frequency offset (CFO) that causes inter-carrier interference (ICI). In this paper, we present two schemes for the CFO estimation, which are based on rejection sampling (RS) and a form of particle filtering (PF) called kernel smoothing technique, respectively. The first scheme is offline estimation, where the observations contained in the OFDM training symbol are treated in the batch mode. The second scheme is online estimation, where the observations in the OFDM training symbol are treated in the sequential manner. Simulations are provided to illustrate the performances of the schemes. Performance comparisons of the two schemes and with other Bayesian methods are provided. Simulation results show that the two schemes are effective when estimating the CFO and can effectively combat the effect of ICI in OFDM systems.

  12. Advances in Bayesian Model Based Clustering Using Particle Learning

    Energy Technology Data Exchange (ETDEWEB)

    Merl, D M

    2009-11-19

    Recent work by Carvalho, Johannes, Lopes and Polson and Carvalho, Lopes, Polson and Taddy introduced a sequential Monte Carlo (SMC) alternative to traditional iterative Monte Carlo strategies (e.g. MCMC and EM) for Bayesian inference for a large class of dynamic models. The basis of SMC techniques involves representing the underlying inference problem as one of state space estimation, thus giving way to inference via particle filtering. The key insight of Carvalho et al was to construct the sequence of filtering distributions so as to make use of the posterior predictive distribution of the observable, a distribution usually only accessible in certain Bayesian settings. Access to this distribution allows a reversal of the usual propagate and resample steps characteristic of many SMC methods, thereby alleviating to a large extent many problems associated with particle degeneration. Furthermore, Carvalho et al point out that for many conjugate models the posterior distribution of the static variables can be parametrized in terms of [recursively defined] sufficient statistics of the previously observed data. For models where such sufficient statistics exist, particle learning as it is being called, is especially well suited for the analysis of streaming data do to the relative invariance of its algorithmic complexity with the number of data observations. Through a particle learning approach, a statistical model can be fit to data as the data is arriving, allowing at any instant during the observation process direct quantification of uncertainty surrounding underlying model parameters. Here we describe the use of a particle learning approach for fitting a standard Bayesian semiparametric mixture model as described in Carvalho, Lopes, Polson and Taddy. In Section 2 we briefly review the previously presented particle learning algorithm for the case of a Dirichlet process mixture of multivariate normals. In Section 3 we describe several novel extensions to the original

  13. Posterior consistency for Bayesian inverse problems through stability and regression results

    International Nuclear Information System (INIS)

    Vollmer, Sebastian J

    2013-01-01

    In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes’ formula, giving rise to the posterior distribution on the unknown input. In this setting we prove posterior consistency for nonlinear inverse problems: a sequence of data is considered, with diminishing fluctuations around a single truth and it is then of interest to show that the resulting sequence of posterior measures arising from this sequence of data concentrates around the truth used to generate the data. Posterior consistency justifies the use of the Bayesian approach very much in the same way as error bounds and convergence results for regularization techniques do. As a guiding example, we consider the inverse problem of reconstructing the diffusion coefficient from noisy observations of the solution to an elliptic PDE in divergence form. This problem is approached by splitting the forward operator into the underlying continuum model and a simpler observation operator based on the output of the model. In general, these splittings allow us to conclude posterior consistency provided a deterministic stability result for the underlying inverse problem and a posterior consistency result for the Bayesian regression problem with the push-forward prior. Moreover, we prove posterior consistency for the Bayesian regression problem based on the regularity, the tail behaviour and the small ball probabilities of the prior. (paper)

  14. Bayesianism and inference to the best explanation

    Directory of Open Access Journals (Sweden)

    Valeriano IRANZO

    2008-01-01

    Full Text Available Bayesianism and Inference to the best explanation (IBE are two different models of inference. Recently there has been some debate about the possibility of “bayesianizing” IBE. Firstly I explore several alternatives to include explanatory considerations in Bayes’s Theorem. Then I distinguish two different interpretations of prior probabilities: “IBE-Bayesianism” (IBE-Bay and “frequentist-Bayesianism” (Freq-Bay. After detailing the content of the latter, I propose a rule for assessing the priors. I also argue that Freq-Bay: (i endorses a role for explanatory value in the assessment of scientific hypotheses; (ii avoids a purely subjectivist reading of prior probabilities; and (iii fits better than IBE-Bayesianism with two basic facts about science, i.e., the prominent role played by empirical testing and the existence of many scientific theories in the past that failed to fulfil their promises and were subsequently abandoned.

  15. Modelling dependable systems using hybrid Bayesian networks

    International Nuclear Information System (INIS)

    Neil, Martin; Tailor, Manesh; Marquez, David; Fenton, Norman; Hearty, Peter

    2008-01-01

    A hybrid Bayesian network (BN) is one that incorporates both discrete and continuous nodes. In our extensive applications of BNs for system dependability assessment, the models are invariably hybrid and the need for efficient and accurate computation is paramount. We apply a new iterative algorithm that efficiently combines dynamic discretisation with robust propagation algorithms on junction tree structures to perform inference in hybrid BNs. We illustrate its use in the field of dependability with two example of reliability estimation. Firstly we estimate the reliability of a simple single system and next we implement a hierarchical Bayesian model. In the hierarchical model we compute the reliability of two unknown subsystems from data collected on historically similar subsystems and then input the result into a reliability block model to compute system level reliability. We conclude that dynamic discretisation can be used as an alternative to analytical or Monte Carlo methods with high precision and can be applied to a wide range of dependability problems

  16. Bayesian Peak Picking for NMR Spectra

    KAUST Repository

    Cheng, Yichen

    2014-02-01

    Protein structure determination is a very important topic in structural genomics, which helps people to understand varieties of biological functions such as protein-protein interactions, protein–DNA interactions and so on. Nowadays, nuclear magnetic resonance (NMR) has often been used to determine the three-dimensional structures of protein in vivo. This study aims to automate the peak picking step, the most important and tricky step in NMR structure determination. We propose to model the NMR spectrum by a mixture of bivariate Gaussian densities and use the stochastic approximation Monte Carlo algorithm as the computational tool to solve the problem. Under the Bayesian framework, the peak picking problem is casted as a variable selection problem. The proposed method can automatically distinguish true peaks from false ones without preprocessing the data. To the best of our knowledge, this is the first effort in the literature that tackles the peak picking problem for NMR spectrum data using Bayesian method.

  17. Bayesian Modelling of Functional Whole Brain Connectivity

    DEFF Research Database (Denmark)

    Røge, Rasmus

    the prevalent strategy of standardizing of fMRI time series and model data using directional statistics or we model the variability in the signal across the brain and across multiple subjects. In either case, we use Bayesian nonparametric modeling to automatically learn from the fMRI data the number......This thesis deals with parcellation of whole-brain functional magnetic resonance imaging (fMRI) using Bayesian inference with mixture models tailored to the fMRI data. In the three included papers and manuscripts, we analyze two different approaches to modeling fMRI signal; either we accept...... of funcional units, i.e. parcels. We benchmark the proposed mixture models against state of the art methods of brain parcellation, both probabilistic and non-probabilistic. The time series of each voxel are most often standardized using z-scoring which projects the time series data onto a hypersphere...

  18. Software Health Management with Bayesian Networks

    Science.gov (United States)

    Mengshoel, Ole; Schumann, JOhann

    2011-01-01

    Most modern aircraft as well as other complex machinery is equipped with diagnostics systems for its major subsystems. During operation, sensors provide important information about the subsystem (e.g., the engine) and that information is used to detect and diagnose faults. Most of these systems focus on the monitoring of a mechanical, hydraulic, or electromechanical subsystem of the vehicle or machinery. Only recently, health management systems that monitor software have been developed. In this paper, we will discuss our approach of using Bayesian networks for Software Health Management (SWHM). We will discuss SWHM requirements, which make advanced reasoning capabilities for the detection and diagnosis important. Then we will present our approach to using Bayesian networks for the construction of health models that dynamically monitor a software system and is capable of detecting and diagnosing faults.

  19. Narrowband interference parameterization for sparse Bayesian recovery

    KAUST Repository

    Ali, Anum

    2015-09-11

    This paper addresses the problem of narrowband interference (NBI) in SC-FDMA systems by using tools from compressed sensing and stochastic geometry. The proposed NBI cancellation scheme exploits the frequency domain sparsity of the unknown signal and adopts a Bayesian sparse recovery procedure. This is done by keeping a few randomly chosen sub-carriers data free to sense the NBI signal at the receiver. As Bayesian recovery requires knowledge of some NBI parameters (i.e., mean, variance and sparsity rate), we use tools from stochastic geometry to obtain analytical expressions for the required parameters. Our simulation results validate the analysis and depict suitability of the proposed recovery method for NBI mitigation. © 2015 IEEE.

  20. Machine learning a Bayesian and optimization perspective

    CERN Document Server

    Theodoridis, Sergios

    2015-01-01

    This tutorial text gives a unifying perspective on machine learning by covering both probabilistic and deterministic approaches, which rely on optimization techniques, as well as Bayesian inference, which is based on a hierarchy of probabilistic models. The book presents the major machine learning methods as they have been developed in different disciplines, such as statistics, statistical and adaptive signal processing and computer science. Focusing on the physical reasoning behind the mathematics, all the various methods and techniques are explained in depth, supported by examples and problems, giving an invaluable resource to the student and researcher for understanding and applying machine learning concepts. The book builds carefully from the basic classical methods to the most recent trends, with chapters written to be as self-contained as possible, making the text suitable for different courses: pattern recognition, statistical/adaptive signal processing, statistical/Bayesian learning, as well as shor...

  1. Bayesian calibration : past achievements and future challenges

    International Nuclear Information System (INIS)

    Christen, J.A.

    2001-01-01

    Due to variations of the radiocarbon content in the biosphere over time, radiocarbon determinations need to be calibrated to obtain calendar years. Over the past decade a series of researchers have investigated the possibility of using Bayesian statistics to calibrate radiocarbon determinations, the main feature being the inclusion of contextual information into the calibration process. This allows for a coherent calibration of groups of determinations arising from related contexts (stratigraphical layers, peat cores, cultural events, ect.). Moreover, the 'related contexts' are also dated, and not only the material radiocarbon dated itself. We review Bayesian Calibration and state some of its current challenges like: software development, prior specification, robustness, etc. (author). 14 refs., 4 figs

  2. Disentangling Complexity in Bayesian Automatic Adaptive Quadrature

    Science.gov (United States)

    Adam, Gheorghe; Adam, Sanda

    2018-02-01

    The paper describes a Bayesian automatic adaptive quadrature (BAAQ) solution for numerical integration which is simultaneously robust, reliable, and efficient. Detailed discussion is provided of three main factors which contribute to the enhancement of these features: (1) refinement of the m-panel automatic adaptive scheme through the use of integration-domain-length-scale-adapted quadrature sums; (2) fast early problem complexity assessment - enables the non-transitive choice among three execution paths: (i) immediate termination (exceptional cases); (ii) pessimistic - involves time and resource consuming Bayesian inference resulting in radical reformulation of the problem to be solved; (iii) optimistic - asks exclusively for subrange subdivision by bisection; (3) use of the weaker accuracy target from the two possible ones (the input accuracy specifications and the intrinsic integrand properties respectively) - results in maximum possible solution accuracy under minimum possible computing time.

  3. Bayesian network modelling of upper gastrointestinal bleeding

    Science.gov (United States)

    Aisha, Nazziwa; Shohaimi, Shamarina; Adam, Mohd Bakri

    2013-09-01

    Bayesian networks are graphical probabilistic models that represent causal and other relationships between domain variables. In the context of medical decision making, these models have been explored to help in medical diagnosis and prognosis. In this paper, we discuss the Bayesian network formalism in building medical support systems and we learn a tree augmented naive Bayes Network (TAN) from gastrointestinal bleeding data. The accuracy of the TAN in classifying the source of gastrointestinal bleeding into upper or lower source is obtained. The TAN achieves a high classification accuracy of 86% and an area under curve of 92%. A sensitivity analysis of the model shows relatively high levels of entropy reduction for color of the stool, history of gastrointestinal bleeding, consistency and the ratio of blood urea nitrogen to creatinine. The TAN facilitates the identification of the source of GIB and requires further validation.

  4. Bayesian Prior Probability Distributions for Internal Dosimetry

    Energy Technology Data Exchange (ETDEWEB)

    Miller, G.; Inkret, W.C.; Little, T.T.; Martz, H.F.; Schillaci, M.E

    2001-07-01

    The problem of choosing a prior distribution for the Bayesian interpretation of measurements (specifically internal dosimetry measurements) is considered using a theoretical analysis and by examining historical tritium and plutonium urine bioassay data from Los Alamos. Two models for the prior probability distribution are proposed: (1) the log-normal distribution, when there is some additional information to determine the scale of the true result, and (2) the 'alpha' distribution (a simplified variant of the gamma distribution) when there is not. These models have been incorporated into version 3 of the Bayesian internal dosimetric code in use at Los Alamos (downloadable from our web site). Plutonium internal dosimetry at Los Alamos is now being done using prior probability distribution parameters determined self-consistently from population averages of Los Alamos data. (author)

  5. Probabilistic forecasting and Bayesian data assimilation

    CERN Document Server

    Reich, Sebastian

    2015-01-01

    In this book the authors describe the principles and methods behind probabilistic forecasting and Bayesian data assimilation. Instead of focusing on particular application areas, the authors adopt a general dynamical systems approach, with a profusion of low-dimensional, discrete-time numerical examples designed to build intuition about the subject. Part I explains the mathematical framework of ensemble-based probabilistic forecasting and uncertainty quantification. Part II is devoted to Bayesian filtering algorithms, from classical data assimilation algorithms such as the Kalman filter, variational techniques, and sequential Monte Carlo methods, through to more recent developments such as the ensemble Kalman filter and ensemble transform filters. The McKean approach to sequential filtering in combination with coupling of measures serves as a unifying mathematical framework throughout Part II. Assuming only some basic familiarity with probability, this book is an ideal introduction for graduate students in ap...

  6. Bayesian networks and boundedly rational expectations

    OpenAIRE

    Ran Spiegler

    2014-01-01

    I present a framework for analyzing decision makers with an imperfect understanding of their environment's correlation structure. The framework borrows the tool of "Bayesian networks", which is ubiquitous in statistics and artificial intelligence. In the model, a decision maker faces an objective multivariate probability distribution (his own action is one of the random variables). He is characterized by a directed acyclic graph over the set of random variables. His subjective belief filters ...

  7. Approximation of Bayesian Inverse Problems for PDEs

    OpenAIRE

    Cotter, S. L.; Dashti, M.; Stuart, A. M.

    2010-01-01

    Inverse problems are often ill posed, with solutions that depend sensitively on data.n any numerical approach to the solution of such problems, regularization of some form is needed to counteract the resulting instability. This paper is based on an approach to regularization, employing a Bayesian formulation of the problem, which leads to a notion of well posedness for inverse problems, at the level of probability measures. The stability which results from this well posedness may be used as t...

  8. Multilevel Monte Carlo in Approximate Bayesian Computation

    KAUST Repository

    Jasra, Ajay

    2017-02-13

    In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.

  9. Centralized Bayesian reliability modelling with sensor networks

    Czech Academy of Sciences Publication Activity Database

    Dedecius, Kamil; Sečkárová, Vladimíra

    2013-01-01

    Roč. 19, č. 5 (2013), s. 471-482 ISSN 1387-3954 R&D Projects: GA MŠk 7D12004 Grant - others:GA MŠk(CZ) SVV-265315 Keywords : Bayesian modelling * Sensor network * Reliability Subject RIV: BD - Theory of Information Impact factor: 0.984, year: 2013 http://library.utia.cas.cz/separaty/2013/AS/dedecius-0392551.pdf

  10. Essays on portfolio choice with Bayesian methods

    OpenAIRE

    Kebabci, Deniz

    2007-01-01

    How investors should allocate assets to their portfolios in the presence of predictable components in asset returns is a question of great importance in finance. While early studies took the return generating process as given, recent studies have addressed issues such as parameter estimation and model uncertainty. My dissertation develops Bayesian methods for portfolio choice - and industry allocation in particular - under parameter and model uncertainty. The first chapter of my dissertation,...

  11. Bayesian estimation of Weibull distribution parameters

    International Nuclear Information System (INIS)

    Bacha, M.; Celeux, G.; Idee, E.; Lannoy, A.; Vasseur, D.

    1994-11-01

    In this paper, we expose SEM (Stochastic Expectation Maximization) and WLB-SIR (Weighted Likelihood Bootstrap - Sampling Importance Re-sampling) methods which are used to estimate Weibull distribution parameters when data are very censored. The second method is based on Bayesian inference and allow to take into account available prior informations on parameters. An application of this method, with real data provided by nuclear power plants operation feedback analysis has been realized. (authors). 8 refs., 2 figs., 2 tabs

  12. A theory of Bayesian decision making

    OpenAIRE

    Karni, Edi

    2009-01-01

    This paper presents a complete, choice-based, axiomatic Bayesian decision theory. It introduces a new choice set consisting of information-contingent plans for choosing actions and bets and subjective expected utility model with effect-dependent utility functions and action-dependent subjective probabilities which, in conjunction with the updating of the probabilities using Bayes’ rule, gives rise to a unique prior and a set of action-dependent posterior probabilities representing the decisio...

  13. Constrained bayesian inference of project performance models

    OpenAIRE

    Sunmola, Funlade

    2013-01-01

    Project performance models play an important role in the management of project success. When used for monitoring projects, they can offer predictive ability such as indications of possible delivery problems. Approaches for monitoring project performance relies on available project information including restrictions imposed on the project, particularly the constraints of cost, quality, scope and time. We study in this paper a Bayesian inference methodology for project performance modelling in ...

  14. Virtual Vector Machine for Bayesian Online Classification

    OpenAIRE

    Minka, Thomas P.; Xiang, Rongjing; Yuan; Qi

    2012-01-01

    In a typical online learning scenario, a learner is required to process a large data stream using a small memory buffer. Such a requirement is usually in conflict with a learner's primary pursuit of prediction accuracy. To address this dilemma, we introduce a novel Bayesian online classi cation algorithm, called the Virtual Vector Machine. The virtual vector machine allows you to smoothly trade-off prediction accuracy with memory size. The virtual vector machine summarizes the information con...

  15. Characteristic imsets for learning Bayesian network structure

    Czech Academy of Sciences Publication Activity Database

    Hemmecke, R.; Lindner, S.; Studený, Milan

    2012-01-01

    Roč. 53, č. 9 (2012), s. 1336-1349 ISSN 0888-613X R&D Projects: GA MŠk(CZ) 1M0572; GA ČR GA201/08/0539 Institutional support: RVO:67985556 Keywords : learning Bayesian network structure * essential graph * standard imset * characteristic imset * LP relaxation of a polytope Subject RIV: BA - General Mathematics Impact factor: 1.729, year: 2012 http://library.utia.cas.cz/separaty/2012/MTR/studeny-0382596.pdf

  16. Bayesian analysis of Markov point processes

    DEFF Research Database (Denmark)

    Berthelsen, Kasper Klitgaard; Møller, Jesper

    2006-01-01

    Recently Møller, Pettitt, Berthelsen and Reeves introduced a new MCMC methodology for drawing samples from a posterior distribution when the likelihood function is only specified up to a normalising constant. We illustrate the method in the setting of Bayesian inference for Markov point processes...... a partially ordered Markov point process as the auxiliary variable. As the method requires simulation from the "unknown" likelihood, perfect simulation algorithms for spatial point processes become useful....

  17. Decisions under uncertainty using Bayesian analysis

    Directory of Open Access Journals (Sweden)

    Stelian STANCU

    2006-01-01

    Full Text Available The present paper makes a short presentation of the Bayesian decions method, where extrainformation brings a great support to decision making process, but also attract new costs. In this situation, getting new information, generally experimentaly based, contributes to diminushing the uncertainty degree that influences decision making process. As a conclusion, in a large number of decision problems, there is the possibility that the decision makers will renew some decisions already taken because of the facilities offered by obtainig extrainformation.

  18. Assessing global vegetation activity using spatio-temporal Bayesian modelling

    Science.gov (United States)

    Mulder, Vera L.; van Eck, Christel M.; Friedlingstein, Pierre; Regnier, Pierre A. G.

    2016-04-01

    This work demonstrates the potential of modelling vegetation activity using a hierarchical Bayesian spatio-temporal model. This approach allows modelling changes in vegetation and climate simultaneous in space and time. Changes of vegetation activity such as phenology are modelled as a dynamic process depending on climate variability in both space and time. Additionally, differences in observed vegetation status can be contributed to other abiotic ecosystem properties, e.g. soil and terrain properties. Although these properties do not change in time, they do change in space and may provide valuable information in addition to the climate dynamics. The spatio-temporal Bayesian models were calibrated at a regional scale because the local trends in space and time can be better captured by the model. The regional subsets were defined according to the SREX segmentation, as defined by the IPCC. Each region is considered being relatively homogeneous in terms of large-scale climate and biomes, still capturing small-scale (grid-cell level) variability. Modelling within these regions is hence expected to be less uncertain due to the absence of these large-scale patterns, compared to a global approach. This overall modelling approach allows the comparison of model behavior for the different regions and may provide insights on the main dynamic processes driving the interaction between vegetation and climate within different regions. The data employed in this study encompasses the global datasets for soil properties (SoilGrids), terrain properties (Global Relief Model based on SRTM DEM and ETOPO), monthly time series of satellite-derived vegetation indices (GIMMS NDVI3g) and climate variables (Princeton Meteorological Forcing Dataset). The findings proved the potential of a spatio-temporal Bayesian modelling approach for assessing vegetation dynamics, at a regional scale. The observed interrelationships of the employed data and the different spatial and temporal trends support

  19. Network structure exploration via Bayesian nonparametric models

    International Nuclear Information System (INIS)

    Chen, Y; Wang, X L; Xiang, X; Tang, B Z; Bu, J Z

    2015-01-01

    Complex networks provide a powerful mathematical representation of complex systems in nature and society. To understand complex networks, it is crucial to explore their internal structures, also called structural regularities. The task of network structure exploration is to determine how many groups there are in a complex network and how to group the nodes of the network. Most existing structure exploration methods need to specify either a group number or a certain type of structure when they are applied to a network. In the real world, however, the group number and also the certain type of structure that a network has are usually unknown in advance. To explore structural regularities in complex networks automatically, without any prior knowledge of the group number or the certain type of structure, we extend a probabilistic mixture model that can handle networks with any type of structure but needs to specify a group number using Bayesian nonparametric theory. We also propose a novel Bayesian nonparametric model, called the Bayesian nonparametric mixture (BNPM) model. Experiments conducted on a large number of networks with different structures show that the BNPM model is able to explore structural regularities in networks automatically with a stable, state-of-the-art performance. (paper)

  20. Bayesian analyses of seasonal runoff forecasts

    Science.gov (United States)

    Krzysztofowicz, R.; Reese, S.

    1991-12-01

    Forecasts of seasonal snowmelt runoff volume provide indispensable information for rational decision making by water project operators, irrigation district managers, and farmers in the western United States. Bayesian statistical models and communication frames have been researched in order to enhance the forecast information disseminated to the users, and to characterize forecast skill from the decision maker's point of view. Four products are presented: (i) a Bayesian Processor of Forecasts, which provides a statistical filter for calibrating the forecasts, and a procedure for estimating the posterior probability distribution of the seasonal runoff; (ii) the Bayesian Correlation Score, a new measure of forecast skill, which is related monotonically to the ex ante economic value of forecasts for decision making; (iii) a statistical predictor of monthly cumulative runoffs within the snowmelt season, conditional on the total seasonal runoff forecast; and (iv) a framing of the forecast message that conveys the uncertainty associated with the forecast estimates to the users. All analyses are illustrated with numerical examples of forecasts for six gauging stations from the period 1971 1988.

  1. Bayesian Recurrent Neural Network for Language Modeling.

    Science.gov (United States)

    Chien, Jen-Tzung; Ku, Yuan-Chu

    2016-02-01

    A language model (LM) is calculated as the probability of a word sequence that provides the solution to word prediction for a variety of information systems. A recurrent neural network (RNN) is powerful to learn the large-span dynamics of a word sequence in the continuous space. However, the training of the RNN-LM is an ill-posed problem because of too many parameters from a large dictionary size and a high-dimensional hidden layer. This paper presents a Bayesian approach to regularize the RNN-LM and apply it for continuous speech recognition. We aim to penalize the too complicated RNN-LM by compensating for the uncertainty of the estimated model parameters, which is represented by a Gaussian prior. The objective function in a Bayesian classification network is formed as the regularized cross-entropy error function. The regularized model is constructed not only by calculating the regularized parameters according to the maximum a posteriori criterion but also by estimating the Gaussian hyperparameter by maximizing the marginal likelihood. A rapid approximation to a Hessian matrix is developed to implement the Bayesian RNN-LM (BRNN-LM) by selecting a small set of salient outer-products. The proposed BRNN-LM achieves a sparser model than the RNN-LM. Experiments on different corpora show the robustness of system performance by applying the rapid BRNN-LM under different conditions.

  2. Bayesian Analysis of Individual Level Personality Dynamics

    Directory of Open Access Journals (Sweden)

    Edward Cripps

    2016-07-01

    Full Text Available A Bayesian technique with analyses of within-person processes at the level of the individual is presented. The approach is used to examine if the patterns of within-person responses on a 12 trial simulation task are consistent with the predictions of ITA theory (Dweck, 1999. ITA theory states that the performance of an individual with an entity theory of ability is more likely to spiral down following a failure experience than the performance of an individual with an incremental theory of ability. This is because entity theorists interpret failure experiences as evidence of a lack of ability, which they believe is largely innate and therefore relatively fixed; whilst incremental theorists believe in the malleability of abilities and interpret failure experiences as evidence of more controllable factors such as poor strategy or lack of effort. The results of our analyses support ITA theory at both the within- and between-person levels of analyses and demonstrate the benefits of Bayesian techniques for the analysis of within-person processes. These include more formal specification of the theory and the ability to draw inferences about each individual, which allows for more nuanced interpretations of individuals within a personality category, such as differences in the individual probabilities of spiralling. While Bayesian techniques have many potential advantages for the analyses of within-person processes at the individual level, ease of use is not one of them for psychologists trained in traditional frequentist statistical techniques.

  3. Particle identification in ALICE: a Bayesian approach

    CERN Document Server

    Adam, Jaroslav; Aggarwal, Madan Mohan; Aglieri Rinella, Gianluca; Agnello, Michelangelo; Agrawal, Neelima; Ahammed, Zubayer; Ahmad, Shakeel; Ahn, Sang Un; Aiola, Salvatore; Akindinov, Alexander; Alam, Sk Noor; Silva De Albuquerque, Danilo; Aleksandrov, Dmitry; Alessandro, Bruno; Alexandre, Didier; Alfaro Molina, Jose Ruben; Alici, Andrea; Alkin, Anton; Millan Almaraz, Jesus Roberto; Alme, Johan; Alt, Torsten; Altinpinar, Sedat; Altsybeev, Igor; Alves Garcia Prado, Caio; Andrei, Cristian; Andronic, Anton; Anguelov, Venelin; Anticic, Tome; Antinori, Federico; Antonioli, Pietro; Aphecetche, Laurent Bernard; Appelshaeuser, Harald; Arcelli, Silvia; Arnaldi, Roberta; Arnold, Oliver Werner; Arsene, Ionut Cristian; Arslandok, Mesut; Audurier, Benjamin; Augustinus, Andre; Averbeck, Ralf Peter; Azmi, Mohd Danish; Badala, Angela; Baek, Yong Wook; Bagnasco, Stefano; Bailhache, Raphaelle Marie; Bala, Renu; Balasubramanian, Supraja; Baldisseri, Alberto; Baral, Rama Chandra; Barbano, Anastasia Maria; 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    2016-05-25

    We present a Bayesian approach to particle identification (PID) within the ALICE experiment. The aim is to more effectively combine the particle identification capabilities of its various detectors. After a brief explanation of the adopted methodology and formalism, the performance of the Bayesian PID approach for charged pions, kaons and protons in the central barrel of ALICE is studied. PID is performed via measurements of specific energy loss (dE/dx) and time-of-flight. PID efficiencies and misidentification probabilities are extracted and compared with Monte Carlo simulations using high purity samples of identified particles in the decay channels ${\\rm K}_{\\rm S}^{\\rm 0}\\rightarrow \\pi^+\\pi^-$, $\\phi\\rightarrow {\\rm K}^-{\\rm K}^+$ and $\\Lambda\\rightarrow{\\rm p}\\pi^-$ in p–Pb collisions at $\\sqrt{s_{\\rm NN}}= 5.02$TeV. In order to thoroughly assess the validity of the Bayesian approach, this methodology was used to obtain corrected $p_{\\rm T}$ spectra of pions, kaons, protons, and D$^0$ mesons in pp coll...

  4. Discriminative Bayesian Dictionary Learning for Classification.

    Science.gov (United States)

    Akhtar, Naveed; Shafait, Faisal; Mian, Ajmal

    2016-12-01

    We propose a Bayesian approach to learn discriminative dictionaries for sparse representation of data. The proposed approach infers probability distributions over the atoms of a discriminative dictionary using a finite approximation of Beta Process. It also computes sets of Bernoulli distributions that associate class labels to the learned dictionary atoms. This association signifies the selection probabilities of the dictionary atoms in the expansion of class-specific data. Furthermore, the non-parametric character of the proposed approach allows it to infer the correct size of the dictionary. We exploit the aforementioned Bernoulli distributions in separately learning a linear classifier. The classifier uses the same hierarchical Bayesian model as the dictionary, which we present along the analytical inference solution for Gibbs sampling. For classification, a test instance is first sparsely encoded over the learned dictionary and the codes are fed to the classifier. We performed experiments for face and action recognition; and object and scene-category classification using five public datasets and compared the results with state-of-the-art discriminative sparse representation approaches. Experiments show that the proposed Bayesian approach consistently outperforms the existing approaches.

  5. Bayesian Inference of a Multivariate Regression Model

    Directory of Open Access Journals (Sweden)

    Marick S. Sinay

    2014-01-01

    Full Text Available We explore Bayesian inference of a multivariate linear regression model with use of a flexible prior for the covariance structure. The commonly adopted Bayesian setup involves the conjugate prior, multivariate normal distribution for the regression coefficients and inverse Wishart specification for the covariance matrix. Here we depart from this approach and propose a novel Bayesian estimator for the covariance. A multivariate normal prior for the unique elements of the matrix logarithm of the covariance matrix is considered. Such structure allows for a richer class of prior distributions for the covariance, with respect to strength of beliefs in prior location hyperparameters, as well as the added ability, to model potential correlation amongst the covariance structure. The posterior moments of all relevant parameters of interest are calculated based upon numerical results via a Markov chain Monte Carlo procedure. The Metropolis-Hastings-within-Gibbs algorithm is invoked to account for the construction of a proposal density that closely matches the shape of the target posterior distribution. As an application of the proposed technique, we investigate a multiple regression based upon the 1980 High School and Beyond Survey.

  6. Bayesian posterior distributions without Markov chains.

    Science.gov (United States)

    Cole, Stephen R; Chu, Haitao; Greenland, Sander; Hamra, Ghassan; Richardson, David B

    2012-03-01

    Bayesian posterior parameter distributions are often simulated using Markov chain Monte Carlo (MCMC) methods. However, MCMC methods are not always necessary and do not help the uninitiated understand Bayesian inference. As a bridge to understanding Bayesian inference, the authors illustrate a transparent rejection sampling method. In example 1, they illustrate rejection sampling using 36 cases and 198 controls from a case-control study (1976-1983) assessing the relation between residential exposure to magnetic fields and the development of childhood cancer. Results from rejection sampling (odds ratio (OR) = 1.69, 95% posterior interval (PI): 0.57, 5.00) were similar to MCMC results (OR = 1.69, 95% PI: 0.58, 4.95) and approximations from data-augmentation priors (OR = 1.74, 95% PI: 0.60, 5.06). In example 2, the authors apply rejection sampling to a cohort study of 315 human immunodeficiency virus seroconverters (1984-1998) to assess the relation between viral load after infection and 5-year incidence of acquired immunodeficiency syndrome, adjusting for (continuous) age at seroconversion and race. In this more complex example, rejection sampling required a notably longer run time than MCMC sampling but remained feasible and again yielded similar results. The transparency of the proposed approach comes at a price of being less broadly applicable than MCMC.

  7. Risk-sensitivity in Bayesian sensorimotor integration.

    Directory of Open Access Journals (Sweden)

    Jordi Grau-Moya

    Full Text Available Information processing in the nervous system during sensorimotor tasks with inherent uncertainty has been shown to be consistent with Bayesian integration. Bayes optimal decision-makers are, however, risk-neutral in the sense that they weigh all possibilities based on prior expectation and sensory evidence when they choose the action with highest expected value. In contrast, risk-sensitive decision-makers are sensitive to model uncertainty and bias their decision-making processes when they do inference over unobserved variables. In particular, they allow deviations from their probabilistic model in cases where this model makes imprecise predictions. Here we test for risk-sensitivity in a sensorimotor integration task where subjects exhibit Bayesian information integration when they infer the position of a target from noisy sensory feedback. When introducing a cost associated with subjects' response, we found that subjects exhibited a characteristic bias towards low cost responses when their uncertainty was high. This result is in accordance with risk-sensitive decision-making processes that allow for deviations from Bayes optimal decision-making in the face of uncertainty. Our results suggest that both Bayesian integration and risk-sensitivity are important factors to understand sensorimotor integration in a quantitative fashion.

  8. Bayesian outcome-based strategy classification.

    Science.gov (United States)

    Lee, Michael D

    2016-03-01

    Hilbig and Moshagen (Psychonomic Bulletin & Review, 21, 1431-1443, 2014) recently developed a method for making inferences about the decision processes people use in multi-attribute forced choice tasks. Their paper makes a number of worthwhile theoretical and methodological contributions. Theoretically, they provide an insightful psychological motivation for a probabilistic extension of the widely-used "weighted additive" (WADD) model, and show how this model, as well as other important models like "take-the-best" (TTB), can and should be expressed in terms of meaningful priors. Methodologically, they develop an inference approach based on the Minimum Description Length (MDL) principles that balances both the goodness-of-fit and complexity of the decision models they consider. This paper aims to preserve these useful contributions, but provide a complementary Bayesian approach with some theoretical and methodological advantages. We develop a simple graphical model, implemented in JAGS, that allows for fully Bayesian inferences about which models people use to make decisions. To demonstrate the Bayesian approach, we apply it to the models and data considered by Hilbig and Moshagen (Psychonomic Bulletin & Review, 21, 1431-1443, 2014), showing how a prior predictive analysis of the models, and posterior inferences about which models people use and the parameter settings at which they use them, can contribute to our understanding of human decision making.

  9. Being Bayesian in a quantum world

    International Nuclear Information System (INIS)

    Fuchs, C.

    2005-01-01

    Full text: To be a Bayesian about probability theory is to accept that probabilities represent subjective degrees of belief and nothing more. This is in distinction to the idea that probabilities represent long-term frequencies or objective propensities. But, how can a subjective account of probabilities coexist with the existence of quantum mechanics? To accept quantum mechanics is to accept the calculational apparatus of quantum states and the Born rule for determining probabilities in a quantum measurement. If there ever were a place for probabilities to be objective, it ought to be here. This raises the question of whether Bayesianism and quantum mechanics are compatible at all. For the Bayesian, it only suggests that we should rethink what quantum mechanics is about. Is it 'law of nature' or really more 'law of thought'? From transistors to lasers, the evidence is in that we live in a quantum world. One could infer from this that all the elements in the quantum formalism necessarily mirror nature itself: wave functions are so successful as calculational tools precisely because they represent elements of reality. A more Bayesian-like perspective is that if wave functions generate probabilities, then they too must be Bayesian degrees of belief, with all that such a radical idea entails. In particular, quantum probabilities have no firmer hold on reality than the word 'belief' in 'degrees of belief' already indicates. From this perspective, the only sense in which the quantum formalism mirrors nature is through the constraints it places on gambling agents who would like to better navigate through world. One might think that this is thin information, but it is not insubstantial. To the extent that an agent should use quantum mechanics for his uncertainty accounting rather than some other theory tells us something about the world itself - i.e., the world independent of the agent and his particular beliefs at any moment. In this talk, I will try to shore up these

  10. Learning Local Components to Understand Large Bayesian Networks

    DEFF Research Database (Denmark)

    Zeng, Yifeng; Xiang, Yanping; Cordero, Jorge

    2009-01-01

    (domain experts) to extract accurate information from a large Bayesian network due to dimensional difficulty. We define a formulation of local components and propose a clustering algorithm to learn such local components given complete data. The algorithm groups together most inter-relevant attributes......Bayesian networks are known for providing an intuitive and compact representation of probabilistic information and allowing the creation of models over a large and complex domain. Bayesian learning and reasoning are nontrivial for a large Bayesian network. In parallel, it is a tough job for users...... in a domain. We evaluate its performance on three benchmark Bayesian networks and provide results in support. We further show that the learned components may represent local knowledge more precisely in comparison to the full Bayesian networks when working with a small amount of data....

  11. An introduction to using Bayesian linear regression with clinical data.

    Science.gov (United States)

    Baldwin, Scott A; Larson, Michael J

    2017-11-01

    Statistical training psychology focuses on frequentist methods. Bayesian methods are an alternative to standard frequentist methods. This article provides researchers with an introduction to fundamental ideas in Bayesian modeling. We use data from an electroencephalogram (EEG) and anxiety study to illustrate Bayesian models. Specifically, the models examine the relationship between error-related negativity (ERN), a particular event-related potential, and trait anxiety. Methodological topics covered include: how to set up a regression model in a Bayesian framework, specifying priors, examining convergence of the model, visualizing and interpreting posterior distributions, interval estimates, expected and predicted values, and model comparison tools. We also discuss situations where Bayesian methods can outperform frequentist methods as well has how to specify more complicated regression models. Finally, we conclude with recommendations about reporting guidelines for those using Bayesian methods in their own research. We provide data and R code for replicating our analyses. Copyright © 2017 Elsevier Ltd. All rights reserved.

  12. Uncertainty Quantification Bayesian Framework for Porous Media Flows

    Science.gov (United States)

    Demyanov, V.; Christie, M.; Erbas, D.

    2005-12-01

    Uncertainty quantification is an increasingly important aspect of many areas of applied science, where the challenge is to make reliable predictions about the performance of complex physical systems in the absence of complete or reliable data. Predicting flows of fluids through undersurface reservoirs is an example of a complex system where accuracy in prediction is needed (e.g. in oil industry it is essential for financial reasons). Simulation of fluid flow in oil reservoirs is usually carried out using large commercially written finite difference simulators solving conservation equations describing the multi-phase flow through the porous reservoir rocks, which is a highly computationally expensive task. This work examines a Bayesian Framework for uncertainty quantification in porous media flows that uses a stochastic sampling algorithm to generate models that match observed time series data. The framework is flexible for a wide range of general physical/statistical parametric models, which are used to describe the underlying hydro-geological process in its temporal dynamics. The approach is based on exploration of the parameter space and update of the prior beliefs about what the most likely model definitions are. Optimization problem for a highly parametric physical model usually have multiple solutions, which impact the uncertainty of the made predictions. Stochastic search algorithm (e.g. genetic algorithm) allows to identify multiple "good enough" models in the parameter space. Furthermore, inference of the generated model ensemble via MCMC based algorithm evaluates the posterior probability of the generated models and quantifies uncertainty of the predictions. Machine learning algorithm - Artificial Neural Networks - are used to speed up the identification of regions in parameter space where good matches to observed data can be found. Adaptive nature of ANN allows to develop different ways of integrating them into the Bayesian framework: as direct time

  13. Towards Bayesian Inference of the Fast-Ion Distribution Function

    DEFF Research Database (Denmark)

    Stagner, L.; Heidbrink, W.W.; Salewski, Mirko

    2012-01-01

    sensitivity of the measurements are incorporated into Bayesian likelihood probabilities, while prior probabilities enforce physical constraints. As an initial step, this poster uses Bayesian statistics to infer the DIII-D electron density profile from multiple diagnostic measurements. Likelihood functions....... However, when theory and experiment disagree (for one or more diagnostics), it is unclear how to proceed. Bayesian statistics provides a framework to infer the DF, quantify errors, and reconcile discrepant diagnostic measurements. Diagnostic errors and ``weight functions" that describe the phase space...

  14. Bayesian non- and semi-parametric methods and applications

    CERN Document Server

    Rossi, Peter

    2014-01-01

    This book reviews and develops Bayesian non-parametric and semi-parametric methods for applications in microeconometrics and quantitative marketing. Most econometric models used in microeconomics and marketing applications involve arbitrary distributional assumptions. As more data becomes available, a natural desire to provide methods that relax these assumptions arises. Peter Rossi advocates a Bayesian approach in which specific distributional assumptions are replaced with more flexible distributions based on mixtures of normals. The Bayesian approach can use either a large but fixed number

  15. Sparse Event Modeling with Hierarchical Bayesian Kernel Methods

    Science.gov (United States)

    2016-01-05

    SECURITY CLASSIFICATION OF: The research objective of this proposal was to develop a predictive Bayesian kernel approach to model count data based on...several predictive variables. Such an approach, which we refer to as the Poisson Bayesian kernel model, is able to model the rate of occurrence of... kernel methods made use of: (i) the Bayesian property of improving predictive accuracy as data are dynamically obtained, and (ii) the kernel function

  16. Learning Bayesian Networks with Incomplete Data by Augmentation

    OpenAIRE

    Adel, Tameem; de Campos, Cassio P.

    2016-01-01

    We present new algorithms for learning Bayesian networks from data with missing values using a data augmentation approach. An exact Bayesian network learning algorithm is obtained by recasting the problem into a standard Bayesian network learning problem without missing data. To the best of our knowledge, this is the first exact algorithm for this problem. As expected, the exact algorithm does not scale to large domains. We build on the exact method to create an approximate algorithm using a ...

  17. Bayesian emulation for optimization in multi-step portfolio decisions

    OpenAIRE

    Irie, Kaoru; West, Mike

    2016-01-01

    We discuss the Bayesian emulation approach to computational solution of multi-step portfolio studies in financial time series. "Bayesian emulation for decisions" involves mapping the technical structure of a decision analysis problem to that of Bayesian inference in a purely synthetic "emulating" statistical model. This provides access to standard posterior analytic, simulation and optimization methods that yield indirect solutions of the decision problem. We develop this in time series portf...

  18. Online variational Bayesian filtering-based mobile target tracking in wireless sensor networks.

    Science.gov (United States)

    Zhou, Bingpeng; Chen, Qingchun; Li, Tiffany Jing; Xiao, Pei

    2014-11-11

    The received signal strength (RSS)-based online tracking for a mobile node in wireless sensor networks (WSNs) is investigated in this paper. Firstly, a multi-layer dynamic Bayesian network (MDBN) is introduced to characterize the target mobility with either directional or undirected movement. In particular, it is proposed to employ the Wishart distribution to approximate the time-varying RSS measurement precision's randomness due to the target movement. It is shown that the proposed MDBN offers a more general analysis model via incorporating the underlying statistical information of both the target movement and observations, which can be utilized to improve the online tracking capability by exploiting the Bayesian statistics. Secondly, based on the MDBN model, a mean-field variational Bayesian filtering (VBF) algorithm is developed to realize the online tracking of a mobile target in the presence of nonlinear observations and time-varying RSS precision, wherein the traditional Bayesian filtering scheme cannot be directly employed. Thirdly, a joint optimization between the real-time velocity and its prior expectation is proposed to enable online velocity tracking in the proposed online tacking scheme. Finally, the associated Bayesian Cramer-Rao Lower Bound (BCRLB) analysis and numerical simulations are conducted. Our analysis unveils that, by exploiting the potential state information via the general MDBN model, the proposed VBF algorithm provides a promising solution to the online tracking of a mobile node in WSNs. In addition, it is shown that the final tracking accuracy linearly scales with its expectation when the RSS measurement precision is time-varying.

  19. Spatio-Temporal Series Remote Sensing Image Prediction Based on Multi-Dictionary Bayesian Fusion

    Directory of Open Access Journals (Sweden)

    Chu He

    2017-11-01

    Full Text Available Contradictions in spatial resolution and temporal coverage emerge from earth observation remote sensing images due to limitations in technology and cost. Therefore, how to combine remote sensing images with low spatial yet high temporal resolution as well as those with high spatial yet low temporal resolution to construct images with both high spatial resolution and high temporal coverage has become an important problem called spatio-temporal fusion problem in both research and practice. A Multi-Dictionary Bayesian Spatio-Temporal Reflectance Fusion Model (MDBFM has been proposed in this paper. First, multiple dictionaries from regions of different classes are trained. Second, a Bayesian framework is constructed to solve the dictionary selection problem. A pixel-dictionary likehood function and a dictionary-dictionary prior function are constructed under the Bayesian framework. Third, remote sensing images before and after the middle moment are combined to predict images at the middle moment. Diverse shapes and textures information is learned from different landscapes in multi-dictionary learning to help dictionaries capture the distinctions between regions. The Bayesian framework makes full use of the priori information while the input image is classified. The experiments with one simulated dataset and two satellite datasets validate that the MDBFM is highly effective in both subjective and objective evaluation indexes. The results of MDBFM show more precise details and have a higher similarity with real images when dealing with both type changes and phenology changes.

  20. Estimation of the order of an autoregressive time series: a Bayesian approach

    International Nuclear Information System (INIS)

    Robb, L.J.

    1980-01-01

    Finite-order autoregressive models for time series are often used for prediction and other inferences. Given the order of the model, the parameters of the models can be estimated by least-squares, maximum-likelihood, or Yule-Walker method. The basic problem is estimating the order of the model. The problem of autoregressive order estimation is placed in a Bayesian framework. This approach illustrates how the Bayesian method brings the numerous aspects of the problem together into a coherent structure. A joint prior probability density is proposed for the order, the partial autocorrelation coefficients, and the variance; and the marginal posterior probability distribution for the order, given the data, is obtained. It is noted that the value with maximum posterior probability is the Bayes estimate of the order with respect to a particular loss function. The asymptotic posterior distribution of the order is also given. In conclusion, Wolfer's sunspot data as well as simulated data corresponding to several autoregressive models are analyzed according to Akaike's method and the Bayesian method. Both methods are observed to perform quite well, although the Bayesian method was clearly superior, in most cases

  1. Bayesian Hierarchical Scale Mixtures of Log-Normal Models for Inference in Reliability with Stochastic Constraint

    Directory of Open Access Journals (Sweden)

    Hea-Jung Kim

    2017-06-01

    Full Text Available This paper develops Bayesian inference in reliability of a class of scale mixtures of log-normal failure time (SMLNFT models with stochastic (or uncertain constraint in their reliability measures. The class is comprehensive and includes existing failure time (FT models (such as log-normal, log-Cauchy, and log-logistic FT models as well as new models that are robust in terms of heavy-tailed FT observations. Since classical frequency approaches to reliability analysis based on the SMLNFT model with stochastic constraint are intractable, the Bayesian method is pursued utilizing a Markov chain Monte Carlo (MCMC sampling based approach. This paper introduces a two-stage maximum entropy (MaxEnt prior, which elicits a priori uncertain constraint and develops Bayesian hierarchical SMLNFT model by using the prior. The paper also proposes an MCMC method for Bayesian inference in the SMLNFT model reliability and calls attention to properties of the MaxEnt prior that are useful for method development. Finally, two data sets are used to illustrate how the proposed methodology works.

  2. A surrogate-based sensitivity quantification and Bayesian inversion of a regional groundwater flow model

    Science.gov (United States)

    Chen, Mingjie; Izady, Azizallah; Abdalla, Osman A.; Amerjeed, Mansoor

    2018-02-01

    Bayesian inference using Markov Chain Monte Carlo (MCMC) provides an explicit framework for stochastic calibration of hydrogeologic models accounting for uncertainties; however, the MCMC sampling entails a large number of model calls, and could easily become computationally unwieldy if the high-fidelity hydrogeologic model simulation is time consuming. This study proposes a surrogate-based Bayesian framework to address this notorious issue, and illustrates the methodology by inverse modeling a regional MODFLOW model. The high-fidelity groundwater model is approximated by a fast statistical model using Bagging Multivariate Adaptive Regression Spline (BMARS) algorithm, and hence the MCMC sampling can be efficiently performed. In this study, the MODFLOW model is developed to simulate the groundwater flow in an arid region of Oman consisting of mountain-coast aquifers, and used to run representative simulations to generate training dataset for BMARS model construction. A BMARS-based Sobol' method is also employed to efficiently calculate input parameter sensitivities, which are used to evaluate and rank their importance for the groundwater flow model system. According to sensitivity analysis, insensitive parameters are screened out of Bayesian inversion of the MODFLOW model, further saving computing efforts. The posterior probability distribution of input parameters is efficiently inferred from the prescribed prior distribution using observed head data, demonstrating that the presented BMARS-based Bayesian framework is an efficient tool to reduce parameter uncertainties of a groundwater system.

  3. Theoretical evaluation of the detectability of random lesions in bayesian emission reconstruction

    International Nuclear Information System (INIS)

    Qi, Jinyi

    2003-01-01

    Detecting cancerous lesion is an important task in positron emission tomography (PET). Bayesian methods based on the maximum a posteriori principle (also called penalized maximum likelihood methods) have been developed to deal with the low signal to noise ratio in the emission data. Similar to the filter cut-off frequency in the filtered backprojection method, the prior parameters in Bayesian reconstruction control the resolution and noise trade-off and hence affect detectability of lesions in reconstructed images. Bayesian reconstructions are difficult to analyze because the resolution and noise properties are nonlinear and object-dependent. Most research has been based on Monte Carlo simulations, which are very time consuming. Building on the recent progress on the theoretical analysis of image properties of statistical reconstructions and the development of numerical observers, here we develop a theoretical approach for fast computation of lesion detectability in Bayesian reconstruction. The results can be used to choose the optimum hyperparameter for the maximum lesion detectability. New in this work is the use of theoretical expressions that explicitly model the statistical variation of the lesion and background without assuming that the object variation is (locally) stationary. The theoretical results are validated using Monte Carlo simulations. The comparisons show good agreement between the theoretical predications and the Monte Carlo results

  4. Clinical Outcome Prediction in Aneurysmal Subarachnoid Hemorrhage Using Bayesian Neural Networks with Fuzzy Logic Inferences

    Directory of Open Access Journals (Sweden)

    Benjamin W. Y. Lo

    2013-01-01

    Full Text Available Objective. The novel clinical prediction approach of Bayesian neural networks with fuzzy logic inferences is created and applied to derive prognostic decision rules in cerebral aneurysmal subarachnoid hemorrhage (aSAH. Methods. The approach of Bayesian neural networks with fuzzy logic inferences was applied to data from five trials of Tirilazad for aneurysmal subarachnoid hemorrhage (3551 patients. Results. Bayesian meta-analyses of observational studies on aSAH prognostic factors gave generalizable posterior distributions of population mean log odd ratios (ORs. Similar trends were noted in Bayesian and linear regression ORs. Significant outcome predictors include normal motor response, cerebral infarction, history of myocardial infarction, cerebral edema, history of diabetes mellitus, fever on day 8, prior subarachnoid hemorrhage, admission angiographic vasospasm, neurological grade, intraventricular hemorrhage, ruptured aneurysm size, history of hypertension, vasospasm day, age and mean arterial pressure. Heteroscedasticity was present in the nontransformed dataset. Artificial neural networks found nonlinear relationships with 11 hidden variables in 1 layer, using the multilayer perceptron model. Fuzzy logic decision rules (centroid defuzzification technique denoted cut-off points for poor prognosis at greater than 2.5 clusters. Discussion. This aSAH prognostic system makes use of existing knowledge, recognizes unknown areas, incorporates one's clinical reasoning, and compensates for uncertainty in prognostication.

  5. On Bayesian treatment of systematic uncertainties in confidence interval calculation

    CERN Document Server

    Tegenfeldt, Fredrik

    2005-01-01

    In high energy physics, a widely used method to treat systematic uncertainties in confidence interval calculations is based on combining a frequentist construction of confidence belts with a Bayesian treatment of systematic uncertainties. In this note we present a study of the coverage of this method for the standard Likelihood Ratio (aka Feldman & Cousins) construction for a Poisson process with known background and Gaussian or log-Normal distributed uncertainties in the background or signal efficiency. For uncertainties in the signal efficiency of upto 40 % we find over-coverage on the level of 2 to 4 % depending on the size of uncertainties and the region in signal space. Uncertainties in the background generally have smaller effect on the coverage. A considerable smoothing of the coverage curves is observed. A software package is presented which allows fast calculation of the confidence intervals for a variety of assumptions on shape and size of systematic uncertainties for different nuisance paramete...

  6. iSEDfit: Bayesian spectral energy distribution modeling of galaxies

    Science.gov (United States)

    Moustakas, John

    2017-08-01

    iSEDfit uses Bayesian inference to extract the physical properties of galaxies from their observed broadband photometric spectral energy distribution (SED). In its default mode, the inputs to iSEDfit are the measured photometry (fluxes and corresponding inverse variances) and a measurement of the galaxy redshift. Alternatively, iSEDfit can be used to estimate photometric redshifts from the input photometry alone. After the priors have been specified, iSEDfit calculates the marginalized posterior probability distributions for the physical parameters of interest, including the stellar mass, star-formation rate, dust content, star formation history, and stellar metallicity. iSEDfit also optionally computes K-corrections and produces multiple "quality assurance" (QA) plots at each stage of the modeling procedure to aid in the interpretation of the prior parameter choices and subsequent fitting results. The software is distributed as part of the impro IDL suite.

  7. A Bayesian Analysis of Unobserved Component Models Using Ox

    Directory of Open Access Journals (Sweden)

    Charles S. Bos

    2011-05-01

    Full Text Available This article details a Bayesian analysis of the Nile river flow data, using a similar state space model as other articles in this volume. For this data set, Metropolis-Hastings and Gibbs sampling algorithms are implemented in the programming language Ox. These Markov chain Monte Carlo methods only provide output conditioned upon the full data set. For filtered output, conditioning only on past observations, the particle filter is introduced. The sampling methods are flexible, and this advantage is used to extend the model to incorporate a stochastic volatility process. The volatility changes both in the Nile data and also in daily S&P 500 return data are investigated. The posterior density of parameters and states is found to provide information on which elements of the model are easily identifiable, and which elements are estimated with less precision.

  8. An Active Lattice Model in a Bayesian Framework

    DEFF Research Database (Denmark)

    Carstensen, Jens Michael

    1996-01-01

    A Markov Random Field is used as a structural model of a deformable rectangular lattice. When used as a template prior in a Bayesian framework this model is powerful for making inferences about lattice structures in images. The model assigns maximum probability to the perfect regular lattice...... by penalizing deviations in alignment and lattice node distance. The Markov random field represents prior knowledge about the lattice structure, and through an observation model that incorporates the visual appearance of the nodes, we can simulate realizations from the posterior distribution. A maximum...... a posteriori (MAP) estimate, found by simulated annealing, is used as the reconstructed lattice. The model was developed as a central part of an algorithm for automatic analylsis of genetic experiments, positioned in a lattice structure by a robot. The algorithm has been successfully applied to many images...

  9. Counting and confusion: Bayesian rate estimation with multiple populations

    Science.gov (United States)

    Farr, Will M.; Gair, Jonathan R.; Mandel, Ilya; Cutler, Curt

    2015-01-01

    We show how to obtain a Bayesian estimate of the rates or numbers of signal and background events from a set of events when the shapes of the signal and background distributions are known, can be estimated, or approximated; our method works well even if the foreground and background event distributions overlap significantly and the nature of any individual event cannot be determined with any certainty. We give examples of determining the rates of gravitational-wave events in the presence of background triggers from a template bank when noise parameters are known and/or can be fit from the trigger data. We also give an example of determining globular-cluster shape, location, and density from an observation of a stellar field that contains a nonuniform background density of stars superimposed on the cluster stars.

  10. Designing and testing inflationary models with Bayesian networks

    Energy Technology Data Exchange (ETDEWEB)

    Price, Layne C. [Carnegie Mellon Univ., Pittsburgh, PA (United States). Dept. of Physics; Auckland Univ. (New Zealand). Dept. of Physics; Peiris, Hiranya V. [Univ. College London (United Kingdom). Dept. of Physics and Astronomy; Frazer, Jonathan [DESY Hamburg (Germany). Theory Group; Univ. of the Basque Country, Bilbao (Spain). Dept. of Theoretical Physics; Basque Foundation for Science, Bilbao (Spain). IKERBASQUE; Easther, Richard [Auckland Univ. (New Zealand). Dept. of Physics

    2015-11-15

    Even simple inflationary scenarios have many free parameters. Beyond the variables appearing in the inflationary action, these include dynamical initial conditions, the number of fields, and couplings to other sectors. These quantities are often ignored but cosmological observables can depend on the unknown parameters. We use Bayesian networks to account for a large set of inflationary parameters, deriving generative models for the primordial spectra that are conditioned on a hierarchical set of prior probabilities describing the initial conditions, reheating physics, and other free parameters. We use N{sub f}-quadratic inflation as an illustrative example, finding that the number of e-folds N{sub *} between horizon exit for the pivot scale and the end of inflation is typically the most important parameter, even when the number of fields, their masses and initial conditions are unknown, along with possible conditional dependencies between these parameters.

  11. Designing and testing inflationary models with Bayesian networks

    Energy Technology Data Exchange (ETDEWEB)

    Price, Layne C. [McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213 (United States); Peiris, Hiranya V. [Department of Physics and Astronomy, University College London, London WC1E 6BT (United Kingdom); Frazer, Jonathan [Deutsches Elektronen-Synchrotron DESY, Theory Group, 22603 Hamburg (Germany); Easther, Richard, E-mail: laynep@andrew.cmu.edu, E-mail: h.peiris@ucl.ac.uk, E-mail: jonathan.frazer@desy.de, E-mail: r.easther@auckland.ac.nz [Department of Physics, University of Auckland, Private Bag 92019, Auckland (New Zealand)

    2016-02-01

    Even simple inflationary scenarios have many free parameters. Beyond the variables appearing in the inflationary action, these include dynamical initial conditions, the number of fields, and couplings to other sectors. These quantities are often ignored but cosmological observables can depend on the unknown parameters. We use Bayesian networks to account for a large set of inflationary parameters, deriving generative models for the primordial spectra that are conditioned on a hierarchical set of prior probabilities describing the initial conditions, reheating physics, and other free parameters. We use N{sub f}-quadratic inflation as an illustrative example, finding that the number of e-folds N{sub *} between horizon exit for the pivot scale and the end of inflation is typically the most important parameter, even when the number of fields, their masses and initial conditions are unknown, along with possible conditional dependencies between these parameters.

  12. Bayesian approach to errors-in-variables in regression models

    Science.gov (United States)

    Rozliman, Nur Aainaa; Ibrahim, Adriana Irawati Nur; Yunus, Rossita Mohammad

    2017-05-01

    In many applications and experiments, data sets are often contaminated with error or mismeasured covariates. When at least one of the covariates in a model is measured with error, Errors-in-Variables (EIV) model can be used. Measurement error, when not corrected, would cause misleading statistical inferences and analysis. Therefore, our goal is to examine the relationship of the outcome variable and the unobserved exposure variable given the observed mismeasured surrogate by applying the Bayesian formulation to the EIV model. We shall extend the flexible parametric method proposed by Hossain and Gustafson (2009) to another nonlinear regression model which is the Poisson regression model. We shall then illustrate the application of this approach via a simulation study using Markov chain Monte Carlo sampling methods.

  13. Designing and testing inflationary models with Bayesian networks

    International Nuclear Information System (INIS)

    Price, Layne C.; Auckland Univ.; Peiris, Hiranya V.; Frazer, Jonathan; Univ. of the Basque Country, Bilbao; Basque Foundation for Science, Bilbao; Easther, Richard

    2015-11-01

    Even simple inflationary scenarios have many free parameters. Beyond the variables appearing in the inflationary action, these include dynamical initial conditions, the number of fields, and couplings to other sectors. These quantities are often ignored but cosmological observables can depend on the unknown parameters. We use Bayesian networks to account for a large set of inflationary parameters, deriving generative models for the primordial spectra that are conditioned on a hierarchical set of prior probabilities describing the initial conditions, reheating physics, and other free parameters. We use N f -quadratic inflation as an illustrative example, finding that the number of e-folds N * between horizon exit for the pivot scale and the end of inflation is typically the most important parameter, even when the number of fields, their masses and initial conditions are unknown, along with possible conditional dependencies between these parameters.

  14. Variational Bayesian Causal Connectivity Analysis for fMRI

    Directory of Open Access Journals (Sweden)

    Martin eLuessi

    2014-05-01

    Full Text Available The ability to accurately estimate effective connectivity among brain regions from neuroimaging data could help answering many open questions in neuroscience. We propose a method which uses causality to obtain a measure of effective connectivity from fMRI data. The method uses a vector autoregressive model for the latent variables describing neuronal activity in combination with a linear observation model based on a convolution with a hemodynamic response function. Due to the employed modeling, it is possible to efficiently estimate all latent variables of the model using a variational Bayesian inference algorithm. The computational efficiency of the method enables us to apply it to large scale problems with high sampling rates and several hundred regions of interest. We use a comprehensive empirical evaluation with synthetic and real fMRI data to evaluate the performance of our method under various conditions.

  15. Optimal Experimental Design for Large-Scale Bayesian Inverse Problems

    KAUST Repository

    Ghattas, Omar

    2014-01-06

    We develop a Bayesian framework for the optimal experimental design of the shock tube experiments which are being carried out at the KAUST Clean Combustion Research Center. The unknown parameters are the pre-exponential parameters and the activation energies in the reaction rate expressions. The control parameters are the initial mixture composition and the temperature. The approach is based on first building a polynomial based surrogate model for the observables relevant to the shock tube experiments. Based on these surrogates, a novel MAP based approach is used to estimate the expected information gain in the proposed experiments, and to select the best experimental set-ups yielding the optimal expected information gains. The validity of the approach is tested using synthetic data generated by sampling the PC surrogate. We finally outline a methodology for validation using actual laboratory experiments, and extending experimental design methodology to the cases where the control parameters are noisy.

  16. Doing bayesian data analysis a tutorial with R and BUGS

    CERN Document Server

    Kruschke, John K

    2011-01-01

    There is an explosion of interest in Bayesian statistics, primarily because recently created computational methods have finally made Bayesian analysis obtainable to a wide audience. Doing Bayesian Data Analysis, A Tutorial Introduction with R and BUGS provides an accessible approach to Bayesian data analysis, as material is explained clearly with concrete examples. The book begins with the basics, including essential concepts of probability and random sampling, and gradually progresses to advanced hierarchical modeling methods for realistic data. The text delivers comprehensive coverage of all

  17. A Bayesian Justification for Random Sampling in Sample Survey

    Directory of Open Access Journals (Sweden)

    Glen Meeden

    2012-07-01

    Full Text Available In the usual Bayesian approach to survey sampling the sampling design, plays a minimal role, at best. Although a close relationship between exchangeable prior distributions and simple random sampling has been noted; how to formally integrate simple random sampling into the Bayesian paradigm is not clear. Recently it has been argued that the sampling design can be thought of as part of a Bayesian's prior distribution. We will show here that under this scenario simple random sample can be given a Bayesian justification in survey sampling.

  18. Comparative Study of Inference Methods for Bayesian Nonnegative Matrix Factorisation

    DEFF Research Database (Denmark)

    Brouwer, Thomas; Frellsen, Jes; Liò, Pietro

    2017-01-01

    In this paper, we study the trade-offs of different inference approaches for Bayesian matrix factorisation methods, which are commonly used for predicting missing values, and for finding patterns in the data. In particular, we consider Bayesian nonnegative variants of matrix factorisation and tri......-factorisation, and compare non-probabilistic inference, Gibbs sampling, variational Bayesian inference, and a maximum-a-posteriori approach. The variational approach is new for the Bayesian nonnegative models. We compare their convergence, and robustness to noise and sparsity of the data, on both synthetic and real...

  19. A Bayesian Network Schema for Lessening Database Inference

    National Research Council Canada - National Science Library

    Chang, LiWu; Moskowitz, Ira S

    2001-01-01

    .... The authors introduce a formal schema for database inference analysis, based upon a Bayesian network structure, which identifies critical parameters involved in the inference problem and represents...

  20. What do parameterized Om(z) diagnostics tell us in light of recent observations?

    Science.gov (United States)

    Qi, Jing-Zhao; Cao, Shuo; Biesiada, Marek; Xu, Teng-Peng; Wu, Yan; Zhang, Si-Xuan; Zhu, Zong-Hong

    2018-06-01

    In this paper, we propose a new parametrization for Om(z) diagnostics and show how the most recent and significantly improved observations concerning the H(z) and SN Ia measurements can be used to probe the consistency or tension between the ΛCDM model and observations. Our results demonstrate that H 0 plays a very important role in the consistency test of ΛCDM with H(z) data. Adopting the Hubble constant priors from Planck 2013 and Riess, one finds considerable tension between the current H(z) data and ΛCDM model and confirms the conclusions obtained previously by others. However, with the Hubble constant prior taken from WMAP9, the discrepancy between H(z) data and ΛCDM disappears, i.e., the current H(z) observations still support the cosmological constant scenario. This conclusion is also supported by the results derived from the Joint Light-curve Analysis (JLA) SN Ia sample. The best-fit Hubble constant from the combination of H(z)+JLA ({H}0={68.81}-1.49+1.50 km s‑1 Mpc‑1) is very consistent with results derived both by Planck 2013 and WMAP9, but is significantly different from the recent local measurement by Riess.