Directory of Open Access Journals (Sweden)
Ben Wielstra
Full Text Available The phylogenetic relationships for rapid species radiations are difficult to disentangle. Here we study one such case, namely the genus Triturus, which is composed of the marbled and crested newts. We analyze data for 38 genetic markers, positioned in 3-prime untranslated regions of protein-coding genes, obtained with 454 sequencing. Our dataset includes twenty Triturus newts and represents all nine species. Bayesian analysis of population structure allocates all individuals to their respective species. The branching patterns obtained by data concatenation, Bayesian concordance analysis and coalescent-based estimations of the species tree differ from one another. The data concatenation based species tree shows high branch support but branching order is considerably affected by allele choice in the case of heterozygotes in the concatenation process. Bayesian concordance analysis expresses the conflict between individual gene trees for part of the Triturus species tree as low concordance factors. The coalescent-based species tree is relatively similar to a previously published species tree based upon morphology and full mtDNA and any conflicting internal branches are not highly supported. Our findings reflect high gene tree discordance due to incomplete lineage sorting (possibly aggravated by hybridization in combination with low information content of the markers employed (as can be expected for relatively recent species radiations. This case study highlights the complexity of resolving rapid radiations and we acknowledge that to convincingly resolve the Triturus species tree even more genes will have to be consulted.
DEFF Research Database (Denmark)
Heller, Rasmus; Lorenzen, Eline D.; Okello, J.B.A;
2008-01-01
pandemic in the late 1800s, but little is known about the earlier demographic history of the species. We analysed genetic variation at 17 microsatellite loci and a 302-bp fragment of the mitochondrial DNA control region to infer past demographic changes in buffalo populations from East Africa. Two Bayesian...
Bayesian Uncertainty Analyses Via Deterministic Model
Krzysztofowicz, R.
2001-05-01
Rational decision-making requires that the total uncertainty about a variate of interest (a predictand) be quantified in terms of a probability distribution, conditional on all available information and knowledge. Suppose the state-of-knowledge is embodied in a deterministic model, which is imperfect and outputs only an estimate of the predictand. Fundamentals are presented of three Bayesian approaches to producing a probability distribution of the predictand via any deterministic model. The Bayesian Processor of Output (BPO) quantifies the total uncertainty in terms of a posterior distribution, conditional on model output. The Bayesian Processor of Ensemble (BPE) quantifies the total uncertainty in terms of a posterior distribution, conditional on an ensemble of model output. The Bayesian Forecasting System (BFS) decomposes the total uncertainty into input uncertainty and model uncertainty, which are characterized independently and then integrated into a predictive distribution.
Small sample Bayesian analyses in assessment of weapon performance
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Abundant test data are required in assessment of weapon performance.When weapon test data are insufficient,Bayesian analyses in small sample circumstance should be considered and the test data should be provided by simulations.The several Bayesian approaches are discussed and some limitations are founded.An improvement is put forward after limitations of Bayesian approaches available are analyzed and t he improved approach is applied to assessment of some new weapon performance.
The application of Bayesian networks in natural hazard analyses
Directory of Open Access Journals (Sweden)
K. Vogel
2013-10-01
Full Text Available In natural hazards we face several uncertainties due to our lack of knowledge and/or the intrinsic randomness of the underlying natural processes. Nevertheless, deterministic analysis approaches are still widely used in natural hazard assessments, with the pitfall of underestimating the hazard with potentially disastrous consequences. In this paper we show that the Bayesian network approach offers a flexible framework for capturing and expressing a broad range of different uncertainties as those encountered in natural hazard assessments. Although well studied in theory, the application of Bayesian networks on real-world data is often not straightforward and requires specific tailoring and adaption of existing algorithms. We demonstrate by way of three case studies (a ground motion model for a seismic hazard analysis, a flood damage assessment, and a landslide susceptibility study the applicability of Bayesian networks across different domains showcasing various properties and benefits of the Bayesian network framework. We offer suggestions as how to tackle practical problems arising along the way, mainly concentrating on the handling of continuous variables, missing observations, and the interaction of both. We stress that our networks are completely data-driven, although prior domain knowledge can be included if desired.
Analysing uncertainties: Towards comparing Bayesian and interval probabilities'
Blockley, David
2013-05-01
Two assumptions, commonly made in risk and reliability studies, have a long history. The first is that uncertainty is either aleatoric or epistemic. The second is that standard probability theory is sufficient to express uncertainty. The purposes of this paper are to provide a conceptual analysis of uncertainty and to compare Bayesian approaches with interval approaches with an example relevant to research on climate change. The analysis reveals that the categorisation of uncertainty as either aleatoric or epistemic is unsatisfactory for practical decision making. It is argued that uncertainty emerges from three conceptually distinctive and orthogonal attributes FIR i.e., fuzziness, incompleteness (epistemic) and randomness (aleatory). Characterisations of uncertainty, such as ambiguity, dubiety and conflict, are complex mixes of interactions in an FIR space. To manage future risks in complex systems it will be important to recognise the extent to which we 'don't know' about possible unintended and unwanted consequences or unknown-unknowns. In this way we may be more alert to unexpected hazards. The Bayesian approach is compared with an interval probability approach to show one way in which conflict due to incomplete information can be managed.
Using ancient DNA and coalescent-based methods to infer extinction.
Chang, Dan; Shapiro, Beth
2016-02-01
DNA sequences extracted from preserved remains can add considerable resolution to inference of past population dynamics. For example, coalescent-based methods have been used to correlate declines in some arctic megafauna populations with habitat fragmentation during the last ice age. These methods, however, often fail to detect population declines preceding extinction, most likely owing to a combination of sparse sampling, uninformative genetic markers, and models that cannot account for the increasingly structured nature of populations as habitats decline. As ancient DNA research expands to include full-genome analyses, these data will provide greater resolution of the genomic consequences of environmental change and the genetic signatures of extinction.
Using ancient DNA and coalescent-based methods to infer extinction.
Chang, Dan; Shapiro, Beth
2016-02-01
DNA sequences extracted from preserved remains can add considerable resolution to inference of past population dynamics. For example, coalescent-based methods have been used to correlate declines in some arctic megafauna populations with habitat fragmentation during the last ice age. These methods, however, often fail to detect population declines preceding extinction, most likely owing to a combination of sparse sampling, uninformative genetic markers, and models that cannot account for the increasingly structured nature of populations as habitats decline. As ancient DNA research expands to include full-genome analyses, these data will provide greater resolution of the genomic consequences of environmental change and the genetic signatures of extinction. PMID:26864783
Bayesian inference analyses of the polygenic architecture of rheumatoid arthritis
Stahl, Eli A.; Wegmann, Daniel; Trynka, Gosia; Gutierrez-Achury, Javier; Do, Ron; Voight, Benjamin F.; Kraft, Peter; Chen, Robert; Kallberg, Henrik J.; Kurreeman, Fina A. S.; Kathiresan, Sekar; Wijmenga, Cisca; Gregersen, Peter K.; Alfredsson, Lars; Siminovitch, Katherine A.; Worthington, Jane; de Bakker, Paul I. W.; Raychaudhuri, Soumya; Plenge, Robert M.
2012-01-01
The genetic architectures of common, complex diseases are largely uncharacterized. We modeled the genetic architecture underlying genome-wide association study (GWAS) data for rheumatoid arthritis and developed a new method using polygenic risk-score analyses to infer the total liability-scale varia
Kadarmideen, H.N.; Janss, L.L.G.
2005-01-01
Bayesian segregation analyses were used to investigate the mode of inheritance of osteochondral lesions (osteochondrosis, OC) in pigs. Data consisted of 1163 animals with OC and their pedigrees included 2891 animals. Mixed-inheritance threshold models (MITM) and several variants of MITM, in conjunct
A space-time multivariate Bayesian model to analyse road traffic accidents by severity
Boulieri, A; Liverani, S; Hoogh, K. de; Blangiardo, M.
2016-01-01
The paper investigates the dependences between levels of severity of road traffic accidents, accounting at the same time for spatial and temporal correlations. The study analyses road traffic accidents data at ward level in England over the period 2005–2013. We include in our model multivariate spatially structured and unstructured effects to capture the dependences between severities, within a Bayesian hierarchical formulation. We also include a temporal component to capture the time effects...
Siwek, M; Finocchiaro, R; Curik, I; Portolano, B
2011-02-01
Genetic structure and relationship amongst the main goat populations in Sicily (Girgentana, Derivata di Siria, Maltese and Messinese) were analysed using information from 19 microsatellite markers genotyped on 173 individuals. A posterior Bayesian approach implemented in the program STRUCTURE revealed a hierarchical structure with two clusters at the first level (Girgentana vs. Messinese, Derivata di Siria and Maltese), explaining 4.8% of variation (amovaФ(ST) estimate). Seven clusters nested within these first two clusters (further differentiations of Girgentana, Derivata di Siria and Maltese), explaining 8.5% of variation (amovaФ(SC) estimate). The analyses and methods applied in this study indicate their power to detect subtle population structure.
Directory of Open Access Journals (Sweden)
Velimir Gayevskiy
Full Text Available Bayesian inference methods are extensively used to detect the presence of population structure given genetic data. The primary output of software implementing these methods are ancestry profiles of sampled individuals. While these profiles robustly partition the data into subgroups, currently there is no objective method to determine whether the fixed factor of interest (e.g. geographic origin correlates with inferred subgroups or not, and if so, which populations are driving this correlation. We present ObStruct, a novel tool to objectively analyse the nature of structure revealed in Bayesian ancestry profiles using established statistical methods. ObStruct evaluates the extent of structural similarity between sampled and inferred populations, tests the significance of population differentiation, provides information on the contribution of sampled and inferred populations to the observed structure and crucially determines whether the predetermined factor of interest correlates with inferred population structure. Analyses of simulated and experimental data highlight ObStruct's ability to objectively assess the nature of structure in populations. We show the method is capable of capturing an increase in the level of structure with increasing time since divergence between simulated populations. Further, we applied the method to a highly structured dataset of 1,484 humans from seven continents and a less structured dataset of 179 Saccharomyces cerevisiae from three regions in New Zealand. Our results show that ObStruct provides an objective metric to classify the degree, drivers and significance of inferred structure, as well as providing novel insights into the relationships between sampled populations, and adds a final step to the pipeline for population structure analyses.
Odbert, Henry; Hincks, Thea; Aspinall, Willy
2015-04-01
Volcanic hazard assessments must combine information about the physical processes of hazardous phenomena with observations that indicate the current state of a volcano. Incorporating both these lines of evidence can inform our belief about the likelihood (probability) and consequences (impact) of possible hazardous scenarios, forming a basis for formal quantitative hazard assessment. However, such evidence is often uncertain, indirect or incomplete. Approaches to volcano monitoring have advanced substantially in recent decades, increasing the variety and resolution of multi-parameter timeseries data recorded at volcanoes. Interpreting these multiple strands of parallel, partial evidence thus becomes increasingly complex. In practice, interpreting many timeseries requires an individual to be familiar with the idiosyncrasies of the volcano, monitoring techniques, configuration of recording instruments, observations from other datasets, and so on. In making such interpretations, an individual must consider how different volcanic processes may manifest as measureable observations, and then infer from the available data what can or cannot be deduced about those processes. We examine how parts of this process may be synthesised algorithmically using Bayesian inference. Bayesian Belief Networks (BBNs) use probability theory to treat and evaluate uncertainties in a rational and auditable scientific manner, but only to the extent warranted by the strength of the available evidence. The concept is a suitable framework for marshalling multiple strands of evidence (e.g. observations, model results and interpretations) and their associated uncertainties in a methodical manner. BBNs are usually implemented in graphical form and could be developed as a tool for near real-time, ongoing use in a volcano observatory, for example. We explore the application of BBNs in analysing volcanic data from the long-lived eruption at Soufriere Hills Volcano, Montserrat. We show how our method
Chen, Cong; Zhang, Guohui; Tarefder, Rafiqul; Ma, Jianming; Wei, Heng; Guan, Hongzhi
2015-07-01
Rear-end crash is one of the most common types of traffic crashes in the U.S. A good understanding of its characteristics and contributing factors is of practical importance. Previously, both multinomial Logit models and Bayesian network methods have been used in crash modeling and analysis, respectively, although each of them has its own application restrictions and limitations. In this study, a hybrid approach is developed to combine multinomial logit models and Bayesian network methods for comprehensively analyzing driver injury severities in rear-end crashes based on state-wide crash data collected in New Mexico from 2010 to 2011. A multinomial logit model is developed to investigate and identify significant contributing factors for rear-end crash driver injury severities classified into three categories: no injury, injury, and fatality. Then, the identified significant factors are utilized to establish a Bayesian network to explicitly formulate statistical associations between injury severity outcomes and explanatory attributes, including driver behavior, demographic features, vehicle factors, geometric and environmental characteristics, etc. The test results demonstrate that the proposed hybrid approach performs reasonably well. The Bayesian network reference analyses indicate that the factors including truck-involvement, inferior lighting conditions, windy weather conditions, the number of vehicles involved, etc. could significantly increase driver injury severities in rear-end crashes. The developed methodology and estimation results provide insights for developing effective countermeasures to reduce rear-end crash injury severities and improve traffic system safety performance. PMID:25888994
Directory of Open Access Journals (Sweden)
Karacaören Burak
2011-05-01
Full Text Available Abstract Background It has been shown that if genetic relationships among individuals are not taken into account for genome wide association studies, this may lead to false positives. To address this problem, we used Genome-wide Rapid Association using Mixed Model and Regression and principal component stratification analyses. To account for linkage disequilibrium among the significant markers, principal components loadings obtained from top markers can be included as covariates. Estimation of Bayesian networks may also be useful to investigate linkage disequilibrium among SNPs and their relation with environmental variables. For the quantitative trait we first estimated residuals while taking polygenic effects into account. We then used a single SNP approach to detect the most significant SNPs based on the residuals and applied principal component regression to take linkage disequilibrium among these SNPs into account. For the categorical trait we used principal component stratification methodology to account for background effects. For correction of linkage disequilibrium we used principal component logit regression. Bayesian networks were estimated to investigate relationship among SNPs. Results Using the Genome-wide Rapid Association using Mixed Model and Regression and principal component stratification approach we detected around 100 significant SNPs for the quantitative trait (p Conclusions GRAMMAR could efficiently incorporate the information regarding random genetic effects. Principal component stratification should be cautiously used with stringent multiple hypothesis testing correction to correct for ancestral stratification and association analyses for binary traits when there are systematic genetic effects such as half sib family structures. Bayesian networks are useful to investigate relationships among SNPs and environmental variables.
Predictability of Regional Climate: A Bayesian Approach to Analysing a WRF Model Ensemble
Bruyere, C. L.; Mesquita, M. D. S.; Paimazumder, D.
2013-12-01
This study investigates aspects of climate predictability with a focus on climatic variables and different characteristics of extremes over nine North American climatic regions and two selected Atlantic sectors. An ensemble of state-of-the-art Weather Research and Forecasting Model (WRF) simulations is used for the analysis. The ensemble is comprised of a combination of various physics schemes, initial conditions, domain sizes, boundary conditions and breeding techniques. The main objectives of this research are: 1) to increase our understanding of the ability of WRF to capture regional climate information - both at the individual and collective ensemble members, 2) to investigate the role of different members and their synergy in reproducing regional climate 3) to estimate the associated uncertainty. In this study, we propose a Bayesian framework to study the predictability of extremes and associated uncertainties in order to provide a wealth of knowledge about WRF reliability and provide further clarity and understanding of the sensitivities and optimal combinations. The choice of the Bayesian model, as opposed to standard methods, is made because: a) this method has a mean square error that is less than standard statistics, which makes it a more robust method; b) it allows for the use of small sample sizes, which are typical in high-resolution modeling; c) it provides a probabilistic view of uncertainty, which is useful when making decisions concerning ensemble members.
Jomelli, Vincent; Pavlova, Irina; Eckert, Nicolas; Grancher, Delphine; Brunstein, Daniel
2015-12-01
How can debris flow occurrences be modelled at regional scale and take both environmental and climatic conditions into account? And, of the two, which has the most influence on debris flow activity? In this paper, we try to answer these questions with an innovative Bayesian hierarchical probabilistic model that simultaneously accounts for how debris flows respond to environmental and climatic variables. In it, full decomposition of space and time effects in occurrence probabilities is assumed, revealing an environmental and a climatic trend shared by all years/catchments, respectively, clearly distinguished from residual "random" effects. The resulting regional and annual occurrence probabilities evaluated as functions of the covariates make it possible to weight the respective contribution of the different terms and, more generally, to check the model performances at different spatio-temporal scales. After suitable validation, the model can be used to make predictions at undocumented sites and could be used in further studies for predictions under future climate conditions. Also, the Bayesian paradigm easily copes with missing data, thus making it possible to account for events that may have been missed during surveys. As a case study, we extract 124 debris flow event triggered between 1970 and 2005 in 27 catchments located in the French Alps from the French national natural hazard survey and model their variability of occurrence considering environmental and climatic predictors at the same time. We document the environmental characteristics of each debris flow catchment (morphometry, lithology, land cover, and the presence of permafrost). We also compute 15 climate variables including mean temperature and precipitation between May and October and the number of rainy days with daily cumulative rainfall greater than 10/15/20/25/30/40 mm day- 1. Application of our model shows that the combination of environmental and climatic predictors explained 77% of the overall
Directory of Open Access Journals (Sweden)
Salvidio Sebastiano
2010-02-01
Full Text Available Abstract Background It has been suggested that Plethodontid salamanders are excellent candidates for indicating ecosystem health. However, detailed, long-term data sets of their populations are rare, limiting our understanding of the demographic processes underlying their population fluctuations. Here we present a demographic analysis based on a 1996 - 2008 data set on an underground population of Speleomantes strinatii (Aellen in NW Italy. We utilised a Bayesian state-space approach allowing us to parameterise a stage-structured Lefkovitch model. We used all the available population data from annual temporary removal experiments to provide us with the baseline data on the numbers of juveniles, subadults and adult males and females present at any given time. Results Sampling the posterior chains of the converged state-space model gives us the likelihood distributions of the state-specific demographic rates and the associated uncertainty of these estimates. Analysing the resulting parameterised Lefkovitch matrices shows that the population growth is very close to 1, and that at population equilibrium we expect half of the individuals present to be adults of reproductive age which is what we also observe in the data. Elasticity analysis shows that adult survival is the key determinant for population growth. Conclusion This analysis demonstrates how an understanding of population demography can be gained from structured population data even in a case where following marked individuals over their whole lifespan is not practical.
Directory of Open Access Journals (Sweden)
Harlow Timothy J
2005-01-01
Full Text Available Abstract Background Bayesian phylogenetic inference holds promise as an alternative to maximum likelihood, particularly for large molecular-sequence data sets. We have investigated the performance of Bayesian inference with empirical and simulated protein-sequence data under conditions of relative branch-length differences and model violation. Results With empirical protein-sequence data, Bayesian posterior probabilities provide more-generous estimates of subtree reliability than does the nonparametric bootstrap combined with maximum likelihood inference, reaching 100% posterior probability at bootstrap proportions around 80%. With simulated 7-taxon protein-sequence datasets, Bayesian posterior probabilities are somewhat more generous than bootstrap proportions, but do not saturate. Compared with likelihood, Bayesian phylogenetic inference can be as or more robust to relative branch-length differences for datasets of this size, particularly when among-sites rate variation is modeled using a gamma distribution. When the (known correct model was used to infer trees, Bayesian inference recovered the (known correct tree in 100% of instances in which one or two branches were up to 20-fold longer than the others. At ratios more extreme than 20-fold, topological accuracy of reconstruction degraded only slowly when only one branch was of relatively greater length, but more rapidly when there were two such branches. Under an incorrect model of sequence change, inaccurate trees were sometimes observed at less extreme branch-length ratios, and (particularly for trees with single long branches such trees tended to be more inaccurate. The effect of model violation on accuracy of reconstruction for trees with two long branches was more variable, but gamma-corrected Bayesian inference nonetheless yielded more-accurate trees than did either maximum likelihood or uncorrected Bayesian inference across the range of conditions we examined. Assuming an exponential
GeneRecon Users' Manual — A coalescent based tool for fine-scale association mapping
DEFF Research Database (Denmark)
Mailund, T
2006-01-01
GeneRecon is a software package for linkage disequilibrium mapping using coalescent theory. It is based on Bayesian Markov-chain Monte Carlo (MCMC) method for fine-scale linkage-disequilibrium gene mapping using high-density marker maps. GeneRecon explicitly models the genealogy of a sample...
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Le Roy Pascale
2003-07-01
Full Text Available Abstract Segregation analyses were performed using both maximum likelihood – via a Quasi Newton algorithm – (ML-QN and Bayesian – via Gibbs sampling – (Bayesian-GS approaches in the Chinese European Tiameslan pig line. Major genes were searched for average ultrasonic backfat thickness (ABT, carcass fat (X2 and X4 and lean (X5 depths, days from 20 to 100 kg (D20100, Napole technological yield (NTY, number of false (FTN and good (GTN teats, as well as total teat number (TTN. The discrete nature of FTN was additionally considered using a threshold model under ML methodology. The results obtained with both methods consistently suggested the presence of major genes affecting ABT, X2, NTY, GTN and FTN. Major genes were also suggested for X4 and X5 using ML-QN, but not the Bayesian-GS, approach. The major gene affecting FTN was confirmed using the threshold model. Genetic correlations as well as gene effect and genotype frequency estimates suggested the presence of four different major genes. The first gene would affect fatness traits (ABT, X2 and X4, the second one a leanness trait (X5, the third one NTY and the last one GTN and FTN. Genotype frequencies of breeding animals and their evolution over time were consistent with the selection performed in the Tiameslan line.
Wafer, Lucas; Kloczewiak, Marek; Luo, Yin
2016-07-01
Analytical ultracentrifugation-sedimentation velocity (AUC-SV) is often used to quantify high molar mass species (HMMS) present in biopharmaceuticals. Although these species are often present in trace quantities, they have received significant attention due to their potential immunogenicity. Commonly, AUC-SV data is analyzed as a diffusion-corrected, sedimentation coefficient distribution, or c(s), using SEDFIT to numerically solve Lamm-type equations. SEDFIT also utilizes maximum entropy or Tikhonov-Phillips regularization to further allow the user to determine relevant sample information, including the number of species present, their sedimentation coefficients, and their relative abundance. However, this methodology has several, often unstated, limitations, which may impact the final analysis of protein therapeutics. These include regularization-specific effects, artificial "ripple peaks," and spurious shifts in the sedimentation coefficients. In this investigation, we experimentally verified that an explicit Bayesian approach, as implemented in SEDFIT, can largely correct for these effects. Clear guidelines on how to implement this technique and interpret the resulting data, especially for samples containing micro-heterogeneity (e.g., differential glycosylation), are also provided. In addition, we demonstrated how the Bayesian approach can be combined with F statistics to draw more accurate conclusions and rigorously exclude artifactual peaks. Numerous examples with an antibody and an antibody-drug conjugate were used to illustrate the strengths and drawbacks of each technique.
Directory of Open Access Journals (Sweden)
Yann Reynaud
Full Text Available Tuberculosis (TB remains broadly present in the Americas despite intense global efforts for its control and elimination. Starting from a large dataset comprising spoligotyping (n = 21183 isolates and 12-loci MIRU-VNTRs data (n = 4022 isolates from a total of 31 countries of the Americas (data extracted from the SITVIT2 database, this study aimed to get an overview of lineages circulating in the Americas. A total of 17119 (80.8% strains belonged to the Euro-American lineage 4, among which the most predominant genotypic family belonged to the Latin American and Mediterranean (LAM lineage (n = 6386, 30.1% of strains. By combining classical phylogenetic analyses and Bayesian approaches, this study revealed for the first time a clear genetic structuration of LAM9 sublineage into two subpopulations named LAM9C1 and LAM9C2, with distinct genetic characteristics. LAM9C1 was predominant in Chile, Colombia and USA, while LAM9C2 was predominant in Brazil, Dominican Republic, Guadeloupe and French Guiana. Globally, LAM9C2 was characterized by higher allelic richness as compared to LAM9C1 isolates. Moreover, LAM9C2 sublineage appeared to expand close to twenty times more than LAM9C1 and showed older traces of expansion. Interestingly, a significant proportion of LAM9C2 isolates presented typical signature of ancestral LAM-RDRio MIRU-VNTR type (224226153321. Further studies based on Whole Genome Sequencing of LAM strains will provide the needed resolution to decipher the biogeographical structure and evolutionary history of this successful family.
Can novel genetic analyses help to identify low-dispersal marine invasive species?
Teske, Peter R; Sandoval-Castillo, Jonathan; Waters, Jonathan M; Beheregaray, Luciano B
2014-07-01
Genetic methods can be a powerful tool to resolve the native versus introduced status of populations whose taxonomy and biogeography are poorly understood. The genetic study of introduced species is presently dominated by analyses that identify signatures of recent colonization by means of summary statistics. Unfortunately, such approaches cannot be used in low-dispersal species, in which recently established populations originating from elsewhere in the species' native range also experience periods of low population size because they are founded by few individuals. We tested whether coalescent-based molecular analyses that provide detailed information about demographic history supported the hypothesis that a sea squirt whose distribution is centered on Tasmania was recently introduced to mainland Australia and New Zealand through human activities. Methods comparing trends in population size (Bayesian Skyline Plots and Approximate Bayesian Computation) were no more informative than summary statistics, likely because of recent intra-Tasmanian dispersal. However, IMa2 estimates of divergence between putatively native and introduced populations provided information at a temporal scale suitable to differentiate between recent (potentially anthropogenic) introductions and ancient divergence, and indicated that all three non-Tasmanian populations were founded during the period of European settlement. While this approach can be affected by inaccurate molecular dating, it has considerable (albeit largely unexplored) potential to corroborate nongenetic information in species with limited dispersal capabilities.
Galbraith, Craig S.; Merrill, Gregory B.; Kline, Doug M.
2012-01-01
In this study we investigate the underlying relational structure between student evaluations of teaching effectiveness (SETEs) and achievement of student learning outcomes in 116 business related courses. Utilizing traditional statistical techniques, a neural network analysis and a Bayesian data reduction and classification algorithm, we find…
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
Draper, D.
2001-01-01
© 2012 Springer Science+Business Media, LLC. All rights reserved. Article Outline: Glossary Definition of the Subject and Introduction The Bayesian Statistical Paradigm Three Examples Comparison with the Frequentist Statistical Paradigm Future Directions Bibliography
Hotaling, Scott; Foley, Mary E; Lawrence, Nicolette M; Bocanegra, Jose; Blanco, Marina B; Rasoloarison, Rodin; Kappeler, Peter M; Barrett, Meredith A; Yoder, Anne D; Weisrock, David W
2016-05-01
Implementation of the coalescent model in a Bayesian framework is an emerging strength in genetically based species delimitation studies. By providing an objective measure of species diagnosis, these methods represent a quantitative enhancement to the analysis of multilocus data, and complement more traditional methods based on phenotypic and ecological characteristics. Recognized as two species 20 years ago, mouse lemurs (genus Microcebus) now comprise more than 20 species, largely diagnosed from mtDNA sequence data. With each new species description, enthusiasm has been tempered with scientific scepticism. Here, we present a statistically justified and unbiased Bayesian approach towards mouse lemur species delimitation. We perform validation tests using multilocus sequence data and two methodologies: (i) reverse-jump Markov chain Monte Carlo sampling to assess the likelihood of different models defined a priori by a guide tree, and (ii) a Bayes factor delimitation test that compares different species-tree models without a guide tree. We assess the sensitivity of these methods using randomized individual assignments, which has been used in bpp studies, but not with Bayes factor delimitation tests. Our results validate previously diagnosed taxa, as well as new species hypotheses, resulting in support for three new mouse lemur species. As the challenge of multiple researchers using differing criteria to describe diversity is not unique to Microcebus, the methods used here have significant potential for clarifying diversity in other taxonomic groups. We echo previous studies in advocating that multiple lines of evidence, including use of the coalescent model, should be trusted to delimit new species. PMID:26946180
Vangelder, B. H. W.
1978-01-01
Non-Bayesian statistics were used in simulation studies centered around laser range observations to LAGEOS. The capabilities of satellite laser ranging especially in connection with relative station positioning are evaluated. The satellite measurement system under investigation may fall short in precise determinations of the earth's orientation (precession and nutation) and earth's rotation as opposed to systems as very long baseline interferometry (VLBI) and lunar laser ranging (LLR). Relative station positioning, determination of (differential) polar motion, positioning of stations with respect to the earth's center of mass and determination of the earth's gravity field should be easily realized by satellite laser ranging (SLR). The last two features should be considered as best (or solely) determinable by SLR in contrast to VLBI and LLR.
Directory of Open Access Journals (Sweden)
Kanagi Kanapathy
2014-01-01
Full Text Available The research question is whether the positive relationship found between supplier involvement practices and new product development performances in developed economies also holds in emerging economies. The role of supplier involvement practices in new product development performance is yet to be substantially investigated in the emerging economies (other than China. This premise was examined by distributing a survey instrument (Jayaram’s (2008 published survey instrument that has been utilised in developed economies to Malaysian manufacturing companies. To gauge the relationship between the supplier involvement practices and new product development (NPD project performance of 146 companies, structural equation modelling was adopted. Our findings prove that supplier involvement practices have a significant positive impact on NPD project performance in an emerging economy with respect to quality objectives, design objectives, cost objectives, and “time-to-market” objectives. Further analysis using the Bayesian Markov Chain Monte Carlo algorithm, yielding a more credible and feasible differentiation, confirmed these results (even in the case of an emerging economy and indicated that these practices have a 28% impact on variance of NPD project performance. This considerable effect implies that supplier involvement is a must have, although further research is needed to identify the contingencies for its practices.
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
Institute of Scientific and Technical Information of China (English)
岳秀廷; 李志农; 陈金刚
2012-01-01
用独立分量分析(ICA)分解和表示数据时,假设整个数据分布完全可以用一个坐标系来描述.然而,当观测数据是由许多自相似的、非高斯的流形组成时,则硬是用一个单独的、全局的表示是不合适的,这样会产生一个次优的表示.针对ICA在盲源分离中的不足,在变分贝叶斯理论的基础上提出了一种基于变分贝叶斯混合独立分量分析的机械故障源盲分离方法.该方法是考虑到源信号来自于多个坐标系,然后在多个坐标系下建立独立分量分析混合模型对观测信号进行学习分离.实验结果表明,本文提出的方法是非常有效的.%Decomposing and representing data using independent component analysers(ICA)assumes that the whole data distribution is adequately described by one coordinate frame.However,if the observed data consists of various self-similar,non-Gaussian manifolds, enforcing a single, global representation is not appropriate and will produce a sub-optimal representation.In order to make up the lack of independent component analyser in blind sources separations, blind separation of mechanical fault sources based on variational Bayesian mixture of independent component analysers is presented based on variational Bayesian theory in this paper.Conside.ring the source signals coming from multiple frames, the method creats a mixture model of independent component analysers in multiple frameworks for learning the observed signals and separating thenuThe experimental results show that the method proposed in this paper is very effective.
Singh, Garima; Dal Grande, Francesco; Divakar, Pradeep K; Otte, Jürgen; Leavitt, Steven D; Szczepanska, Katarzyna; Crespo, Ana; Rico, Víctor J; Aptroot, André; Cáceres, Marcela Eugenia da Silva; Lumbsch, H Thorsten; Schmitt, Imke
2015-01-01
Species recognition in lichen-forming fungi has been a challenge because of unsettled species concepts, few taxonomically relevant traits, and limitations of traditionally used morphological and chemical characters for identifying closely related species. Here we analyze species diversity in the cosmopolitan genus Protoparmelia s.l. The ~25 described species in this group occur across diverse habitats from the boreal-arctic/alpine to the tropics, but their relationship to each other remains unexplored. In this study, we inferred the phylogeny of 18 species currently assigned to this genus based on 160 specimens and six markers: mtSSU, nuLSU, ITS, RPB1, MCM7, and TSR1. We assessed the circumscription of species-level lineages in Protoparmelia s. str. using two coalescent-based species delimitation methods--BP&P and spedeSTEM. Our results suggest the presence of a tropical and an extra-tropical lineage, and eleven previously unrecognized distinct species-level lineages in Protoparmelia s. str. Several cryptic lineages were discovered as compared to phenotype-based species delimitation. Many of the putative species are supported by geographic evidence. PMID:25932996
Directory of Open Access Journals (Sweden)
Garima Singh
Full Text Available Species recognition in lichen-forming fungi has been a challenge because of unsettled species concepts, few taxonomically relevant traits, and limitations of traditionally used morphological and chemical characters for identifying closely related species. Here we analyze species diversity in the cosmopolitan genus Protoparmelia s.l. The ~25 described species in this group occur across diverse habitats from the boreal-arctic/alpine to the tropics, but their relationship to each other remains unexplored. In this study, we inferred the phylogeny of 18 species currently assigned to this genus based on 160 specimens and six markers: mtSSU, nuLSU, ITS, RPB1, MCM7, and TSR1. We assessed the circumscription of species-level lineages in Protoparmelia s. str. using two coalescent-based species delimitation methods--BP&P and spedeSTEM. Our results suggest the presence of a tropical and an extra-tropical lineage, and eleven previously unrecognized distinct species-level lineages in Protoparmelia s. str. Several cryptic lineages were discovered as compared to phenotype-based species delimitation. Many of the putative species are supported by geographic evidence.
Introduction to Bayesian statistics
Bolstad, William M
2016-01-01
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...
Bayesian artificial intelligence
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.
Bayesian artificial intelligence
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
Bayesian networks as a tool for epidemiological systems analysis
Lewis, F.I.
2012-01-01
Bayesian network analysis is a form of probabilistic modeling which derives from empirical data a directed acyclic graph (DAG) describing the dependency structure between random variables. Bayesian networks are increasingly finding application in areas such as computational and systems biology, and more recently in epidemiological analyses. The key distinction between standard empirical modeling approaches, such as generalised linear modeling, and Bayesian network analyses is that the latter ...
Gelman, Andrew; Stern, Hal S; Dunson, David B; Vehtari, Aki; Rubin, Donald B
2013-01-01
FUNDAMENTALS OF BAYESIAN INFERENCEProbability and InferenceSingle-Parameter Models Introduction to Multiparameter Models Asymptotics and Connections to Non-Bayesian ApproachesHierarchical ModelsFUNDAMENTALS OF BAYESIAN DATA ANALYSISModel Checking Evaluating, Comparing, and Expanding ModelsModeling Accounting for Data Collection Decision AnalysisADVANCED COMPUTATION Introduction to Bayesian Computation Basics of Markov Chain Simulation Computationally Efficient Markov Chain Simulation Modal and Distributional ApproximationsREGRESSION MODELS Introduction to Regression Models Hierarchical Linear
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...
Bayesian Games with Intentions
Bjorndahl, Adam; Halpern, Joseph Y.; Pass, Rafael
2016-01-01
We show that standard Bayesian games cannot represent the full spectrum of belief-dependent preferences. However, by introducing a fundamental distinction between intended and actual strategies, we remove this limitation. We define Bayesian games with intentions, generalizing both Bayesian games and psychological games, and prove that Nash equilibria in psychological games correspond to a special class of equilibria as defined in our setting.
Institute of Scientific and Technical Information of China (English)
Konstantinos ANGELIS; Mario DOS REIS
2015-01-01
Although the effects of the coalescent process on sequence divergence and genealogies are well understood, the vir-tual majority of studies that use molecular sequences to estimate times of divergence among species have failed to account for the coalescent process. Here we study the impact of ancestral population size and incomplete lineage sorting on Bayesian estimates of species divergence times under the molecular clock when the inference model ignores the coalescent process. Using a combi-nation of mathematical analysis, computer simulations and analysis of real data, we find that the errors on estimates of times and the molecular rate can be substantial when ancestral populations are large and when there is substantial incomplete lineage sort-ing. For example, in a simple three-species case, we find that if the most precise fossil calibration is placed on the root of the phylogeny, the age of the internal node is overestimated, while if the most precise calibration is placed on the internal node, then the age of the root is underestimated. In both cases, the molecular rate is overestimated. Using simulations on a phylogeny of nine species, we show that substantial errors in time and rate estimates can be obtained even when dating ancient divergence events. We analyse the hominoid phylogeny and show that estimates of the neutral mutation rate obtained while ignoring the coalescent are too high. Using a coalescent-based technique to obtain geological times of divergence, we obtain estimates of the mutation rate that are within experimental estimates and we also obtain substantially older divergence times within the phylogeny [Current Zoology 61 (5): 874–885, 2015].
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...... and edges. The nodes represent variables, which may be either discrete or continuous. An edge between two nodes A and B indicates a direct influence between the state of A and the state of B, which in some domains can also be interpreted as a causal relation. The wide-spread use of Bayesian networks...... is largely due to the availability of efficient inference algorithms for answering probabilistic queries about the states of the variables in the network. Furthermore, to support the construction of Bayesian network models, learning algorithms are also available. We give an overview of the Bayesian network...
Bayesian inference of population size history from multiple loci
Directory of Open Access Journals (Sweden)
Drummond Alexei J
2008-10-01
Full Text Available Abstract Background Effective population size (Ne is related to genetic variability and is a basic parameter in many models of population genetics. A number of methods for inferring current and past population sizes from genetic data have been developed since JFC Kingman introduced the n-coalescent in 1982. Here we present the Extended Bayesian Skyline Plot, a non-parametric Bayesian Markov chain Monte Carlo algorithm that extends a previous coalescent-based method in several ways, including the ability to analyze multiple loci. Results Through extensive simulations we show the accuracy and limitations of inferring population size as a function of the amount of data, including recovering information about evolutionary bottlenecks. We also analyzed two real data sets to demonstrate the behavior of the new method; a single gene Hepatitis C virus data set sampled from Egypt and a 10 locus Drosophila ananassae data set representing 16 different populations. Conclusion The results demonstrate the essential role of multiple loci in recovering population size dynamics. Multi-locus data from a small number of individuals can precisely recover past bottlenecks in population size which can not be characterized by analysis of a single locus. We also demonstrate that sequence data quality is important because even moderate levels of sequencing errors result in a considerable decrease in estimation accuracy for realistic levels of population genetic variability.
Understanding Computational Bayesian Statistics
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
Bayesian statistics an introduction
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
The bugs book a practical introduction to Bayesian analysis
Lunn, David; Best, Nicky; Thomas, Andrew; Spiegelhalter, David
2012-01-01
Introduction: Probability and ParametersProbabilityProbability distributionsCalculating properties of probability distributionsMonte Carlo integrationMonte Carlo Simulations Using BUGSIntroduction to BUGSDoodleBUGSUsing BUGS to simulate from distributionsTransformations of random variablesComplex calculations using Monte CarloMultivariate Monte Carlo analysisPredictions with unknown parametersIntroduction to Bayesian InferenceBayesian learningPosterior predictive distributionsConjugate Bayesian inferenceInference about a discrete parameterCombinations of conjugate analysesBayesian and classica
Frühwirth-Schnatter, Sylvia
1990-01-01
In the paper at hand we apply it to Bayesian statistics to obtain "Fuzzy Bayesian Inference". In the subsequent sections we will discuss a fuzzy valued likelihood function, Bayes' theorem for both fuzzy data and fuzzy priors, a fuzzy Bayes' estimator, fuzzy predictive densities and distributions, and fuzzy H.P.D .-Regions. (author's abstract)
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…
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.
Space Shuttle RTOS Bayesian Network
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
Directory of Open Access Journals (Sweden)
P.R.C. Nobre
2003-08-01
Full Text Available Growth curves of Nellore cattle were analyzed using body weights measured at ages ranging from 1 day (birth weight to 733 days. Traits considered were birth weight, 10 to 110 days weight, 102 to 202 days weight, 193 to 293 days weight, 283 to 383 days weight, 376 to 476 days weight, 551 to 651 days weight, and 633 to 733 days weight. Two data samples were created: one with 79,849 records from herds that had missing traits and another with 74,601 from herds with no missing traits. Records preadjusted to a fixed age were analyzed by a multiple trait model (MTM, which included the effects of contemporary group, age of dam class, additive direct, additive maternal, and maternal permanent environment. Analyses were carried out by a Bayesian method for all nine traits. The random regression model (RRM included the effects of age of animal, contemporary group, age of dam class, additive direct, permanent environment, additive maternal, and maternal permanent environment. Legendre cubic polynomials were used to describe random effects. MTM estimated covariance components and genetic parameters for birth weight and sequential weights and RRM for all ages. Due to the fact that covariance components based on RRM were inflated for herds with missing traits, MTM should be used and converted to covariance functions.Curvas de crescimento de gado Nelore foram analisadas com base nos pesos corporais coletados do nascer aos 733 dias de idade. As características consideradas foram peso ao nascer e pesos dos 10 aos 110, dos 102 aos 202, dos 193 aos 293, dos 283 aos 383, dos 376 aos 476, dos 467 aos 567, dos 551 aos 651 e dos 633 aos 733 dias de idade. Duas amostras foram geradas: a primeira, constituída de 79.849 medidas, continha dados de rebanhos com informações perdidas, e a segunda, de 74.601 medidas, originou-se de rebanhos com informações completas. Os pesos pré-ajustados para as idades fixas foram analisados por meio de um modelo de características m
Granade, Christopher; Cory, D G
2015-01-01
In recent years, Bayesian methods have been proposed as a solution to a wide range of issues in quantum state and process tomography. State-of- the-art Bayesian tomography solutions suffer from three problems: numerical intractability, a lack of informative prior distributions, and an inability to track time-dependent processes. Here, we solve all three problems. First, we use modern statistical methods, as pioneered by Husz\\'ar and Houlsby and by Ferrie, to make Bayesian tomography numerically tractable. Our approach allows for practical computation of Bayesian point and region estimators for quantum states and channels. Second, we propose the first informative priors on quantum states and channels. Finally, we develop a method that allows online tracking of time-dependent states and estimates the drift and diffusion processes affecting a state. We provide source code and animated visual examples for our methods.
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...
Bayesian Lensing Shear Measurement
Bernstein, Gary M
2013-01-01
We derive an estimator of weak gravitational lensing shear from background galaxy images that avoids noise-induced biases through a rigorous Bayesian treatment of the measurement. The Bayesian formalism requires a prior describing the (noiseless) distribution of the target galaxy population over some parameter space; this prior can be constructed from low-noise images of a subsample of the target population, attainable from long integrations of a fraction of the survey field. We find two ways to combine this exact treatment of noise with rigorous treatment of the effects of the instrumental point-spread function and sampling. The Bayesian model fitting (BMF) method assigns a likelihood of the pixel data to galaxy models (e.g. Sersic ellipses), and requires the unlensed distribution of galaxies over the model parameters as a prior. The Bayesian Fourier domain (BFD) method compresses galaxies to a small set of weighted moments calculated after PSF correction in Fourier space. It requires the unlensed distributi...
An introduction to Gaussian Bayesian networks.
Grzegorczyk, Marco
2010-01-01
The extraction of regulatory networks and pathways from postgenomic data is important for drug -discovery and development, as the extracted pathways reveal how genes or proteins regulate each other. Following up on the seminal paper of Friedman et al. (J Comput Biol 7:601-620, 2000), Bayesian networks have been widely applied as a popular tool to this end in systems biology research. Their popularity stems from the tractability of the marginal likelihood of the network structure, which is a consistent scoring scheme in the Bayesian context. This score is based on an integration over the entire parameter space, for which highly expensive computational procedures have to be applied when using more complex -models based on differential equations; for example, see (Bioinformatics 24:833-839, 2008). This chapter gives an introduction to reverse engineering regulatory networks and pathways with Gaussian Bayesian networks, that is Bayesian networks with the probabilistic BGe scoring metric [see (Geiger and Heckerman 235-243, 1995)]. In the BGe model, the data are assumed to stem from a Gaussian distribution and a normal-Wishart prior is assigned to the unknown parameters. Gaussian Bayesian network methodology for analysing static observational, static interventional as well as dynamic (observational) time series data will be described in detail in this chapter. Finally, we apply these Bayesian network inference methods (1) to observational and interventional flow cytometry (protein) data from the well-known RAF pathway to evaluate the global network reconstruction accuracy of Bayesian network inference and (2) to dynamic gene expression time series data of nine circadian genes in Arabidopsis thaliana to reverse engineer the unknown regulatory network topology for this domain. PMID:20824469
Malicious Bayesian Congestion Games
Gairing, Martin
2008-01-01
In this paper, we introduce malicious Bayesian congestion games as an extension to congestion games where players might act in a malicious way. In such a game each player has two types. Either the player is a rational player seeking to minimize her own delay, or - with a certain probability - the player is malicious in which case her only goal is to disturb the other players as much as possible. We show that such games do in general not possess a Bayesian Nash equilibrium in pure strategies (i.e. a pure Bayesian Nash equilibrium). Moreover, given a game, we show that it is NP-complete to decide whether it admits a pure Bayesian Nash equilibrium. This result even holds when resource latency functions are linear, each player is malicious with the same probability, and all strategy sets consist of singleton sets. For a slightly more restricted class of malicious Bayesian congestion games, we provide easy checkable properties that are necessary and sufficient for the existence of a pure Bayesian Nash equilibrium....
Dynamic Bayesian Combination of Multiple Imperfect Classifiers
Simpson, Edwin; Psorakis, Ioannis; Smith, Arfon
2012-01-01
Classifier combination methods need to make best use of the outputs of multiple, imperfect classifiers to enable higher accuracy classifications. In many situations, such as when human decisions need to be combined, the base decisions can vary enormously in reliability. A Bayesian approach to such uncertain combination allows us to infer the differences in performance between individuals and to incorporate any available prior knowledge about their abilities when training data is sparse. In this paper we explore Bayesian classifier combination, using the computationally efficient framework of variational Bayesian inference. We apply the approach to real data from a large citizen science project, Galaxy Zoo Supernovae, and show that our method far outperforms other established approaches to imperfect decision combination. We go on to analyse the putative community structure of the decision makers, based on their inferred decision making strategies, and show that natural groupings are formed. Finally we present ...
Bayesian inference of the metazoan phylogeny
DEFF Research Database (Denmark)
Glenner, Henrik; Hansen, Anders J; Sørensen, Martin V;
2004-01-01
been the only feasible combined approach but is highly sensitive to long-branch attraction. Recent development of stochastic models for discrete morphological characters and computationally efficient methods for Bayesian inference has enabled combined molecular and morphological data analysis...... with rigorous statistical approaches less prone to such inconsistencies. We present the first statistically founded analysis of a metazoan data set based on a combination of morphological and molecular data and compare the results with a traditional parsimony analysis. Interestingly, the Bayesian analyses...... such as the ecdysozoans and lophotrochozoans. Parsimony, on the contrary, shows conflicting results, with morphology being congruent to the Bayesian results and the molecular data set producing peculiarities that are largely reflected in the combined analysis....
Computational statistics using the bBayesian Inference Engine
Weinberg, Martin D
2012-01-01
This paper introduces the Bayesian Inference Engine (BIE), a general parallel-optimised software package for parameter inference and model selection. This package is motivated by the analysis needs of modern astronomical surveys and the need to organise and reuse expensive derived data. I describe key concepts that illustrate the power of Bayesian inference to address these needs and outline the computational challenge. The techniques presented are based on experience gained in modelling star-counts and stellar populations, analysing the morphology of galaxy images, and performing Bayesian investigations of semi-analytic models of galaxy formation. These inference problems require advanced Markov chain Monte Carlo (MCMC) algorithms that expedite sampling, mixing, and the analysis of the Bayesian posterior distribution. The BIE was designed to be a collaborative platform for applying Bayesian methodology to astronomy. By providing a variety of statistical algorithms for all phases of the inference problem, a u...
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.
Institute of Scientific and Technical Information of China (English)
闫放; 许开立; 姚锡文; 王文菁
2015-01-01
Fussell-Vesely worth of each event is calculated by Bayesian network .Prevention measures are adopted to the reason event with higher worth .The event tree analysis is conducted to determine control measures and calculate the probability of biomass gasification poisoning accidents before and after measures are taken .Finally the biomass gasification poisoning acci-dents after using bow-tie analysis based on Bayesian network are evaluated by risk assessment matrix .As the result ,this method can reduce probability and risk of accidents by adopting safety measures to parts of the whole points of the system .%本文通过贝叶斯网络计算各原因事件的弗塞－维思利重要度，选取重要度较高的原因事件采取预防措施；并通过事件树分析确定控制措施，计算采取措施前后生物质气化中毒事故发生的概率，最后通过危险性评价矩阵对采取基于贝叶斯网络的bow－tie分析后的生物质气化中毒事故风险进行评价。结果表明，采用该方法只需对系统中部分节点采取安全措施即可有效降低事故发生概率，从而降低事故风险。
Bayesian least squares deconvolution
Ramos, A Asensio
2015-01-01
Aims. To develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods. We consider LSD under the Bayesian framework and we introduce a flexible Gaussian Process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results. We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.
Bayesian least squares deconvolution
Asensio Ramos, A.; Petit, P.
2015-11-01
Aims: We develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods: We consider LSD under the Bayesian framework and we introduce a flexible Gaussian process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results: We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.
Hybrid Batch Bayesian Optimization
Azimi, Javad; Fern, Xiaoli
2012-01-01
Bayesian Optimization aims at optimizing an unknown non-convex/concave function that is costly to evaluate. We are interested in application scenarios where concurrent function evaluations are possible. Under such a setting, BO could choose to either sequentially evaluate the function, one input at a time and wait for the output of the function before making the next selection, or evaluate the function at a batch of multiple inputs at once. These two different settings are commonly referred to as the sequential and batch settings of Bayesian Optimization. In general, the sequential setting leads to better optimization performance as each function evaluation is selected with more information, whereas the batch setting has an advantage in terms of the total experimental time (the number of iterations). In this work, our goal is to combine the strength of both settings. Specifically, we systematically analyze Bayesian optimization using Gaussian process as the posterior estimator and provide a hybrid algorithm t...
Loredo, T J
2004-01-01
I describe a framework for adaptive scientific exploration based on iterating an Observation--Inference--Design cycle that allows adjustment of hypotheses and observing protocols in response to the results of observation on-the-fly, as data are gathered. The framework uses a unified Bayesian methodology for the inference and design stages: Bayesian inference to quantify what we have learned from the available data and predict future data, and Bayesian decision theory to identify which new observations would teach us the most. When the goal of the experiment is simply to make inferences, the framework identifies a computationally efficient iterative ``maximum entropy sampling'' strategy as the optimal strategy in settings where the noise statistics are independent of signal properties. Results of applying the method to two ``toy'' problems with simulated data--measuring the orbit of an extrasolar planet, and locating a hidden one-dimensional object--show the approach can significantly improve observational eff...
Bayesian Exploratory Factor Analysis
DEFF Research Database (Denmark)
Conti, Gabriella; Frühwirth-Schnatter, Sylvia; Heckman, James J.;
2014-01-01
This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on ad hoc classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor, and the corr......This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on ad hoc classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor......, and the corresponding factor loadings. Classical identification criteria are applied and integrated into our Bayesian procedure to generate models that are stable and clearly interpretable. A Monte Carlo study confirms the validity of the approach. The method is used to produce interpretable low dimensional aggregates...
Bayesian multiple target tracking
Streit, Roy L
2013-01-01
This second edition has undergone substantial revision from the 1999 first edition, recognizing that a lot has changed in the multiple target tracking field. One of the most dramatic changes is in the widespread use of particle filters to implement nonlinear, non-Gaussian Bayesian trackers. This book views multiple target tracking as a Bayesian inference problem. Within this framework it develops the theory of single target tracking, multiple target tracking, and likelihood ratio detection and tracking. In addition to providing a detailed description of a basic particle filter that implements
Bayesian and frequentist inequality tests
David M. Kaplan; Zhuo, Longhao
2016-01-01
Bayesian and frequentist criteria are fundamentally different, but often posterior and sampling distributions are asymptotically equivalent (and normal). We compare Bayesian and frequentist hypothesis tests of inequality restrictions in such cases. For finite-dimensional parameters, if the null hypothesis is that the parameter vector lies in a certain half-space, then the Bayesian test has (frequentist) size $\\alpha$; if the null hypothesis is any other convex subspace, then the Bayesian test...
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.
Bayesian Analysis of Individual Level Personality Dynamics
Cripps, Edward; Wood, Robert E.; Beckmann, Nadin; Lau, John; Beckmann, Jens F.; Cripps, Sally Ann
2016-01-01
A Bayesian technique with analyses of within-person processes at the level of the individual is presented. The approach is used to examine whether 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 spiraling. While Bayesian techniques have many potential advantages for the analyses of processes at the level of the individual, ease of use is not one of them for psychologists trained in traditional frequentist statistical techniques. PMID:27486415
Bayesian Analysis of Individual Level Personality Dynamics.
Cripps, Edward; Wood, Robert E; Beckmann, Nadin; Lau, John; Beckmann, Jens F; Cripps, Sally Ann
2016-01-01
A Bayesian technique with analyses of within-person processes at the level of the individual is presented. The approach is used to examine whether 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 spiraling. While Bayesian techniques have many potential advantages for the analyses of processes at the level of the individual, ease of use is not one of them for psychologists trained in traditional frequentist statistical techniques. PMID:27486415
A. Korattikara; V. Rathod; K. Murphy; M. Welling
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 ap
Bayesian logistic regression analysis
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
Loredo, Thomas J.
2004-04-01
I describe a framework for adaptive scientific exploration based on iterating an Observation-Inference-Design cycle that allows adjustment of hypotheses and observing protocols in response to the results of observation on-the-fly, as data are gathered. The framework uses a unified Bayesian methodology for the inference and design stages: Bayesian inference to quantify what we have learned from the available data and predict future data, and Bayesian decision theory to identify which new observations would teach us the most. When the goal of the experiment is simply to make inferences, the framework identifies a computationally efficient iterative ``maximum entropy sampling'' strategy as the optimal strategy in settings where the noise statistics are independent of signal properties. Results of applying the method to two ``toy'' problems with simulated data-measuring the orbit of an extrasolar planet, and locating a hidden one-dimensional object-show the approach can significantly improve observational efficiency in settings that have well-defined nonlinear models. I conclude with a list of open issues that must be addressed to make Bayesian adaptive exploration a practical and reliable tool for optimizing scientific exploration.
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 experimental...
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...
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...
Bayesian Networks and Influence Diagrams
DEFF Research Database (Denmark)
Kjærulff, Uffe Bro; Madsen, Anders Læsø
, and exercises are included for the reader to check his/her level of understanding. The techniques and methods presented for knowledge elicitation, model construction and verification, modeling techniques and tricks, learning models from data, and analyses of models have all been developed and refined......, 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...... primarily for practitioners, this book does not require sophisticated mathematical skills or deep understanding of the underlying theory and methods nor does it discuss alternative technologies for reasoning under uncertainty. The theory and methods presented are illustrated through more than 140 examples...
Ildikó Ungvári; Gábor Hullám; Péter Antal; Petra Sz Kiszel; András Gézsi; Éva Hadadi; Viktor Virág; Gergely Hajós; András Millinghoffer; Adrienne Nagy; András Kiss; Semsei, Ágnes F.; Gergely Temesi; Béla Melegh; Péter Kisfali
2012-01-01
Genetic studies indicate high number of potential factors related to asthma. Based on earlier linkage analyses we selected the 11q13 and 14q22 asthma susceptibility regions, for which we designed a partial genome screening study using 145 SNPs in 1201 individuals (436 asthmatic children and 765 controls). The results were evaluated with traditional frequentist methods and we applied a new statistical method, called bayesian network based bayesian multilevel analysis of relevance (BN-BMLA). Th...
Improving Environmental Scanning Systems Using Bayesian Networks
Simon Welter; Jörg H. Mayer; Reiner Quick
2013-01-01
As companies’ environment is becoming increasingly volatile, scanning systems gain in importance. We propose a hybrid process model for such systems' information gathering and interpretation tasks that combines quantitative information derived from regression analyses and qualitative knowledge from expert interviews. For the latter, we apply Bayesian networks. We derive the need for such a hybrid process model from a literature review. We lay out our model to find a suitable set of business e...
Yu, Jihnhee; Hutson, Alan D; Siddiqui, Adnan H; Kedron, Mary A
2016-02-01
In some small clinical trials, toxicity is not a primary endpoint; however, it often has dire effects on patients' quality of life and is even life-threatening. For such clinical trials, rigorous control of the overall incidence of adverse events is desirable, while simultaneously collecting safety information. In this article, we propose group sequential toxicity monitoring strategies to control overall toxicity incidents below a certain level as opposed to performing hypothesis testing, which can be incorporated into an existing study design based on the primary endpoint. We consider two sequential methods: a non-Bayesian approach in which stopping rules are obtained based on the 'future' probability of an excessive toxicity rate; and a Bayesian adaptation modifying the proposed non-Bayesian approach, which can use the information obtained at interim analyses. Through an extensive Monte Carlo study, we show that the Bayesian approach often provides better control of the overall toxicity rate than the non-Bayesian approach. We also investigate adequate toxicity estimation after the studies. We demonstrate the applicability of our proposed methods in controlling the symptomatic intracranial hemorrhage rate for treating acute ischemic stroke patients.
Bayesian data analysis in population ecology: motivations, methods, and benefits
Dorazio, Robert
2016-01-01
During the 20th century ecologists largely relied on the frequentist system of inference for the analysis of their data. However, in the past few decades ecologists have become increasingly interested in the use of Bayesian methods of data analysis. In this article I provide guidance to ecologists who would like to decide whether Bayesian methods can be used to improve their conclusions and predictions. I begin by providing a concise summary of Bayesian methods of analysis, including a comparison of differences between Bayesian and frequentist approaches to inference when using hierarchical models. Next I provide a list of problems where Bayesian methods of analysis may arguably be preferred over frequentist methods. These problems are usually encountered in analyses based on hierarchical models of data. I describe the essentials required for applying modern methods of Bayesian computation, and I use real-world examples to illustrate these methods. I conclude by summarizing what I perceive to be the main strengths and weaknesses of using Bayesian methods to solve ecological inference problems.
Probability and Bayesian statistics
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...
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....
Brody, Samuel; Lapata, Mirella
2009-01-01
Sense induction seeks to automatically identify word senses directly from a corpus. A key assumption underlying previous work is that the context surrounding an ambiguous word is indicative of its meaning. Sense induction is thus typically viewed as an unsupervised clustering problem where the aim is to partition a word’s contexts into different classes, each representing a word sense. Our work places sense induction in a Bayesian context by modeling the contexts of the ambiguous word as samp...
Bayesian Generalized Rating Curves
Helgi Sigurðarson 1985
2014-01-01
A rating curve is a curve or a model that describes the relationship between water elevation, or stage, and discharge in an observation site in a river. The rating curve is fit from paired observations of stage and discharge. The rating curve then predicts discharge given observations of stage and this methodology is applied as stage is substantially easier to directly observe than discharge. In this thesis a statistical rating curve model is proposed working within the framework of Bayesian...
Efficient Bayesian Phase Estimation
Wiebe, Nathan; Granade, Chris
2016-07-01
We introduce a new method called rejection filtering that we use to perform adaptive Bayesian phase estimation. Our approach has several advantages: it is classically efficient, easy to implement, achieves Heisenberg limited scaling, resists depolarizing noise, tracks time-dependent eigenstates, recovers from failures, and can be run on a field programmable gate array. It also outperforms existing iterative phase estimation algorithms such as Kitaev's method.
Editorial: Bayesian benefits for child psychology and psychiatry researchers.
Oldehinkel, Albertine J
2016-09-01
For many scientists, performing statistical tests has become an almost automated routine. However, p-values are frequently used and interpreted incorrectly; and even when used appropriately, p-values tend to provide answers that do not match researchers' questions and hypotheses well. Bayesian statistics present an elegant and often more suitable alternative. The Bayesian approach has rarely been applied in child psychology and psychiatry research so far, but the development of user-friendly software packages and tutorials has placed it well within reach now. Because Bayesian analyses require a more refined definition of hypothesized probabilities of possible outcomes than the classical approach, going Bayesian may offer the additional benefit of sparkling the development and refinement of theoretical models in our field. PMID:27535649
Bayesian multimodel inference for dose-response studies
Link, W.A.; Albers, P.H.
2007-01-01
Statistical inference in dose?response studies is model-based: The analyst posits a mathematical model of the relation between exposure and response, estimates parameters of the model, and reports conclusions conditional on the model. Such analyses rarely include any accounting for the uncertainties associated with model selection. The Bayesian inferential system provides a convenient framework for model selection and multimodel inference. In this paper we briefly describe the Bayesian paradigm and Bayesian multimodel inference. We then present a family of models for multinomial dose?response data and apply Bayesian multimodel inferential methods to the analysis of data on the reproductive success of American kestrels (Falco sparveriuss) exposed to various sublethal dietary concentrations of methylmercury.
Editorial: Bayesian benefits for child psychology and psychiatry researchers.
Oldehinkel, Albertine J
2016-09-01
For many scientists, performing statistical tests has become an almost automated routine. However, p-values are frequently used and interpreted incorrectly; and even when used appropriately, p-values tend to provide answers that do not match researchers' questions and hypotheses well. Bayesian statistics present an elegant and often more suitable alternative. The Bayesian approach has rarely been applied in child psychology and psychiatry research so far, but the development of user-friendly software packages and tutorials has placed it well within reach now. Because Bayesian analyses require a more refined definition of hypothesized probabilities of possible outcomes than the classical approach, going Bayesian may offer the additional benefit of sparkling the development and refinement of theoretical models in our field.
Bayesian theory and applications
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...
Wiegerinck, Wim; Schoenaker, Christiaan; Duane, Gregory
2016-04-01
Recently, methods for model fusion by dynamically combining model components in an interactive ensemble have been proposed. In these proposals, fusion parameters have to be learned from data. One can view these systems as parametrized dynamical systems. We address the question of learnability of dynamical systems with respect to both short term (vector field) and long term (attractor) behavior. In particular we are interested in learning in the imperfect model class setting, in which the ground truth has a higher complexity than the models, e.g. due to unresolved scales. We take a Bayesian point of view and we define a joint log-likelihood that consists of two terms, one is the vector field error and the other is the attractor error, for which we take the L1 distance between the stationary distributions of the model and the assumed ground truth. In the context of linear models (like so-called weighted supermodels), and assuming a Gaussian error model in the vector fields, vector field learning leads to a tractable Gaussian solution. This solution can then be used as a prior for the next step, Bayesian attractor learning, in which the attractor error is used as a log-likelihood term. Bayesian attractor learning is implemented by elliptical slice sampling, a sampling method for systems with a Gaussian prior and a non Gaussian likelihood. Simulations with a partially observed driven Lorenz 63 system illustrate the approach.
Bayesian optimization for materials design
Frazier, Peter I.; Wang, Jialei
2015-01-01
We introduce Bayesian optimization, a technique developed for optimizing time-consuming engineering simulations and for fitting machine learning models on large datasets. Bayesian optimization guides the choice of experiments during materials design and discovery to find good material designs in as few experiments as possible. We focus on the case when materials designs are parameterized by a low-dimensional vector. Bayesian optimization is built on a statistical technique called Gaussian pro...
Bayesian Posteriors Without Bayes' Theorem
Hill, Theodore P
2012-01-01
The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the classical Bayesian posterior is the unique posterior that minimizes the loss of Shannon information in combining the prior and the likelihood distributions. These results, direct corollaries of recent results about conflations of probability distributions, reinforce the use of Bayesian posteriors, and may help partially reconcile some of the differences between classical and Bayesian statistics.
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
Computationally efficient Bayesian tracking
Aughenbaugh, Jason; La Cour, Brian
2012-06-01
In this paper, we describe the progress we have achieved in developing a computationally efficient, grid-based Bayesian fusion tracking system. In our approach, the probability surface is represented by a collection of multidimensional polynomials, each computed adaptively on a grid of cells representing state space. Time evolution is performed using a hybrid particle/grid approach and knowledge of the grid structure, while sensor updates use a measurement-based sampling method with a Delaunay triangulation. We present an application of this system to the problem of tracking a submarine target using a field of active and passive sonar buoys.
Bayesian nonparametric data analysis
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.
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......This paper describes the use of model-based geostatistics for choosing the set of sampling locations, collectively called the design, to be used in a geostatistical analysis. Two types of design situation are considered. These are retrospective design, which concerns the addition of sampling...
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....
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.
Bayesian networks as a tool for epidemiological systems analysis
Lewis, F. I.
2012-11-01
Bayesian network analysis is a form of probabilistic modeling which derives from empirical data a directed acyclic graph (DAG) describing the dependency structure between random variables. Bayesian networks are increasingly finding application in areas such as computational and systems biology, and more recently in epidemiological analyses. The key distinction between standard empirical modeling approaches, such as generalised linear modeling, and Bayesian network analyses is that the latter attempts not only to identify statistically associated variables, but to additionally, and empirically, separate these into those directly and indirectly dependent with one or more outcome variables. Such discrimination is vastly more ambitious but has the potential to reveal far more about key features of complex disease systems. Applying Bayesian network modeling to biological and medical data has considerable computational demands, combined with the need to ensure robust model selection given the vast model space of possible DAGs. These challenges require the use of approximation techniques, such as the Laplace approximation, Markov chain Monte Carlo simulation and parametric bootstrapping, along with computational parallelization. A case study in structure discovery - identification of an optimal DAG for given data - is presented which uses additive Bayesian networks to explore veterinary disease data of industrial and medical relevance.
Bayesian analysis of cosmic structures
Kitaura, Francisco-Shu
2011-01-01
We revise the Bayesian inference steps required to analyse the cosmological large-scale structure. Here we make special emphasis in the complications which arise due to the non-Gaussian character of the galaxy and matter distribution. In particular we investigate the advantages and limitations of the Poisson-lognormal model and discuss how to extend this work. With the lognormal prior using the Hamiltonian sampling technique and on scales of about 4 h^{-1} Mpc we find that the over-dense regions are excellent reconstructed, however, under-dense regions (void statistics) are quantitatively poorly recovered. Contrary to the maximum a posteriori (MAP) solution which was shown to over-estimate the density in the under-dense regions we obtain lower densities than in N-body simulations. This is due to the fact that the MAP solution is conservative whereas the full posterior yields samples which are consistent with the prior statistics. The lognormal prior is not able to capture the full non-linear regime at scales ...
Implementing Bayesian Vector Autoregressions Implementing Bayesian Vector Autoregressions
Directory of Open Access Journals (Sweden)
Richard M. Todd
1988-03-01
Full Text Available Implementing Bayesian Vector Autoregressions This paper discusses how the Bayesian approach can be used to construct a type of multivariate forecasting model known as a Bayesian vector autoregression (BVAR. In doing so, we mainly explain Doan, Littermann, and Sims (1984 propositions on how to estimate a BVAR based on a certain family of prior probability distributions. indexed by a fairly small set of hyperparameters. There is also a discussion on how to specify a BVAR and set up a BVAR database. A 4-variable model is used to iliustrate the BVAR approach.
Bayesian Analysis of Type Ia Supernova Data
Institute of Scientific and Technical Information of China (English)
王晓峰; 周旭; 李宗伟; 陈黎
2003-01-01
Recently, the distances to type Ia supernova (SN Ia) at z ～ 0.5 have been measured with the motivation of estimating cosmological parameters. However, different sleuthing techniques tend to give inconsistent measurements for SN Ia distances (～0.3 mag), which significantly affects the determination of cosmological parameters.A Bayesian "hyper-parameter" procedure is used to analyse jointly the current SN Ia data, which considers the relative weights of different datasets. For a flat Universe, the combining analysis yields ΩM = 0.20 ± 0.07.
Dynamic Bayesian diffusion estimation
Dedecius, K
2012-01-01
The rapidly increasing complexity of (mainly wireless) ad-hoc networks stresses the need of reliable distributed estimation of several variables of interest. The widely used centralized approach, in which the network nodes communicate their data with a single specialized point, suffers from high communication overheads and represents a potentially dangerous concept with a single point of failure needing special treatment. This paper's aim is to contribute to another quite recent method called diffusion estimation. By decentralizing the operating environment, the network nodes communicate just within a close neighbourhood. We adopt the Bayesian framework to modelling and estimation, which, unlike the traditional approaches, abstracts from a particular model case. This leads to a very scalable and universal method, applicable to a wide class of different models. A particularly interesting case - the Gaussian regressive model - is derived as an example.
Book review: Bayesian analysis for population ecology
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)
Bayesian model discrimination for glucose-insulin homeostasis
DEFF Research Database (Denmark)
Andersen, Kim Emil; Brooks, Stephen P.; Højbjerre, Malene
In this paper we analyse a set of experimental data on a number of healthy and diabetic patients and discuss a variety of models for describing the physiological processes involved in glucose absorption and insulin secretion within the human body. We adopt a Bayesian approach which facilitates...... the reformulation of existing deterministic models as stochastic state space models which properly accounts for both measurement and process variability. The analysis is further enhanced by Bayesian model discrimination techniques and model averaged parameter estimation which fully accounts for model as well...
Current trends in Bayesian methodology with applications
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
Irregular-Time Bayesian Networks
Ramati, Michael
2012-01-01
In many fields observations are performed irregularly along time, due to either measurement limitations or lack of a constant immanent rate. While discrete-time Markov models (as Dynamic Bayesian Networks) introduce either inefficient computation or an information loss to reasoning about such processes, continuous-time Markov models assume either a discrete state space (as Continuous-Time Bayesian Networks), or a flat continuous state space (as stochastic dif- ferential equations). To address these problems, we present a new modeling class called Irregular-Time Bayesian Networks (ITBNs), generalizing Dynamic Bayesian Networks, allowing substantially more compact representations, and increasing the expressivity of the temporal dynamics. In addition, a globally optimal solution is guaranteed when learning temporal systems, provided that they are fully observed at the same irregularly spaced time-points, and a semiparametric subclass of ITBNs is introduced to allow further adaptation to the irregular nature of t...
Neuronanatomy, neurology and Bayesian networks
Bielza Lozoya, Maria Concepcion
2014-01-01
Bayesian networks are data mining models with clear semantics and a sound theoretical foundation. In this keynote talk we will pinpoint a number of neuroscience problems that can be addressed using Bayesian networks. In neuroanatomy, we will show computer simulation models of dendritic trees and classification of neuron types, both based on morphological features. In neurology, we will present the search for genetic biomarkers in Alzheimer's disease and the prediction of health-related qualit...
A Bayesian approach to combining animal abundance and demographic data
Directory of Open Access Journals (Sweden)
Brooks, S. P.
2004-06-01
Full Text Available In studies of wild animals, one frequently encounters both count and mark-recapture-recovery data. Here, we consider an integrated Bayesian analysis of ring¿recovery and count data using a state-space model. We then impose a Leslie-matrix-based model on the true population counts describing the natural birth-death and age transition processes. We focus upon the analysis of both count and recovery data collected on British lapwings (Vanellus vanellus combined with records of the number of frost days each winter. We demonstrate how the combined analysis of these data provides a more robust inferential framework and discuss how the Bayesian approach using MCMC allows us to remove the potentially restrictive normality assumptions commonly assumed for analyses of this sort. It is shown how WinBUGS may be used to perform the Bayesian analysis. WinBUGS code is provided and its performance is critically discussed.
Elite Athletes Refine Their Internal Clocks: A Bayesian Analysis.
Chen, Yin-Hua; Verdinelli, Isabella; Cesari, Paola
2016-07-01
This paper carries out a full Bayesian analysis for a data set examined in Chen & Cesari (2015). These data were collected for assessing people's ability in evaluating short intervals of time. Chen & Cesari (2015) showed evidence of the existence of two independent internal clocks for evaluating time intervals below and above the second. We reexamine here, the same question by performing a complete statistical Bayesian analysis of the data. The Bayesian approach can be used to analyze these data thanks to the specific trial design. Data were obtained from evaluation of time ranges from two groups of individuals. More specifically, information gathered from a nontrained group (considered as baseline) allowed us to build a prior distribution for the parameter(s) of interest, and data from the trained group determined the likelihood function. This paper's main goals are (i) showing how the Bayesian inferential method can be used in statistical analyses and (ii) showing that the Bayesian methodology gives additional support to the findings presented in Chen & Cesari (2015) regarding the existence of two internal clocks in assessing duration of time intervals.
Dale Poirier
2008-01-01
This paper provides Bayesian rationalizations for White’s heteroskedastic consistent (HC) covariance estimator and various modifications of it. An informed Bayesian bootstrap provides the statistical framework.
Dynamic Batch Bayesian Optimization
Azimi, Javad; Fern, Xiaoli
2011-01-01
Bayesian optimization (BO) algorithms try to optimize an unknown function that is expensive to evaluate using minimum number of evaluations/experiments. Most of the proposed algorithms in BO are sequential, where only one experiment is selected at each iteration. This method can be time inefficient when each experiment takes a long time and more than one experiment can be ran concurrently. On the other hand, requesting a fix-sized batch of experiments at each iteration causes performance inefficiency in BO compared to the sequential policies. In this paper, we present an algorithm that asks a batch of experiments at each time step t where the batch size p_t is dynamically determined in each step. Our algorithm is based on the observation that the sequence of experiments selected by the sequential policy can sometimes be almost independent from each other. Our algorithm identifies such scenarios and request those experiments at the same time without degrading the performance. We evaluate our proposed method us...
Nonparametric Bayesian Classification
Coram, M A
2002-01-01
A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if they are present in the unknown regression function $f_0$. An idealized one-dimensional problem is considered in detail. The proposed nonparametric prior uses random split points to partition the unit interval into a random number of pieces. This prior is found to provide a consistent estimate of the regression function in the $\\L^p$ topology, for any $1 \\leq p < \\infty$, and for arbitrary measurable $f_0:[0,1] \\rightarrow [0,1]$. A Markov chain Monte Carlo (MCMC) implementation is outlined and analyzed. Simulation experiments are conducted to show that the proposed estimate compares favorably with a variety of conventional estimators. A striking resemblance between the posterior mean estimate and the bagged CART estimate is noted and discussed. For higher dimensions, a ...
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
Bayesian models for comparative analysis integrating phylogenetic uncertainty
Directory of Open Access Journals (Sweden)
Villemereuil Pierre de
2012-06-01
Full Text Available Abstract Background Uncertainty in comparative analyses can come from at least two sources: a phylogenetic uncertainty in the tree topology or branch lengths, and b uncertainty due to intraspecific variation in trait values, either due to measurement error or natural individual variation. Most phylogenetic comparative methods do not account for such uncertainties. Not accounting for these sources of uncertainty leads to false perceptions of precision (confidence intervals will be too narrow and inflated significance in hypothesis testing (e.g. p-values will be too small. Although there is some application-specific software for fitting Bayesian models accounting for phylogenetic error, more general and flexible software is desirable. Methods We developed models to directly incorporate phylogenetic uncertainty into a range of analyses that biologists commonly perform, using a Bayesian framework and Markov Chain Monte Carlo analyses. Results We demonstrate applications in linear regression, quantification of phylogenetic signal, and measurement error models. Phylogenetic uncertainty was incorporated by applying a prior distribution for the phylogeny, where this distribution consisted of the posterior tree sets from Bayesian phylogenetic tree estimation programs. The models were analysed using simulated data sets, and applied to a real data set on plant traits, from rainforest plant species in Northern Australia. Analyses were performed using the free and open source software OpenBUGS and JAGS. Conclusions Incorporating phylogenetic uncertainty through an empirical prior distribution of trees leads to more precise estimation of regression model parameters than using a single consensus tree and enables a more realistic estimation of confidence intervals. In addition, models incorporating measurement errors and/or individual variation, in one or both variables, are easily formulated in the Bayesian framework. We show that BUGS is a useful, flexible
Attention in a bayesian framework
DEFF Research Database (Denmark)
Whiteley, Louise Emma; Sahani, Maneesh
2012-01-01
The behavioral phenomena of sensory attention are thought to reflect the allocation of a limited processing resource, but there is little consensus on the nature of the resource or why it should be limited. Here we argue that a fundamental bottleneck emerges naturally within Bayesian models...... of perception, and use this observation to frame a new computational account of the need for, and action of, attention - unifying diverse attentional phenomena in a way that goes beyond previous inferential, probabilistic and Bayesian models. Attentional effects are most evident in cluttered environments......, 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...
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.
Bayesian Methods and Universal Darwinism
Campbell, John
2010-01-01
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 system...
Bayesian modeling using WinBUGS
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 ...
Phycas: software for Bayesian phylogenetic analysis.
Lewis, Paul O; Holder, Mark T; Swofford, David L
2015-05-01
Phycas is open source, freely available Bayesian phylogenetics software written primarily in C++ but with a Python interface. Phycas specializes in Bayesian model selection for nucleotide sequence data, particularly the estimation of marginal likelihoods, central to computing Bayes Factors. Marginal likelihoods can be estimated using newer methods (Thermodynamic Integration and Generalized Steppingstone) that are more accurate than the widely used Harmonic Mean estimator. In addition, Phycas supports two posterior predictive approaches to model selection: Gelfand-Ghosh and Conditional Predictive Ordinates. The General Time Reversible family of substitution models, as well as a codon model, are available, and data can be partitioned with all parameters unlinked except tree topology and edge lengths. Phycas provides for analyses in which the prior on tree topologies allows polytomous trees as well as fully resolved trees, and provides for several choices for edge length priors, including a hierarchical model as well as the recently described compound Dirichlet prior, which helps avoid overly informative induced priors on tree length. PMID:25577605
Case studies in Bayesian microbial risk assessments
Directory of Open Access Journals (Sweden)
Turner Joanne
2009-12-01
case study the effective number of inputs was reduced from 30 to 7 in the screening stage, and just 2 inputs were found to explain 82.8% of the output variance. A combined total of 500 runs of the computer code were used. Conclusion These case studies illustrate the use of Bayesian statistics to perform detailed uncertainty and sensitivity analyses, integrating multiple information sources in a way that is both rigorous and efficient.
Bayesian test and Kuhn's paradigm
Institute of Scientific and Technical Information of China (English)
Chen Xiaoping
2006-01-01
Kuhn's theory of paradigm reveals a pattern of scientific progress,in which normal science alternates with scientific revolution.But Kuhn underrated too much the function of scientific test in his pattern,because he focuses all his attention on the hypothetico-deductive schema instead of Bayesian schema.This paper employs Bayesian schema to re-examine Kuhn's theory of paradigm,to uncover its logical and rational components,and to illustrate the tensional structure of logic and belief,rationality and irrationality,in the process of scientific revolution.
Perception, illusions and Bayesian inference.
Nour, Matthew M; Nour, Joseph M
2015-01-01
Descriptive psychopathology makes a distinction between veridical perception and illusory perception. In both cases a perception is tied to a sensory stimulus, but in illusions the perception is of a false object. This article re-examines this distinction in light of new work in theoretical and computational neurobiology, which views all perception as a form of Bayesian statistical inference that combines sensory signals with prior expectations. Bayesian perceptual inference can solve the 'inverse optics' problem of veridical perception and provides a biologically plausible account of a number of illusory phenomena, suggesting that veridical and illusory perceptions are generated by precisely the same inferential mechanisms.
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....
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.
Bayesian variable order Markov models: Towards Bayesian predictive state representations
C. Dimitrakakis
2009-01-01
We present a Bayesian variable order Markov model that shares many similarities with predictive state representations. The resulting models are compact and much easier to specify and learn than classical predictive state representations. Moreover, we show that they significantly outperform a more st
Bayesian networks and food security - An introduction
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 sup
Bayesian Model Averaging for Propensity Score Analysis
Kaplan, David; Chen, Jianshen
2013-01-01
The purpose of this study is to explore Bayesian model averaging in the propensity score context. Previous research on Bayesian propensity score analysis does not take into account model uncertainty. In this regard, an internally consistent Bayesian framework for model building and estimation must also account for model uncertainty. The…
A Bayesian Nonparametric Approach to Test Equating
Karabatsos, George; Walker, Stephen G.
2009-01-01
A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are…
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...
Bayesian Agglomerative Clustering with Coalescents
Teh, Yee Whye; Daumé III, Hal; Roy, Daniel
2009-01-01
We introduce a new Bayesian model for hierarchical clustering based on a prior over trees called Kingman's coalescent. We develop novel greedy and sequential Monte Carlo inferences which operate in a bottom-up agglomerative fashion. We show experimentally the superiority of our algorithms over others, and demonstrate our approach in document clustering and phylolinguistics.
Bayesian NL interpretation and learning
H. Zeevat
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
Differentiated Bayesian Conjoint Choice Designs
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
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...
Bayesian stable isotope mixing models
In this paper we review recent advances in Stable Isotope Mixing Models (SIMMs) and place them into an over-arching Bayesian statistical framework which allows for several useful extensions. SIMMs are used to quantify the proportional contributions of various sources to a mixtur...
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...
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...
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...
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...
Bayesian Analysis of Experimental Data
Directory of Open Access Journals (Sweden)
Lalmohan Bhar
2013-10-01
Full Text Available Analysis of experimental data from Bayesian point of view has been considered. Appropriate methodology has been developed for application into designed experiments. Normal-Gamma distribution has been considered for prior distribution. Developed methodology has been applied to real experimental data taken from long term fertilizer experiments.
Topics in Bayesian statistics and maximum entropy
International Nuclear Information System (INIS)
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)
Bayesian analysis of rare events
Straub, Daniel; 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.
Bayesian methods for measures of agreement
Broemeling, Lyle D
2009-01-01
Using WinBUGS to implement Bayesian inferences of estimation and testing hypotheses, Bayesian Methods for Measures of Agreement presents useful methods for the design and analysis of agreement studies. It focuses on agreement among the various players in the diagnostic process.The author employs a Bayesian approach to provide statistical inferences based on various models of intra- and interrater agreement. He presents many examples that illustrate the Bayesian mode of reasoning and explains elements of a Bayesian application, including prior information, experimental information, the likelihood function, posterior distribution, and predictive distribution. The appendices provide the necessary theoretical foundation to understand Bayesian methods as well as introduce the fundamentals of programming and executing the WinBUGS software.Taking a Bayesian approach to inference, this hands-on book explores numerous measures of agreement, including the Kappa coefficient, the G coefficient, and intraclass correlation...
Plug & Play object oriented Bayesian networks
DEFF Research Database (Denmark)
Bangsø, Olav; Flores, J.; Jensen, Finn Verner
2003-01-01
Object oriented Bayesian networks have proven themselves useful in recent years. The idea of applying an object oriented approach to Bayesian networks has extended their scope to larger domains that can be divided into autonomous but interrelated entities. Object oriented Bayesian networks have...... 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...... by constructing a junction tree from this network. In this paper we propose a method for translating directly from object oriented Bayesian networks to junction trees, avoiding the intermediate translation. We pursue two main purposes: firstly, to maintain the original structure organized in an instance tree...
Flexible Bayesian Nonparametric Priors and Bayesian Computational Methods
Zhu, Weixuan
2016-01-01
The definition of vectors of dependent random probability measures is a topic of interest in Bayesian nonparametrics. They represent dependent nonparametric prior distributions that are useful for modelling observables for which specific covariate values are known. Our first contribution is the introduction of novel multivariate vectors of two-parameter Poisson-Dirichlet process. The dependence is induced by applying a L´evy copula to the marginal L´evy intensities. Our attenti...
Bayesian versus 'plain-vanilla Bayesian' multitarget statistics
Mahler, Ronald P. S.
2004-08-01
Finite-set statistics (FISST) is a direct generalization of single-sensor, single-target Bayes statistics to the multisensor-multitarget realm, based on random set theory. Various aspects of FISST are being investigated by several research teams around the world. In recent years, however, a few partisans have claimed that a "plain-vanilla Bayesian approach" suffices as down-to-earth, "straightforward," and general "first principles" for multitarget problems. Therefore, FISST is mere mathematical "obfuscation." In this and a companion paper I demonstrate the speciousness of these claims. In this paper I summarize general Bayes statistics, what is required to use it in multisensor-multitarget problems, and why FISST is necessary to make it practical. Then I demonstrate that the "plain-vanilla Bayesian approach" is so heedlessly formulated that it is erroneous, not even Bayesian denigrates FISST concepts while unwittingly assuming them, and has resulted in a succession of algorithms afflicted by inherent -- but less than candidly acknowledged -- computational "logjams."
Bayesian inference on proportional elections.
Brunello, Gabriel Hideki Vatanabe; Nakano, Eduardo Yoshio
2015-01-01
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. PMID:25786259
Bayesian approach to rough set
Marwala, Tshilidzi
2007-01-01
This paper proposes an approach to training rough set models using Bayesian framework trained using Markov Chain Monte Carlo (MCMC) method. The prior probabilities are constructed from the prior knowledge that good rough set models have fewer rules. Markov Chain Monte Carlo sampling is conducted through sampling in the rough set granule space and Metropolis algorithm is used as an acceptance criteria. The proposed method is tested to estimate the risk of HIV given demographic data. The results obtained shows that the proposed approach is able to achieve an average accuracy of 58% with the accuracy varying up to 66%. In addition the Bayesian rough set give the probabilities of the estimated HIV status as well as the linguistic rules describing how the demographic parameters drive the risk of HIV.
Bayesian priors for transiting planets
Kipping, David M
2016-01-01
As astronomers push towards discovering ever-smaller transiting planets, it is increasingly common to deal with low signal-to-noise ratio (SNR) events, where the choice of priors plays an influential role in Bayesian inference. In the analysis of exoplanet data, the selection of priors is often treated as a nuisance, with observers typically defaulting to uninformative distributions. Such treatments miss a key strength of the Bayesian framework, especially in the low SNR regime, where even weak a priori information is valuable. When estimating the parameters of a low-SNR transit, two key pieces of information are known: (i) the planet has the correct geometric alignment to transit and (ii) the transit event exhibits sufficient signal-to-noise to have been detected. These represent two forms of observational bias. Accordingly, when fitting transits, the model parameter priors should not follow the intrinsic distributions of said terms, but rather those of both the intrinsic distributions and the observational ...
Bayesian Source Separation and Localization
Knuth, K H
1998-01-01
The problem of mixed signals occurs in many different contexts; one of the most familiar being acoustics. The forward problem in acoustics consists of finding the sound pressure levels at various detectors resulting from sound signals emanating from the active acoustic sources. The inverse problem consists of using the sound recorded by the detectors to separate the signals and recover the original source waveforms. In general, the inverse problem is unsolvable without additional information. This general problem is called source separation, and several techniques have been developed that utilize maximum entropy, minimum mutual information, and maximum likelihood. In previous work, it has been demonstrated that these techniques can be recast in a Bayesian framework. This paper demonstrates the power of the Bayesian approach, which provides a natural means for incorporating prior information into a source model. An algorithm is developed that utilizes information regarding both the statistics of the amplitudes...
Bayesian Inference for Radio Observations
Lochner, Michelle; Zwart, Jonathan T L; Smirnov, Oleg; Bassett, Bruce A; Oozeer, Nadeem; Kunz, Martin
2015-01-01
(Abridged) New telescopes like the Square Kilometre Array (SKA) will push into a new sensitivity regime and expose systematics, such as direction-dependent effects, that could previously be ignored. Current methods for handling such systematics rely on alternating best estimates of instrumental calibration and models of the underlying sky, which can lead to inaccurate uncertainty estimates and biased results because such methods ignore any correlations between parameters. These deconvolution algorithms produce a single image that is assumed to be a true representation of the sky, when in fact it is just one realisation of an infinite ensemble of images compatible with the noise in the data. In contrast, here we report a Bayesian formalism that simultaneously infers both systematics and science. Our technique, Bayesian Inference for Radio Observations (BIRO), determines all parameters directly from the raw data, bypassing image-making entirely, by sampling from the joint posterior probability distribution. Thi...
A Bayesian Nonparametric IRT Model
Karabatsos, George
2015-01-01
This paper introduces a flexible Bayesian nonparametric Item Response Theory (IRT) model, which applies to dichotomous or polytomous item responses, and which can apply to either unidimensional or multidimensional scaling. This is an infinite-mixture IRT model, with person ability and item difficulty parameters, and with a random intercept parameter that is assigned a mixing distribution, with mixing weights a probit function of other person and item parameters. As a result of its flexibility...
Elements of Bayesian experimental design
Energy Technology Data Exchange (ETDEWEB)
Sivia, D.S. [Rutherford Appleton Lab., Oxon (United Kingdom)
1997-09-01
We consider some elements of the Bayesian approach that are important for optimal experimental design. While the underlying principles used are very general, and are explained in detail in a recent tutorial text, they are applied here to the specific case of characterising the inferential value of different resolution peakshapes. This particular issue was considered earlier by Silver, Sivia and Pynn (1989, 1990a, 1990b), and the following presentation confirms and extends the conclusions of their analysis.
Bayesian kinematic earthquake source models
Minson, S. E.; Simons, M.; Beck, J. L.; Genrich, J. F.; Galetzka, J. E.; Chowdhury, F.; Owen, S. E.; Webb, F.; Comte, D.; Glass, B.; Leiva, C.; Ortega, F. H.
2009-12-01
Most coseismic, postseismic, and interseismic slip models are based on highly regularized optimizations which yield one solution which satisfies the data given a particular set of regularizing constraints. This regularization hampers our ability to answer basic questions such as whether seismic and aseismic slip overlap or instead rupture separate portions of the fault zone. We present a Bayesian methodology for generating kinematic earthquake source models with a focus on large subduction zone earthquakes. Unlike classical optimization approaches, Bayesian techniques sample the ensemble of all acceptable models presented as an a posteriori probability density function (PDF), and thus we can explore the entire solution space to determine, for example, which model parameters are well determined and which are not, or what is the likelihood that two slip distributions overlap in space. Bayesian sampling also has the advantage that all a priori knowledge of the source process can be used to mold the a posteriori ensemble of models. Although very powerful, Bayesian methods have up to now been of limited use in geophysical modeling because they are only computationally feasible for problems with a small number of free parameters due to what is called the "curse of dimensionality." However, our methodology can successfully sample solution spaces of many hundreds of parameters, which is sufficient to produce finite fault kinematic earthquake models. Our algorithm is a modification of the tempered Markov chain Monte Carlo (tempered MCMC or TMCMC) method. In our algorithm, we sample a "tempered" a posteriori PDF using many MCMC simulations running in parallel and evolutionary computation in which models which fit the data poorly are preferentially eliminated in favor of models which better predict the data. We present results for both synthetic test problems as well as for the 2007 Mw 7.8 Tocopilla, Chile earthquake, the latter of which is constrained by InSAR, local high
Bayesian Stable Isotope Mixing Models
Parnell, Andrew C.; Phillips, Donald L.; Bearhop, Stuart; Semmens, Brice X.; Ward, Eric J.; Moore, Jonathan W.; Andrew L Jackson; Inger, Richard
2012-01-01
In this paper we review recent advances in Stable Isotope Mixing Models (SIMMs) and place them into an over-arching Bayesian statistical framework which allows for several useful extensions. SIMMs are used to quantify the proportional contributions of various sources to a mixture. The most widely used application is quantifying the diet of organisms based on the food sources they have been observed to consume. At the centre of the multivariate statistical model we propose is a compositional m...
Bayesian Network--Response Regression
WANG, LU; Durante, Daniele; Dunson, David B.
2016-01-01
There is an increasing interest in learning how human brain networks vary with continuous traits (e.g., personality, cognitive abilities, neurological disorders), but flexible procedures to accomplish this goal are limited. We develop a Bayesian semiparametric model, which combines low-rank factorizations and Gaussian process priors to allow flexible shifts of the conditional expectation for a network-valued random variable across the feature space, while including subject-specific random eff...
Bayesian segmentation of hyperspectral images
Mohammadpour, Adel; Mohammad-Djafari, Ali
2007-01-01
In this paper we consider the problem of joint segmentation of hyperspectral images in the Bayesian framework. The proposed approach is based on a Hidden Markov Modeling (HMM) of the images with common segmentation, or equivalently with common hidden classification label variables which is modeled by a Potts Markov Random Field. We introduce an appropriate Markov Chain Monte Carlo (MCMC) algorithm to implement the method and show some simulation results.
Bayesian segmentation of hyperspectral images
Mohammadpour, Adel; Féron, Olivier; Mohammad-Djafari, Ali
2004-11-01
In this paper we consider the problem of joint segmentation of hyperspectral images in the Bayesian framework. The proposed approach is based on a Hidden Markov Modeling (HMM) of the images with common segmentation, or equivalently with common hidden classification label variables which is modeled by a Potts Markov Random Field. We introduce an appropriate Markov Chain Monte Carlo (MCMC) algorithm to implement the method and show some simulation results.
Bayesian analysis of contingency tables
Gómez Villegas, Miguel A.; González Pérez, Beatriz
2005-01-01
The display of the data by means of contingency tables is used in different approaches to statistical inference, for example, to broach the test of homogeneity of independent multinomial distributions. We develop a Bayesian procedure to test simple null hypotheses versus bilateral alternatives in contingency tables. Given independent samples of two binomial distributions and taking a mixed prior distribution, we calculate the posterior probability that the proportion of successes in the first...
Bayesian estimation of turbulent motion
Héas, P.; Herzet, C.; Mémin, E.; Heitz, D.; P. D. Mininni
2013-01-01
International audience Based on physical laws describing the multi-scale structure of turbulent flows, this article proposes a regularizer for fluid motion estimation from an image sequence. Regularization is achieved by imposing some scale invariance property between histograms of motion increments computed at different scales. By reformulating this problem from a Bayesian perspective, an algorithm is proposed to jointly estimate motion, regularization hyper-parameters, and to select the ...
Bayesian Kernel Mixtures for Counts
Canale, Antonio; David B Dunson
2011-01-01
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 deviatio...
Bayesian network as a modelling tool for risk management in agriculture
DEFF Research Database (Denmark)
Rasmussen, Svend; Madsen, Anders L.; Lund, Mogens
The importance of risk management increases as farmers become more exposed to risk. But risk management is a difficult topic because income risk is the result of the complex interaction of multiple risk factors combined with the effect of an increasing array of possible risk management tools....... In this paper we use Bayesian networks as an integrated modelling approach for representing uncertainty and analysing risk management in agriculture. It is shown how historical farm account data may be efficiently used to estimate conditional probabilities, which are the core elements in Bayesian network models....... We further show how the Bayesian network model RiBay is used for stochastic simulation of farm income, and we demonstrate how RiBay can be used to simulate risk management at the farm level. It is concluded that the key strength of a Bayesian network is the transparency of assumptions...
Bayesian second law of thermodynamics.
Bartolotta, Anthony; Carroll, Sean M; Leichenauer, Stefan; Pollack, Jason
2016-08-01
We derive a generalization of the second law of thermodynamics that uses Bayesian updates to explicitly incorporate the effects of a measurement of a system at some point in its evolution. By allowing an experimenter's knowledge to be updated by the measurement process, this formulation resolves a tension between the fact that the entropy of a statistical system can sometimes fluctuate downward and the information-theoretic idea that knowledge of a stochastically evolving system degrades over time. The Bayesian second law can be written as ΔH(ρ_{m},ρ)+〈Q〉_{F|m}≥0, where ΔH(ρ_{m},ρ) is the change in the cross entropy between the original phase-space probability distribution ρ and the measurement-updated distribution ρ_{m} and 〈Q〉_{F|m} is the expectation value of a generalized heat flow out of the system. We also derive refined versions of the second law that bound the entropy increase from below by a non-negative number, as well as Bayesian versions of integral fluctuation theorems. We demonstrate the formalism using simple analytical and numerical examples. PMID:27627241
Bayesian second law of thermodynamics
Bartolotta, Anthony; Carroll, Sean M.; Leichenauer, Stefan; Pollack, Jason
2016-08-01
We derive a generalization of the second law of thermodynamics that uses Bayesian updates to explicitly incorporate the effects of a measurement of a system at some point in its evolution. By allowing an experimenter's knowledge to be updated by the measurement process, this formulation resolves a tension between the fact that the entropy of a statistical system can sometimes fluctuate downward and the information-theoretic idea that knowledge of a stochastically evolving system degrades over time. The Bayesian second law can be written as Δ H (ρm,ρ ) + F |m≥0 , where Δ H (ρm,ρ ) is the change in the cross entropy between the original phase-space probability distribution ρ and the measurement-updated distribution ρm and F |m is the expectation value of a generalized heat flow out of the system. We also derive refined versions of the second law that bound the entropy increase from below by a non-negative number, as well as Bayesian versions of integral fluctuation theorems. We demonstrate the formalism using simple analytical and numerical examples.
Embracing Uncertainty: The Interface of Bayesian Statistics and Cognitive Psychology
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Judith L. Anderson
1998-06-01
Full Text Available Ecologists working in conservation and resource management are discovering the importance of using Bayesian analytic methods to deal explicitly with uncertainty in data analyses and decision making. However, Bayesian procedures require, as inputs and outputs, an idea that is problematic for the human brain: the probability of a hypothesis ("single-event probability". I describe several cognitive concepts closely related to single-event probabilities, and discuss how their interchangeability in the human mind results in "cognitive illusions," apparent deficits in reasoning about uncertainty. Each cognitive illusion implies specific possible pitfalls for the use of single-event probabilities in ecology and resource management. I then discuss recent research in cognitive psychology showing that simple tactics of communication, suggested by an evolutionary perspective on human cognition, help people to process uncertain information more effectively as they read and talk about probabilities. In addition, I suggest that carefully considered standards for methodology and conventions for presentation may also make Bayesian analyses easier to understand.
12th Brazilian Meeting on Bayesian Statistics
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...
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...... and differentiating these circuits in time linear in their size. We report on experimental results showing the successful compilation, and efficient inference, on relational Bayesian networks whose {\\primula}--generated propositional instances have thousands of variables, and whose jointrees have clusters...
Bayesian Posterior Distributions Without Markov Chains
Cole, Stephen R.; Chu, Haitao; Greenland, Sander; Hamra, Ghassan; Richardson, David B.
2012-01-01
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 ex...
Iskandar, Ismed; Satria Gondokaryono, Yudi
2016-02-01
In reliability theory, the most important problem is to determine the reliability of a complex system from the reliability of its components. The weakness of most reliability theories is that the systems are described and explained as simply functioning or failed. In many real situations, the failures may be from many causes depending upon the age and the environment of the system and its components. Another problem in reliability theory is one of estimating the parameters of the assumed failure models. The estimation may be based on data collected over censored or uncensored life tests. In many reliability problems, the failure data are simply quantitatively inadequate, especially in engineering design and maintenance system. The Bayesian analyses are more beneficial than the classical one in such cases. The Bayesian estimation analyses allow us to combine past knowledge or experience in the form of an apriori distribution with life test data to make inferences of the parameter of interest. In this paper, we have investigated the application of the Bayesian estimation analyses to competing risk systems. The cases are limited to the models with independent causes of failure by using the Weibull distribution as our model. A simulation is conducted for this distribution with the objectives of verifying the models and the estimators and investigating the performance of the estimators for varying sample size. The simulation data are analyzed by using Bayesian and the maximum likelihood analyses. The simulation results show that the change of the true of parameter relatively to another will change the value of standard deviation in an opposite direction. For a perfect information on the prior distribution, the estimation methods of the Bayesian analyses are better than those of the maximum likelihood. The sensitivity analyses show some amount of sensitivity over the shifts of the prior locations. They also show the robustness of the Bayesian analysis within the range
Variational bayesian method of estimating variance components.
Arakawa, Aisaku; Taniguchi, Masaaki; Hayashi, Takeshi; Mikawa, Satoshi
2016-07-01
We developed a Bayesian analysis approach by using a variational inference method, a so-called variational Bayesian method, to determine the posterior distributions of variance components. This variational Bayesian method and an alternative Bayesian method using Gibbs sampling were compared in estimating genetic and residual variance components from both simulated data and publically available real pig data. In the simulated data set, we observed strong bias toward overestimation of genetic variance for the variational Bayesian method in the case of low heritability and low population size, and less bias was detected with larger population sizes in both methods examined. The differences in the estimates of variance components between the variational Bayesian and the Gibbs sampling were not found in the real pig data. However, the posterior distributions of the variance components obtained with the variational Bayesian method had shorter tails than those obtained with the Gibbs sampling. Consequently, the posterior standard deviations of the genetic and residual variances of the variational Bayesian method were lower than those of the method using Gibbs sampling. The computing time required was much shorter with the variational Bayesian method than with the method using Gibbs sampling.
SYNTHESIZED EXPECTED BAYESIAN METHOD OF PARAMETRIC ESTIMATE
Institute of Scientific and Technical Information of China (English)
Ming HAN; Yuanyao DING
2004-01-01
This paper develops a new method of parametric estimate, which is named as "synthesized expected Bayesian method". When samples of products are tested and no failure events occur, thedefinition of expected Bayesian estimate is introduced and the estimates of failure probability and failure rate are provided. After some failure information is introduced by making an extra-test, a synthesized expected Bayesian method is defined and used to estimate failure probability, failure rateand some other parameters in exponential distribution and Weibull distribution of populations. Finally,calculations are performed according to practical problems, which show that the synthesized expected Bayesian method is feasible and easy to operate.
Xu, Chengcheng; Wang, Wei; Liu, Pan; Li, Zhibin
2015-12-01
This study aimed to develop a real-time crash risk model with limited data in China by using Bayesian meta-analysis and Bayesian inference approach. A systematic review was first conducted by using three different Bayesian meta-analyses, including the fixed effect meta-analysis, the random effect meta-analysis, and the meta-regression. The meta-analyses provided a numerical summary of the effects of traffic variables on crash risks by quantitatively synthesizing results from previous studies. The random effect meta-analysis and the meta-regression produced a more conservative estimate for the effects of traffic variables compared with the fixed effect meta-analysis. Then, the meta-analyses results were used as informative priors for developing crash risk models with limited data. Three different meta-analyses significantly affect model fit and prediction accuracy. The model based on meta-regression can increase the prediction accuracy by about 15% as compared to the model that was directly developed with limited data. Finally, the Bayesian predictive densities analysis was used to identify the outliers in the limited data. It can further improve the prediction accuracy by 5.0%.
Directory of Open Access Journals (Sweden)
Ildikó Ungvári
Full Text Available Genetic studies indicate high number of potential factors related to asthma. Based on earlier linkage analyses we selected the 11q13 and 14q22 asthma susceptibility regions, for which we designed a partial genome screening study using 145 SNPs in 1201 individuals (436 asthmatic children and 765 controls. The results were evaluated with traditional frequentist methods and we applied a new statistical method, called bayesian network based bayesian multilevel analysis of relevance (BN-BMLA. This method uses bayesian network representation to provide detailed characterization of the relevance of factors, such as joint significance, the type of dependency, and multi-target aspects. We estimated posteriors for these relations within the bayesian statistical framework, in order to estimate the posteriors whether a variable is directly relevant or its association is only mediated.With frequentist methods one SNP (rs3751464 in the FRMD6 gene provided evidence for an association with asthma (OR = 1.43(1.2-1.8; p = 3×10(-4. The possible role of the FRMD6 gene in asthma was also confirmed in an animal model and human asthmatics.In the BN-BMLA analysis altogether 5 SNPs in 4 genes were found relevant in connection with asthma phenotype: PRPF19 on chromosome 11, and FRMD6, PTGER2 and PTGDR on chromosome 14. In a subsequent step a partial dataset containing rhinitis and further clinical parameters was used, which allowed the analysis of relevance of SNPs for asthma and multiple targets. These analyses suggested that SNPs in the AHNAK and MS4A2 genes were indirectly associated with asthma. This paper indicates that BN-BMLA explores the relevant factors more comprehensively than traditional statistical methods and extends the scope of strong relevance based methods to include partial relevance, global characterization of relevance and multi-target relevance.
Bayesian Methods and Universal Darwinism
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.
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.
Bayesian Query-Focused Summarization
Daumé, Hal
2009-01-01
We present BayeSum (for ``Bayesian summarization''), a model for sentence extraction in query-focused summarization. BayeSum leverages the common case in which multiple documents are relevant to a single query. Using these documents as reinforcement for query terms, BayeSum is not afflicted by the paucity of information in short queries. We show that approximate inference in BayeSum is possible on large data sets and results in a state-of-the-art summarization system. Furthermore, we show how BayeSum can be understood as a justified query expansion technique in the language modeling for IR framework.
Bayesian Sampling using Condition Indicators
DEFF Research Database (Denmark)
Faber, Michael H.; Sørensen, John Dalsgaard
2002-01-01
The problem of control quality of components is considered for the special case where the acceptable failure rate is low, the test costs are high and where it may be difficult or impossible to test the condition of interest directly. Based on the classical control theory and the concept...... 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...
parallelMCMCcombine: an R package for bayesian methods for big data and analytics.
Directory of Open Access Journals (Sweden)
Alexey Miroshnikov
Full Text Available Recent advances in big data and analytics research have provided a wealth of large data sets that are too big to be analyzed in their entirety, due to restrictions on computer memory or storage size. New Bayesian methods have been developed for data sets that are large only due to large sample sizes. These methods partition big data sets into subsets and perform independent Bayesian Markov chain Monte Carlo analyses on the subsets. The methods then combine the independent subset posterior samples to estimate a posterior density given the full data set. These approaches were shown to be effective for Bayesian models including logistic regression models, Gaussian mixture models and hierarchical models. Here, we introduce the R package parallelMCMCcombine which carries out four of these techniques for combining independent subset posterior samples. We illustrate each of the methods using a Bayesian logistic regression model for simulation data and a Bayesian Gamma model for real data; we also demonstrate features and capabilities of the R package. The package assumes the user has carried out the Bayesian analysis and has produced the independent subposterior samples outside of the package. The methods are primarily suited to models with unknown parameters of fixed dimension that exist in continuous parameter spaces. We envision this tool will allow researchers to explore the various methods for their specific applications and will assist future progress in this rapidly developing field.
parallelMCMCcombine: an R package for bayesian methods for big data and analytics.
Miroshnikov, Alexey; Conlon, Erin M
2014-01-01
Recent advances in big data and analytics research have provided a wealth of large data sets that are too big to be analyzed in their entirety, due to restrictions on computer memory or storage size. New Bayesian methods have been developed for data sets that are large only due to large sample sizes. These methods partition big data sets into subsets and perform independent Bayesian Markov chain Monte Carlo analyses on the subsets. The methods then combine the independent subset posterior samples to estimate a posterior density given the full data set. These approaches were shown to be effective for Bayesian models including logistic regression models, Gaussian mixture models and hierarchical models. Here, we introduce the R package parallelMCMCcombine which carries out four of these techniques for combining independent subset posterior samples. We illustrate each of the methods using a Bayesian logistic regression model for simulation data and a Bayesian Gamma model for real data; we also demonstrate features and capabilities of the R package. The package assumes the user has carried out the Bayesian analysis and has produced the independent subposterior samples outside of the package. The methods are primarily suited to models with unknown parameters of fixed dimension that exist in continuous parameter spaces. We envision this tool will allow researchers to explore the various methods for their specific applications and will assist future progress in this rapidly developing field.
Using Bayesian Networks to Improve Knowledge Assessment
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…
Bayesian analysis of exoplanet and binary orbits
Schulze-Hartung, Tim; Launhardt, Ralf; Henning, Thomas
2012-01-01
We introduce BASE (Bayesian astrometric and spectroscopic exoplanet detection and characterisation tool), a novel program for the combined or separate Bayesian analysis of astrometric and radial-velocity measurements of potential exoplanet hosts and binary stars. The capabilities of BASE are demonstrated using all publicly available data of the binary Mizar A.
Bayesian credible interval construction for Poisson statistics
Institute of Scientific and Technical Information of China (English)
ZHU Yong-Sheng
2008-01-01
The construction of the Bayesian credible (confidence) interval for a Poisson observable including both the signal and background with and without systematic uncertainties is presented.Introducing the conditional probability satisfying the requirement of the background not larger than the observed events to construct the Bayesian credible interval is also discussed.A Fortran routine,BPOCI,has been developed to implement the calculation.
Modeling Diagnostic Assessments with Bayesian Networks
Almond, Russell G.; DiBello, Louis V.; Moulder, Brad; Zapata-Rivera, Juan-Diego
2007-01-01
This paper defines Bayesian network models and examines their applications to IRT-based cognitive diagnostic modeling. These models are especially suited to building inference engines designed to be synchronous with the finer grained student models that arise in skills diagnostic assessment. Aspects of the theory and use of Bayesian network models…
Advances in Bayesian Modeling in Educational Research
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…
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...
The Bayesian Revolution Approaches Psychological Development
Shultz, Thomas R.
2007-01-01
This commentary reviews five articles that apply Bayesian ideas to psychological development, some with psychology experiments, some with computational modeling, and some with both experiments and modeling. The reviewed work extends the current Bayesian revolution into tasks often studied in children, such as causal learning and word learning, and…
Bayesian Network for multiple hypthesis tracking
W.P. Zajdel; B.J.A. Kröse
2002-01-01
For a flexible camera-to-camera tracking of multiple objects we model the objects behavior with a Bayesian network and combine it with the multiple hypohesis framework that associates observations with objects. Bayesian networks offer a possibility to factor complex, joint distributions into a produ
2nd Bayesian Young Statisticians Meeting
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 ...
BAYESIAN BICLUSTERING FOR PATIENT STRATIFICATION.
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.
BAYESIAN BICLUSTERING FOR PATIENT STRATIFICATION.
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. PMID:26776199
Halo detection via large-scale Bayesian inference
Merson, Alexander I.; Jasche, Jens; Abdalla, Filipe B.; Lahav, Ofer; Wandelt, Benjamin; Jones, D. Heath; Colless, Matthew
2016-08-01
We present a proof-of-concept of a novel and fully Bayesian methodology designed to detect haloes of different masses in cosmological observations subject to noise and systematic uncertainties. Our methodology combines the previously published Bayesian large-scale structure inference algorithm, HAmiltonian Density Estimation and Sampling algorithm (HADES), and a Bayesian chain rule (the Blackwell-Rao estimator), which we use to connect the inferred density field to the properties of dark matter haloes. To demonstrate the capability of our approach, we construct a realistic galaxy mock catalogue emulating the wide-area 6-degree Field Galaxy Survey, which has a median redshift of approximately 0.05. Application of HADES to the catalogue provides us with accurately inferred three-dimensional density fields and corresponding quantification of uncertainties inherent to any cosmological observation. We then use a cosmological simulation to relate the amplitude of the density field to the probability of detecting a halo with mass above a specified threshold. With this information, we can sum over the HADES density field realisations to construct maps of detection probabilities and demonstrate the validity of this approach within our mock scenario. We find that the probability of successful detection of haloes in the mock catalogue increases as a function of the signal to noise of the local galaxy observations. Our proposed methodology can easily be extended to account for more complex scientific questions and is a promising novel tool to analyse the cosmic large-scale structure in observations.
Bayesian Estimation of Small Effects in Exercise and Sports Science
Mengersen, Kerrie L.; Drovandi, Christopher C.; Robert, Christian P.; Pyne, David B.; Gore, Christopher J.
2016-01-01
The aim of this paper is to provide a Bayesian formulation of the so-called magnitude-based inference approach to quantifying and interpreting effects, and in a case study example provide accurate probabilistic statements that correspond to the intended magnitude-based inferences. The model is described in the context of a published small-scale athlete study which employed a magnitude-based inference approach to compare the effect of two altitude training regimens (live high-train low (LHTL), and intermittent hypoxic exposure (IHE)) on running performance and blood measurements of elite triathletes. The posterior distributions, and corresponding point and interval estimates, for the parameters and associated effects and comparisons of interest, were estimated using Markov chain Monte Carlo simulations. The Bayesian analysis was shown to provide more direct probabilistic comparisons of treatments and able to identify small effects of interest. The approach avoided asymptotic assumptions and overcame issues such as multiple testing. Bayesian analysis of unscaled effects showed a probability of 0.96 that LHTL yields a substantially greater increase in hemoglobin mass than IHE, a 0.93 probability of a substantially greater improvement in running economy and a greater than 0.96 probability that both IHE and LHTL yield a substantially greater improvement in maximum blood lactate concentration compared to a Placebo. The conclusions are consistent with those obtained using a ‘magnitude-based inference’ approach that has been promoted in the field. The paper demonstrates that a fully Bayesian analysis is a simple and effective way of analysing small effects, providing a rich set of results that are straightforward to interpret in terms of probabilistic statements. PMID:27073897
Bayesian Estimation of Small Effects in Exercise and Sports Science.
Mengersen, Kerrie L; Drovandi, Christopher C; Robert, Christian P; Pyne, David B; Gore, Christopher J
2016-01-01
The aim of this paper is to provide a Bayesian formulation of the so-called magnitude-based inference approach to quantifying and interpreting effects, and in a case study example provide accurate probabilistic statements that correspond to the intended magnitude-based inferences. The model is described in the context of a published small-scale athlete study which employed a magnitude-based inference approach to compare the effect of two altitude training regimens (live high-train low (LHTL), and intermittent hypoxic exposure (IHE)) on running performance and blood measurements of elite triathletes. The posterior distributions, and corresponding point and interval estimates, for the parameters and associated effects and comparisons of interest, were estimated using Markov chain Monte Carlo simulations. The Bayesian analysis was shown to provide more direct probabilistic comparisons of treatments and able to identify small effects of interest. The approach avoided asymptotic assumptions and overcame issues such as multiple testing. Bayesian analysis of unscaled effects showed a probability of 0.96 that LHTL yields a substantially greater increase in hemoglobin mass than IHE, a 0.93 probability of a substantially greater improvement in running economy and a greater than 0.96 probability that both IHE and LHTL yield a substantially greater improvement in maximum blood lactate concentration compared to a Placebo. The conclusions are consistent with those obtained using a 'magnitude-based inference' approach that has been promoted in the field. The paper demonstrates that a fully Bayesian analysis is a simple and effective way of analysing small effects, providing a rich set of results that are straightforward to interpret in terms of probabilistic statements.
Bayesian Estimation of Small Effects in Exercise and Sports Science.
Mengersen, Kerrie L; Drovandi, Christopher C; Robert, Christian P; Pyne, David B; Gore, Christopher J
2016-01-01
The aim of this paper is to provide a Bayesian formulation of the so-called magnitude-based inference approach to quantifying and interpreting effects, and in a case study example provide accurate probabilistic statements that correspond to the intended magnitude-based inferences. The model is described in the context of a published small-scale athlete study which employed a magnitude-based inference approach to compare the effect of two altitude training regimens (live high-train low (LHTL), and intermittent hypoxic exposure (IHE)) on running performance and blood measurements of elite triathletes. The posterior distributions, and corresponding point and interval estimates, for the parameters and associated effects and comparisons of interest, were estimated using Markov chain Monte Carlo simulations. The Bayesian analysis was shown to provide more direct probabilistic comparisons of treatments and able to identify small effects of interest. The approach avoided asymptotic assumptions and overcame issues such as multiple testing. Bayesian analysis of unscaled effects showed a probability of 0.96 that LHTL yields a substantially greater increase in hemoglobin mass than IHE, a 0.93 probability of a substantially greater improvement in running economy and a greater than 0.96 probability that both IHE and LHTL yield a substantially greater improvement in maximum blood lactate concentration compared to a Placebo. The conclusions are consistent with those obtained using a 'magnitude-based inference' approach that has been promoted in the field. The paper demonstrates that a fully Bayesian analysis is a simple and effective way of analysing small effects, providing a rich set of results that are straightforward to interpret in terms of probabilistic statements. PMID:27073897
Bayesian analysis of genetic differentiation between populations.
Corander, Jukka; Waldmann, Patrik; Sillanpää, Mikko J
2003-01-01
We introduce a Bayesian method for estimating hidden population substructure using multilocus molecular markers and geographical information provided by the sampling design. The joint posterior distribution of the substructure and allele frequencies of the respective populations is available in an analytical form when the number of populations is small, whereas an approximation based on a Markov chain Monte Carlo simulation approach can be obtained for a moderate or large number of populations. Using the joint posterior distribution, posteriors can also be derived for any evolutionary population parameters, such as the traditional fixation indices. A major advantage compared to most earlier methods is that the number of populations is treated here as an unknown parameter. What is traditionally considered as two genetically distinct populations, either recently founded or connected by considerable gene flow, is here considered as one panmictic population with a certain probability based on marker data and prior information. Analyses of previously published data on the Moroccan argan tree (Argania spinosa) and of simulated data sets suggest that our method is capable of estimating a population substructure, while not artificially enforcing a substructure when it does not exist. The software (BAPS) used for the computations is freely available from http://www.rni.helsinki.fi/~mjs. PMID:12586722
Bayesian analysis of spatial point processes in the neighbourhood of Voronoi networks
DEFF Research Database (Denmark)
Skare, Øivind; Møller, Jesper; Vedel Jensen, Eva B.
A model for an inhomogeneous Poisson process with high intensity near the edges of a Voronoi tessellation in 2D or 3D is proposed. The model is analysed in a Bayesian setting with priors on nuclei of the Voronoi tessellation and other model parameters. An MCMC algorithm is constructed to sample...
Bayesian analysis of spatial point processes in the neighbourhood of Voronoi networks
DEFF Research Database (Denmark)
Skare, Øivind; Møller, Jesper; Jensen, Eva B. Vedel
2007-01-01
A model for an inhomogeneous Poisson process with high intensity near the edges of a Voronoi tessellation in 2D or 3D is proposed. The model is analysed in a Bayesian setting with priors on nuclei of the Voronoi tessellation and other model parameters. An MCMC algorithm is constructed to sample...
In this paper, we present methods for estimating Freundlich isotherm fitting parameters (K and N) and their joint uncertainty, which have been implemented into the freeware software platforms R and WinBUGS. These estimates were determined by both Frequentist and Bayesian analyse...
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.
Quantum Bayesianism at the Perimeter
Fuchs, Christopher A
2010-01-01
The author summarizes the Quantum Bayesian viewpoint of quantum mechanics, developed originally by C. M. Caves, R. Schack, and himself. It is a view crucially dependent upon the tools of quantum information theory. Work at the Perimeter Institute for Theoretical Physics continues the development and is focused on the hard technical problem of a finding a good representation of quantum mechanics purely in terms of probabilities, without amplitudes or Hilbert-space operators. The best candidate representation involves a mysterious entity called a symmetric informationally complete quantum measurement. Contemplation of it gives a way of thinking of the Born Rule as an addition to the rules of probability theory, applicable when one gambles on the consequences of interactions with physical systems. The article ends by outlining some directions for future work.
Hedging Strategies for Bayesian Optimization
Brochu, Eric; de Freitas, Nando
2010-01-01
Bayesian optimization with Gaussian processes has become an increasingly popular tool in the machine learning community. It is efficient and can be used when very little is known about the objective function, making it popular in expensive black-box optimization scenarios. It is able to do this by sampling the objective using an acquisition function which incorporates the model's estimate of the objective and the uncertainty at any given point. However, there are several different parameterized acquisition functions in the literature, and it is often unclear which one to use. Instead of using a single acquisition function, we adopt a portfolio of acquisition functions governed by an online multi-armed bandit strategy. We describe the method, which we call GP-Hedge, and show that this method almost always outperforms the best individual acquisition function.
Bayesian Networks and Influence Diagrams
DEFF Research Database (Denmark)
Kjærulff, Uffe Bro; Madsen, Anders Læsø
under uncertainty. The theory and methods presented are illustrated through more than 140 examples, and exercises are included for the reader to check his or her level of understanding. The techniques and methods presented on model construction and verification, modeling techniques and tricks, learning......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...... sections, in addition to fully-updated examples, tables, figures, and a revised appendix. Intended primarily for practitioners, this book does not require sophisticated mathematical skills or deep understanding of the underlying theory and methods nor does it discuss alternative technologies for reasoning...
State Information in Bayesian Games
Cuff, Paul
2009-01-01
Two-player zero-sum repeated games are well understood. Computing the value of such a game is straightforward. Additionally, if the payoffs are dependent on a random state of the game known to one, both, or neither of the players, the resulting value of the game has been analyzed under the framework of Bayesian games. This investigation considers the optimal performance in a game when a helper is transmitting state information to one of the players. Encoding information for an adversarial setting (game) requires a different result than rate-distortion theory provides. Game theory has accentuated the importance of randomization (mixed strategy), which does not find a significant role in most communication modems and source coding codecs. Higher rates of communication, used in the right way, allow the message to include the necessary random component useful in games.
Multiview Bayesian Correlated Component Analysis
DEFF Research Database (Denmark)
Kamronn, Simon Due; Poulsen, Andreas Trier; Hansen, Lars Kai
2015-01-01
Correlated component analysis as proposed by Dmochowski, Sajda, Dias, and Parra (2012) is a tool for investigating brain process similarity in the responses to multiple views of a given stimulus. Correlated components are identified under the assumption that the involved spatial networks...... 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....
Elvira, Clément; Dobigeon, Nicolas
2015-01-01
Sparse representations have proven their efficiency in solving a wide class of inverse problems encountered in signal and image processing. Conversely, enforcing the information to be spread uniformly over representation coefficients exhibits relevant properties in various applications such as digital communications. Anti-sparse regularization can be naturally expressed through an $\\ell_{\\infty}$-norm penalty. This paper derives a probabilistic formulation of such representations. A new probability distribution, referred to as the democratic prior, is first introduced. Its main properties as well as three random variate generators for this distribution are derived. Then this probability distribution is used as a prior to promote anti-sparsity in a Gaussian linear inverse problem, yielding a fully Bayesian formulation of anti-sparse coding. Two Markov chain Monte Carlo (MCMC) algorithms are proposed to generate samples according to the posterior distribution. The first one is a standard Gibbs sampler. The seco...
Nonparametric Bayesian inference in biostatistics
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...
Bayesian Kernel Mixtures for Counts.
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. PMID:22523437
Bayesian networks in educational assessment
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 ...
Bayesian models a statistical primer for ecologists
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
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...... by evaluating and differentiating these circuits in time linear in their size. We report on experimental results showing successful compilation and efficient inference on relational Bayesian networks, whose PRIMULA--generated propositional instances have thousands of variables, and whose jointrees have clusters...
The Diagnosis of Reciprocating Machinery by Bayesian Networks
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
A Bayesian Network is a reasoning tool based on probability theory and has many advantages that other reasoning tools do not have. This paper discusses the basic theory of Bayesian networks and studies the problems in constructing Bayesian networks. The paper also constructs a Bayesian diagnosis network of a reciprocating compressor. The example helps us to draw a conclusion that Bayesian diagnosis networks can diagnose reciprocating machinery effectively.
Learning Bayesian networks for discrete data
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.
A Bayesian approach to model uncertainty
International Nuclear Information System (INIS)
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
Bayesian Control for Concentrating Mixed Nuclear Waste
Welch, Robert L.; Smith, Clayton
2013-01-01
A control algorithm for batch processing of mixed waste is proposed based on conditional Gaussian Bayesian networks. The network is compiled during batch staging for real-time response to sensor input.
An Intuitive Dashboard for Bayesian Network Inference
International Nuclear Information System (INIS)
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++
An Intuitive Dashboard for Bayesian Network Inference
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++.
Nomograms for Visualization of Naive Bayesian Classifier
Možina, Martin; Demšar, Janez; Michael W Kattan; Zupan, Blaz
2004-01-01
Besides good predictive performance, the naive Bayesian classifier can also offer a valuable insight into the structure of the training data and effects of the attributes on the class probabilities. This structure may be effectively revealed through visualization of the classifier. We propose a new way to visualize the naive Bayesian model in the form of a nomogram. The advantages of the proposed method are simplicity of presentation, clear display of the effects of individual attribute value...
Subjective Bayesian Analysis: Principles and Practice
Goldstein, Michael
2006-01-01
We address the position of subjectivism within Bayesian statistics. We argue, first, that the subjectivist Bayes approach is the only feasible method for tackling many important practical problems. Second, we describe the essential role of the subjectivist approach in scientific analysis. Third, we consider possible modifications to the Bayesian approach from a subjectivist viewpoint. Finally, we address the issue of pragmatism in implementing the subjectivist approach.
Bayesian Analysis of Multivariate Probit Models
Siddhartha Chib; Edward Greenberg
1996-01-01
This paper provides a unified simulation-based Bayesian and non-Bayesian analysis of correlated binary data using the multivariate probit model. The posterior distribution is simulated by Markov chain Monte Carlo methods, and maximum likelihood estimates are obtained by a Markov chain Monte Carlo version of the E-M algorithm. Computation of Bayes factors from the simulation output is also considered. The methods are applied to a bivariate data set, to a 534-subject, four-year longitudinal dat...
Fitness inheritance in the Bayesian optimization algorithm
Pelikan, Martin; Sastry, Kumara
2004-01-01
This paper describes how fitness inheritance can be used to estimate fitness for a proportion of newly sampled candidate solutions in the Bayesian optimization algorithm (BOA). The goal of estimating fitness for some candidate solutions is to reduce the number of fitness evaluations for problems where fitness evaluation is expensive. Bayesian networks used in BOA to model promising solutions and generate the new ones are extended to allow not only for modeling and sampling candidate solutions...
Kernel Bayesian Inference with Posterior Regularization
Song, Yang; Jun ZHU; Ren, Yong
2016-01-01
We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian inference. Moreover, the optimization problem induces a new regularization for the posterior embedding estimator, which is faster and has comparable performance to the squared regularization in kernel Bayes' rule. This regularization coincides with a former th...
Bayesian Classification in Medicine: The Transferability Question *
Zagoria, Ronald J.; Reggia, James A.; Price, Thomas R.; Banko, Maryann
1981-01-01
Using probabilities derived from a geographically distant patient population, we applied Bayesian classification to categorize stroke patients by etiology. Performance was assessed both by error rate and with a new linear accuracy coefficient. This approach to patient classification was found to be surprisingly accurate when compared to classification by two neurologists and to classification by the Bayesian method using “low cost” local and subjective probabilities. We conclude that for some...
Bayesian target tracking based on particle filter
Institute of Scientific and Technical Information of China (English)
无
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.
Bayesian Variable Selection in Spatial Autoregressive Models
Jesus Crespo Cuaresma; Philipp Piribauer
2015-01-01
This paper compares the performance of Bayesian variable selection approaches for spatial autoregressive models. We present two alternative approaches which can be implemented using Gibbs sampling methods in a straightforward way and allow us to deal with the problem of model uncertainty in spatial autoregressive models in a flexible and computationally efficient way. In a simulation study we show that the variable selection approaches tend to outperform existing Bayesian model averaging tech...
Fuzzy Functional Dependencies and Bayesian Networks
Institute of Scientific and Technical Information of China (English)
LIU WeiYi(刘惟一); SONG Ning(宋宁)
2003-01-01
Bayesian networks have become a popular technique for representing and reasoning with probabilistic information. The fuzzy functional dependency is an important kind of data dependencies in relational databases with fuzzy values. The purpose of this paper is to set up a connection between these data dependencies and Bayesian networks. The connection is done through a set of methods that enable people to obtain the most information of independent conditions from fuzzy functional dependencies.
Bayesian Models of Brain and Behaviour
Penny, William
2012-01-01
This paper presents a review of Bayesian models of brain and behaviour. We first review the basic principles of Bayesian inference. This is followed by descriptions of sampling and variational methods for approximate inference, and forward and backward recursions in time for inference in dynamical models. The review of behavioural models covers work in visual processing, sensory integration, sensorimotor integration, and collective decision making. The review of brain models covers a range of...
Bayesian Modeling of a Human MMORPG Player
Synnaeve, Gabriel
2010-01-01
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.
Bayesian Modeling of a Human MMORPG Player
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.
Bayesian Inference of Reticulate Phylogenies under the Multispecies Network Coalescent.
Wen, Dingqiao; Yu, Yun; Nakhleh, Luay
2016-05-01
The multispecies coalescent (MSC) is a statistical framework that models how gene genealogies grow within the branches of a species tree. The field of computational phylogenetics has witnessed an explosion in the development of methods for species tree inference under MSC, owing mainly to the accumulating evidence of incomplete lineage sorting in phylogenomic analyses. However, the evolutionary history of a set of genomes, or species, could be reticulate due to the occurrence of evolutionary processes such as hybridization or horizontal gene transfer. We report on a novel method for Bayesian inference of genome and species phylogenies under the multispecies network coalescent (MSNC). This framework models gene evolution within the branches of a phylogenetic network, thus incorporating reticulate evolutionary processes, such as hybridization, in addition to incomplete lineage sorting. As phylogenetic networks with different numbers of reticulation events correspond to points of different dimensions in the space of models, we devise a reversible-jump Markov chain Monte Carlo (RJMCMC) technique for sampling the posterior distribution of phylogenetic networks under MSNC. We implemented the methods in the publicly available, open-source software package PhyloNet and studied their performance on simulated and biological data. The work extends the reach of Bayesian inference to phylogenetic networks and enables new evolutionary analyses that account for reticulation. PMID:27144273
Bayesian inference for OPC modeling
Burbine, Andrew; Sturtevant, John; Fryer, David; Smith, Bruce W.
2016-03-01
The use of optical proximity correction (OPC) demands increasingly accurate models of the photolithographic process. Model building and inference techniques in the data science community have seen great strides in the past two decades which make better use of available information. This paper aims to demonstrate the predictive power of Bayesian inference as a method for parameter selection in lithographic models by quantifying the uncertainty associated with model inputs and wafer data. Specifically, the method combines the model builder's prior information about each modelling assumption with the maximization of each observation's likelihood as a Student's t-distributed random variable. Through the use of a Markov chain Monte Carlo (MCMC) algorithm, a model's parameter space is explored to find the most credible parameter values. During parameter exploration, the parameters' posterior distributions are generated by applying Bayes' rule, using a likelihood function and the a priori knowledge supplied. The MCMC algorithm used, an affine invariant ensemble sampler (AIES), is implemented by initializing many walkers which semiindependently explore the space. The convergence of these walkers to global maxima of the likelihood volume determine the parameter values' highest density intervals (HDI) to reveal champion models. We show that this method of parameter selection provides insights into the data that traditional methods do not and outline continued experiments to vet the method.
Bayesian analysis of volcanic eruptions
Ho, Chih-Hsiang
1990-10-01
The simple Poisson model generally gives a good fit to many volcanoes for volcanic eruption forecasting. Nonetheless, empirical evidence suggests that volcanic activity in successive equal time-periods tends to be more variable than a simple Poisson with constant eruptive rate. An alternative model is therefore examined in which eruptive rate(λ) for a given volcano or cluster(s) of volcanoes is described by a gamma distribution (prior) rather than treated as a constant value as in the assumptions of a simple Poisson model. Bayesian analysis is performed to link two distributions together to give the aggregate behavior of the volcanic activity. When the Poisson process is expanded to accomodate a gamma mixing distribution on λ, a consequence of this mixed (or compound) Poisson model is that the frequency distribution of eruptions in any given time-period of equal length follows the negative binomial distribution (NBD). Applications of the proposed model and comparisons between the generalized model and simple Poisson model are discussed based on the historical eruptive count data of volcanoes Mauna Loa (Hawaii) and Etna (Italy). Several relevant facts lead to the conclusion that the generalized model is preferable for practical use both in space and time.
BAYESIAN APPROACH OF DECISION PROBLEMS
Directory of Open Access Journals (Sweden)
DRAGOŞ STUPARU
2010-01-01
Full Text Available Management is nowadays a basic vector of economic development, a concept frequently used in our country as well as all over the world. Indifferently of the hierarchical level at which the managerial process is manifested, decision represents its essential moment, the supreme act of managerial activity. Its can be met in all fields of activity, practically having an unlimited degree of coverage, and in all the functions of management. It is common knowledge that the activity of any type of manger, no matter the hierarchical level he occupies, represents a chain of interdependent decisions, their aim being the elimination or limitation of the influence of disturbing factors that may endanger the achievement of predetermined objectives, and the quality of managerial decisions condition the progress and viability of any enterprise. Therefore, one of the principal characteristics of a successful manager is his ability to adopt the most optimal decisions of high quality. The quality of managerial decisions are conditioned by the manager’s general level of education and specialization, the manner in which they are preoccupied to assimilate the latest information and innovations in the domain of management’s theory and practice and the applying of modern managerial methods and techniques in the activity of management. We are presenting below the analysis of decision problems in hazardous conditions in terms of Bayesian theory – a theory that uses the probabilistic calculus.
Bayesian demography 250 years after Bayes.
Bijak, Jakub; Bryant, John
2016-01-01
Bayesian statistics offers an alternative to classical (frequentist) statistics. It is distinguished by its use of probability distributions to describe uncertain quantities, which leads to elegant solutions to many difficult statistical problems. Although Bayesian demography, like Bayesian statistics more generally, is around 250 years old, only recently has it begun to flourish. The aim of this paper is to review the achievements of Bayesian demography, address some misconceptions, and make the case for wider use of Bayesian methods in population studies. We focus on three applications: demographic forecasts, limited data, and highly structured or complex models. The key advantages of Bayesian methods are the ability to integrate information from multiple sources and to describe uncertainty coherently. Bayesian methods also allow for including additional (prior) information next to the data sample. As such, Bayesian approaches are complementary to many traditional methods, which can be productively re-expressed in Bayesian terms. PMID:26902889
Bayesian demography 250 years after Bayes.
Bijak, Jakub; Bryant, John
2016-01-01
Bayesian statistics offers an alternative to classical (frequentist) statistics. It is distinguished by its use of probability distributions to describe uncertain quantities, which leads to elegant solutions to many difficult statistical problems. Although Bayesian demography, like Bayesian statistics more generally, is around 250 years old, only recently has it begun to flourish. The aim of this paper is to review the achievements of Bayesian demography, address some misconceptions, and make the case for wider use of Bayesian methods in population studies. We focus on three applications: demographic forecasts, limited data, and highly structured or complex models. The key advantages of Bayesian methods are the ability to integrate information from multiple sources and to describe uncertainty coherently. Bayesian methods also allow for including additional (prior) information next to the data sample. As such, Bayesian approaches are complementary to many traditional methods, which can be productively re-expressed in Bayesian terms.
Bayesian tomographic reconstruction of microsystems
Salem, Sofia Fekih; Vabre, Alexandre; Mohammad-Djafari, Ali
2007-11-01
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.
Computationally efficient Bayesian inference for inverse problems.
Energy Technology Data Exchange (ETDEWEB)
Marzouk, Youssef M.; Najm, Habib N.; Rahn, Larry A.
2007-10-01
Bayesian statistics provides a foundation for inference from noisy and incomplete data, a natural mechanism for regularization in the form of prior information, and a quantitative assessment of uncertainty in the inferred results. Inverse problems - representing indirect estimation of model parameters, inputs, or structural components - can be fruitfully cast in this framework. Complex and computationally intensive forward models arising in physical applications, however, can render a Bayesian approach prohibitive. This difficulty is compounded by high-dimensional model spaces, as when the unknown is a spatiotemporal field. We present new algorithmic developments for Bayesian inference in this context, showing strong connections with the forward propagation of uncertainty. In particular, we introduce a stochastic spectral formulation that dramatically accelerates the Bayesian solution of inverse problems via rapid evaluation of a surrogate posterior. We also explore dimensionality reduction for the inference of spatiotemporal fields, using truncated spectral representations of Gaussian process priors. These new approaches are demonstrated on scalar transport problems arising in contaminant source inversion and in the inference of inhomogeneous material or transport properties. We also present a Bayesian framework for parameter estimation in stochastic models, where intrinsic stochasticity may be intermingled with observational noise. Evaluation of a likelihood function may not be analytically tractable in these cases, and thus several alternative Markov chain Monte Carlo (MCMC) schemes, operating on the product space of the observations and the parameters, are introduced.
Tactile length contraction as Bayesian inference.
Tong, Jonathan; Ngo, Vy; Goldreich, Daniel
2016-08-01
To perceive, the brain must interpret stimulus-evoked neural activity. This is challenging: The stochastic nature of the neural response renders its interpretation inherently uncertain. Perception would be optimized if the brain used Bayesian inference to interpret inputs in light of expectations derived from experience. Bayesian inference would improve perception on average but cause illusions when stimuli violate expectation. Intriguingly, tactile, auditory, and visual perception are all prone to length contraction illusions, characterized by the dramatic underestimation of the distance between punctate stimuli delivered in rapid succession; the origin of these illusions has been mysterious. We previously proposed that length contraction illusions occur because the brain interprets punctate stimulus sequences using Bayesian inference with a low-velocity expectation. A novel prediction of our Bayesian observer model is that length contraction should intensify if stimuli are made more difficult to localize. Here we report a tactile psychophysical study that tested this prediction. Twenty humans compared two distances on the forearm: a fixed reference distance defined by two taps with 1-s temporal separation and an adjustable comparison distance defined by two taps with temporal separation t ≤ 1 s. We observed significant length contraction: As t was decreased, participants perceived the two distances as equal only when the comparison distance was made progressively greater than the reference distance. Furthermore, the use of weaker taps significantly enhanced participants' length contraction. These findings confirm the model's predictions, supporting the view that the spatiotemporal percept is a best estimate resulting from a Bayesian inference process. PMID:27121574
Dimensionality reduction in Bayesian estimation algorithms
Directory of Open Access Journals (Sweden)
G. W. Petty
2013-03-01
Full Text Available An idealized synthetic database loosely resembling 3-channel passive microwave observations of precipitation against a variable background is employed to examine the performance of a conventional Bayesian retrieval algorithm. For this dataset, algorithm performance is found to be poor owing to an irreconcilable conflict between the need to find matches in the dependent database versus the need to exclude inappropriate matches. It is argued that the likelihood of such conflicts increases sharply with the dimensionality of the observation space of real satellite sensors, which may utilize 9 to 13 channels to retrieve precipitation, for example. An objective method is described for distilling the relevant information content from N real channels into a much smaller number (M of pseudochannels while also regularizing the background (geophysical plus instrument noise component. The pseudochannels are linear combinations of the original N channels obtained via a two-stage principal component analysis of the dependent dataset. Bayesian retrievals based on a single pseudochannel applied to the independent dataset yield striking improvements in overall performance. The differences between the conventional Bayesian retrieval and reduced-dimensional Bayesian retrieval suggest that a major potential problem with conventional multichannel retrievals – whether Bayesian or not – lies in the common but often inappropriate assumption of diagonal error covariance. The dimensional reduction technique described herein avoids this problem by, in effect, recasting the retrieval problem in a coordinate system in which the desired covariance is lower-dimensional, diagonal, and unit magnitude.
Tactile length contraction as Bayesian inference.
Tong, Jonathan; Ngo, Vy; Goldreich, Daniel
2016-08-01
To perceive, the brain must interpret stimulus-evoked neural activity. This is challenging: The stochastic nature of the neural response renders its interpretation inherently uncertain. Perception would be optimized if the brain used Bayesian inference to interpret inputs in light of expectations derived from experience. Bayesian inference would improve perception on average but cause illusions when stimuli violate expectation. Intriguingly, tactile, auditory, and visual perception are all prone to length contraction illusions, characterized by the dramatic underestimation of the distance between punctate stimuli delivered in rapid succession; the origin of these illusions has been mysterious. We previously proposed that length contraction illusions occur because the brain interprets punctate stimulus sequences using Bayesian inference with a low-velocity expectation. A novel prediction of our Bayesian observer model is that length contraction should intensify if stimuli are made more difficult to localize. Here we report a tactile psychophysical study that tested this prediction. Twenty humans compared two distances on the forearm: a fixed reference distance defined by two taps with 1-s temporal separation and an adjustable comparison distance defined by two taps with temporal separation t ≤ 1 s. We observed significant length contraction: As t was decreased, participants perceived the two distances as equal only when the comparison distance was made progressively greater than the reference distance. Furthermore, the use of weaker taps significantly enhanced participants' length contraction. These findings confirm the model's predictions, supporting the view that the spatiotemporal percept is a best estimate resulting from a Bayesian inference process.
Individual organisms as units of analysis: Bayesian-clustering alternatives in population genetics.
Mank, Judith E; Avise, John C
2004-12-01
Population genetic analyses traditionally focus on the frequencies of alleles or genotypes in 'populations' that are delimited a priori. However, there are potential drawbacks of amalgamating genetic data into such composite attributes of assemblages of specimens: genetic information on individual specimens is lost or submerged as an inherent part of the analysis. A potential also exists for circular reasoning when a population's initial identification and subsequent genetic characterization are coupled. In principle, these problems are circumvented by some newer methods of population identification and individual assignment based on statistical clustering of specimen genotypes. Here we evaluate a recent method in this genre--Bayesian clustering--using four genotypic data sets involving different types of molecular markers in non-model organisms from nature. As expected, measures of population genetic structure (F(ST) and phiST) tended to be significantly greater in Bayesian a posteriori data treatments than in analyses where populations were delimited a priori. In the four biological contexts examined, which involved both geographic population structures and hybrid zones, Bayesian clustering was able to recover differentiated populations, and Bayesian assignments were able to identify likely population sources of specific individuals.
Bayesian Methods for Radiation Detection and Dosimetry
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...
Adaptive approximate Bayesian computation for complex models
Lenormand, Maxime; Deffuant, Guillaume
2011-01-01
Approximate Bayesian computation (ABC) is a family of computational techniques in Bayesian statistics. These techniques allow to fit a model to data without relying on the computation of the model likelihood. They instead require to simulate a large number of times the model to be fitted. A number of refinements to the original rejection-based ABC scheme have been proposed, including the sequential improvement of posterior distributions. This technique allows to decrease the number of model simulations required, but it still presents several shortcomings which are particularly problematic for costly to simulate complex models. We here provide a new algorithm to perform adaptive approximate Bayesian computation, which is shown to perform better on both a toy example and a complex social model.
Learning Bayesian Networks from Correlated Data
Bae, Harold; Monti, Stefano; Montano, Monty; Steinberg, Martin H.; Perls, Thomas T.; Sebastiani, Paola
2016-05-01
Bayesian networks are probabilistic models that represent complex distributions in a modular way and have become very popular in many fields. There are many methods to build Bayesian networks from a random sample of independent and identically distributed observations. However, many observational studies are designed using some form of clustered sampling that introduces correlations between observations within the same cluster and ignoring this correlation typically inflates the rate of false positive associations. We describe a novel parameterization of Bayesian networks that uses random effects to model the correlation within sample units and can be used for structure and parameter learning from correlated data without inflating the Type I error rate. We compare different learning metrics using simulations and illustrate the method in two real examples: an analysis of genetic and non-genetic factors associated with human longevity from a family-based study, and an example of risk factors for complications of sickle cell anemia from a longitudinal study with repeated measures.
Bayesian Fusion of Multi-Band Images
Wei, Qi; Tourneret, Jean-Yves
2013-01-01
In this paper, a Bayesian fusion technique for remotely sensed multi-band images is presented. The observed images are related to the high spectral and high spatial resolution image to be recovered through physical degradations, e.g., spatial and spectral blurring and/or subsampling defined by the sensor characteristics. The fusion problem is formulated within a Bayesian estimation framework. An appropriate prior distribution exploiting geometrical consideration is introduced. To compute the Bayesian estimator of the scene of interest from its posterior distribution, a Markov chain Monte Carlo algorithm is designed to generate samples asymptotically distributed according to the target distribution. To efficiently sample from this high-dimension distribution, a Hamiltonian Monte Carlo step is introduced in the Gibbs sampling strategy. The efficiency of the proposed fusion method is evaluated with respect to several state-of-the-art fusion techniques. In particular, low spatial resolution hyperspectral and mult...
Bayesian Image Reconstruction Based on Voronoi Diagrams
Cabrera, G F; Hitschfeld, N
2007-01-01
We present a Bayesian Voronoi image reconstruction technique (VIR) for interferometric data. Bayesian analysis applied to the inverse problem allows us to derive the a-posteriori probability of a novel parameterization of interferometric images. We use a variable Voronoi diagram as our model in place of the usual fixed pixel grid. A quantization of the intensity field allows us to calculate the likelihood function and a-priori probabilities. The Voronoi image is optimized including the number of polygons as free parameters. We apply our algorithm to deconvolve simulated interferometric data. Residuals, restored images and chi^2 values are used to compare our reconstructions with fixed grid models. VIR has the advantage of modeling the image with few parameters, obtaining a better image from a Bayesian point of view.
Variational Bayesian Inference of Line Spectra
DEFF Research Database (Denmark)
Badiu, Mihai Alin; Hansen, Thomas Lundgaard; Fleury, Bernard Henri
2016-01-01
In this paper, we address the fundamental problem of line spectral estimation in a Bayesian framework. We target model order and parameter estimation via variational inference in a probabilistic model in which the frequencies are continuous-valued, i.e., not restricted to a grid; and the coeffici......In this paper, we address the fundamental problem of line spectral estimation in a Bayesian framework. We target model order and parameter estimation via variational inference in a probabilistic model in which the frequencies are continuous-valued, i.e., not restricted to a grid......; and the coefficients are governed by a Bernoulli-Gaussian prior model turning model order selection into binary sequence detection. Unlike earlier works which retain only point estimates of the frequencies, we undertake a more complete Bayesian treatment by estimating the posterior probability density functions (pdfs...
Event generator tuning using Bayesian optimization
Ilten, Philip; Yang, Yunjie
2016-01-01
Monte Carlo event generators contain a large number of parameters that must be determined by comparing the output of the generator with experimental data. Generating enough events with a fixed set of parameter values to enable making such a comparison is extremely CPU intensive, which prohibits performing a simple brute-force grid-based tuning of the parameters. Bayesian optimization is a powerful method designed for such black-box tuning applications. In this article, we show that Monte Carlo event generator parameters can be accurately obtained using Bayesian optimization and minimal expert-level physics knowledge. A tune of the PYTHIA 8 event generator using $e^+e^-$ events, where 20 parameters are optimized, can be run on a modern laptop in just two days. Combining the Bayesian optimization approach with expert knowledge should enable producing better tunes in the future, by making it faster and easier to study discrepancies between Monte Carlo and experimental data.
Hessian PDF reweighting meets the Bayesian methods
Paukkunen, Hannu
2014-01-01
We discuss the Hessian PDF reweighting - a technique intended to estimate the effects that new measurements have on a set of PDFs. The method stems straightforwardly from considering new data in a usual $\\chi^2$-fit and it naturally incorporates also non-zero values for the tolerance, $\\Delta\\chi^2>1$. In comparison to the contemporary Bayesian reweighting techniques, there is no need to generate large ensembles of PDF Monte-Carlo replicas, and the observables need to be evaluated only with the central and the error sets of the original PDFs. In spite of the apparently rather different methodologies, we find that the Hessian and the Bayesian techniques are actually equivalent if the $\\Delta\\chi^2$ criterion is properly included to the Bayesian likelihood function that is a simple exponential.
A Large Sample Study of the Bayesian Bootstrap
Lo, Albert Y.
1987-01-01
An asymptotic justification of the Bayesian bootstrap is given. Large-sample Bayesian bootstrap probability intervals for the mean, the variance and bands for the distribution, the smoothed density and smoothed rate function are also provided.
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.
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.)
Bayesian statistic methods and theri application in probabilistic simulation models
Directory of Open Access Journals (Sweden)
Sergio Iannazzo
2007-03-01
Full Text Available Bayesian statistic methods are facing a rapidly growing level of interest and acceptance in the field of health economics. The reasons of this success are probably to be found on the theoretical fundaments of the discipline that make these techniques more appealing to decision analysis. To this point should be added the modern IT progress that has developed different flexible and powerful statistical software framework. Among them probably one of the most noticeably is the BUGS language project and its standalone application for MS Windows WinBUGS. Scope of this paper is to introduce the subject and to show some interesting applications of WinBUGS in developing complex economical models based on Markov chains. The advantages of this approach reside on the elegance of the code produced and in its capability to easily develop probabilistic simulations. Moreover an example of the integration of bayesian inference models in a Markov model is shown. This last feature let the analyst conduce statistical analyses on the available sources of evidence and exploit them directly as inputs in the economic model.
Bayesian approach in MN low dose of radiation counting
International Nuclear Information System (INIS)
The Micronucleus assay in lymphocytes is a well established technique for the assessment of genetic damage induced by ionizing radiation. Due to the presence of a natural background of MN the net MN is obtained by subtracting this value to the gross value. When very low doses of radiation are given the induced MN is close even lower than the predetermined background value. Furthermore, the damage distribution induced by the radiation follows a Poisson probability distribution. These two facts pose a difficult task to obtain the net counting rate in the exposed situations. It is possible to overcome this problem using a bayesian approach, in which the selection of a priori distributions for the background and net counting rate plays an important role. In the present work we make a detailed analysed using bayesian theory to infer the net counting rate in two different situations: a) when the background is known for an individual sample, using exact value value for the background and Jeffreys prior for the net counting rate, and b) when the background is not known and we make use of a population background distribution as background prior function and constant prior for the net counting rate. (Author)
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.
Bayesian estimation and tracking a practical guide
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
Bayesian Optimisation Algorithm for Nurse Scheduling
Li, Jingpeng
2008-01-01
Our research has shown that schedules can be built mimicking a human scheduler by using a set of rules that involve domain knowledge. This chapter presents a Bayesian Optimization Algorithm (BOA) for the nurse scheduling problem that chooses such suitable scheduling rules from a set for each nurses assignment. Based on the idea of using probabilistic models, the BOA builds a Bayesian network for the set of promising solutions and samples these networks to generate new candidate solutions. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed algorithm may be suitable for other scheduling problems.
A Bayesian Analysis of Spectral ARMA Model
Directory of Open Access Journals (Sweden)
Manoel I. Silvestre Bezerra
2012-01-01
Full Text Available Bezerra et al. (2008 proposed a new method, based on Yule-Walker equations, to estimate the ARMA spectral model. In this paper, a Bayesian approach is developed for this model by using the noninformative prior proposed by Jeffreys (1967. The Bayesian computations, simulation via Markov Monte Carlo (MCMC is carried out and characteristics of marginal posterior distributions such as Bayes estimator and confidence interval for the parameters of the ARMA model are derived. Both methods are also compared with the traditional least squares and maximum likelihood approaches and a numerical illustration with two examples of the ARMA model is presented to evaluate the performance of the procedures.
A Bayesian Concept Learning Approach to Crowdsourcing
DEFF Research Database (Denmark)
Viappiani, Paolo Renato; Zilles, Sandra; Hamilton, Howard J.;
2011-01-01
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...... 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...... that our Bayesian strategies are effective even in large concept spaces with many uninformative experts....
Comparison of the Bayesian and Frequentist Approach to the Statistics
Hakala, Michal
2015-01-01
The Thesis deals with introduction to Bayesian statistics and comparing Bayesian approach with frequentist approach to statistics. Bayesian statistics is modern branch of statistics which provides an alternative comprehensive theory to the frequentist approach. Bayesian concepts provides solution for problems not being solvable by frequentist theory. In the thesis are compared definitions, concepts and quality of statistical inference. The main interest is focused on a point estimation, an in...
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...
A default Bayesian hypothesis test for ANOVA designs
R. Wetzels; R.P.P.P. Grasman; E.J. Wagenmakers
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 desig
A Gentle Introduction to Bayesian Analysis : Applications to Developmental Research
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, t
Bayesian Just-So Stories in Psychology and Neuroscience
Bowers, Jeffrey S.; Davis, Colin J.
2012-01-01
According to Bayesian theories in psychology and neuroscience, minds and brains are (near) optimal in solving a wide range of tasks. We challenge this view and argue that more traditional, non-Bayesian approaches are more promising. We make 3 main arguments. First, we show that the empirical evidence for Bayesian theories in psychology is weak.…
A Bayesian stochastic frontier analysis of Chinese fossil-fuel electricity generation companies
International Nuclear Information System (INIS)
This paper analyses the technical efficiency of Chinese fossil-fuel electricity generation companies from 1999 to 2011, using a Bayesian stochastic frontier model. The results reveal that efficiency varies among the fossil-fuel electricity generation companies that were analysed. We also focus on the factors of size, location, government ownership and mixed sources of electricity generation for the fossil-fuel electricity generation companies, and also examine their effects on the efficiency of these companies. Policy implications are derived. - Highlights: • We analyze the efficiency of 27 quoted Chinese fossil-fuel electricity generation companies during 1999–2011. • We adopt a Bayesian stochastic frontier model taking into consideration the identified heterogeneity. • With reform background in Chinese energy industry, we propose four hypotheses and check their influence on efficiency. • Big size, coastal location, government control and hydro energy sources all have increased costs
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
Most frugal explanations in Bayesian networks
Kwisthout, J.H.P.
2015-01-01
Inferring the most probable explanation to a set of variables, given a partial observation of the remaining variables, is one of the canonical computational problems in Bayesian networks, with widespread applications in AI and beyond. This problem, known as MAP, is computationally intractable (NP-ha
Bayesian semiparametric dynamic Nelson-Siegel model
C. Cakmakli
2011-01-01
This paper proposes the Bayesian semiparametric dynamic Nelson-Siegel model where the density of the yield curve factors and thereby the density of the yields are estimated along with other model parameters. This is accomplished by modeling the error distributions of the factors according to a Diric
Von Neumann was not a Quantum Bayesian.
Stacey, Blake C
2016-05-28
Wikipedia has claimed for over 3 years now that John von Neumann was the 'first quantum Bayesian'. In context, this reads as stating that von Neumann inaugurated QBism, the approach to quantum theory promoted by Fuchs, Mermin and Schack. This essay explores how such a claim is, historically speaking, unsupported. PMID:27091166
Von Neumann Was Not a Quantum Bayesian
Blake C. Stacey
2014-01-01
Wikipedia has claimed for over three years now that John von Neumann was the "first quantum Bayesian." In context, this reads as stating that von Neumann inaugurated QBism, the approach to quantum theory promoted by Fuchs, Mermin and Schack. This essay explores how such a claim is, historically speaking, unsupported.
A Bayesian Approach to Interactive Retrieval
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…
Bayesian regularization of diffusion tensor images
DEFF Research Database (Denmark)
Frandsen, Jesper; Hobolth, Asger; Østergaard, Leif;
2007-01-01
several directions. The measured diffusion coefficients and thereby the diffusion tensors are subject to noise, leading to possibly flawed representations of the three dimensional fibre bundles. In this paper we develop a Bayesian procedure for regularizing the diffusion tensor field, fully utilizing...
Inverse Problems in a Bayesian Setting
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.
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.
Bayesian Vector Autoregressions with Stochastic Volatility
Uhlig, H.F.H.V.S.
1996-01-01
This paper proposes a Bayesian approach to a vector autoregression with stochastic volatility, where the multiplicative evolution of the precision matrix is driven by a multivariate beta variate.Exact updating formulas are given to the nonlinear filtering of the precision matrix.Estimation of the au
Scaling Bayesian network discovery through incremental recovery
Castelo, J.R.; Siebes, A.P.J.M.
1999-01-01
Bayesian networks are a type of graphical models that, e.g., allow one to analyze the interaction among the variables in a database. A well-known problem with the discovery of such models from a database is the ``problem of high-dimensionality''. That is, the discovery of a network from a database w
A Bayesian Bootstrap for a Finite Population
Lo, Albert Y.
1988-01-01
A Bayesian bootstrap for a finite population is introduced; its small-sample distributional properties are discussed and compared with those of the frequentist bootstrap for a finite population. It is also shown that the two are first-order asymptotically equivalent.
Bayesian calibration for forensic age estimation.
Ferrante, Luigi; Skrami, Edlira; Gesuita, Rosaria; Cameriere, Roberto
2015-05-10
Forensic medicine is increasingly called upon to assess the age of individuals. Forensic age estimation is mostly required in relation to illegal immigration and identification of bodies or skeletal remains. A variety of age estimation methods are based on dental samples and use of regression models, where the age of an individual is predicted by morphological tooth changes that take place over time. From the medico-legal point of view, regression models, with age as the dependent random variable entail that age tends to be overestimated in the young and underestimated in the old. To overcome this bias, we describe a new full Bayesian calibration method (asymmetric Laplace Bayesian calibration) for forensic age estimation that uses asymmetric Laplace distribution as the probability model. The method was compared with three existing approaches (two Bayesian and a classical method) using simulated data. Although its accuracy was comparable with that of the other methods, the asymmetric Laplace Bayesian calibration appears to be significantly more reliable and robust in case of misspecification of the probability model. The proposed method was also applied to a real dataset of values of the pulp chamber of the right lower premolar measured on x-ray scans of individuals of known age. PMID:25645903
Exploiting structure in cooperative Bayesian games
F.A. Oliehoek; S. Whiteson; M.T.J. Spaan
2012-01-01
Cooperative Bayesian games (BGs) can model decision-making problems for teams of agents under imperfect information, but require space and computation time that is exponential in the number of agents. While agent independence has been used to mitigate these problems in perfect information settings,
Perfect Bayesian equilibrium. Part II: epistemic foundations
Bonanno, Giacomo
2011-01-01
In a companion paper we introduced a general notion of perfect Bayesian equilibrium which can be applied to arbitrary extensive-form games. The essential ingredient of the proposed definition is the qualitative notion of AGM-consistency. In this paper we provide an epistemic foundation for AGM-consistency based on the AGM theory of belief revision.
Decision generation tools and Bayesian inference
Jannson, Tomasz; Wang, Wenjian; Forrester, Thomas; Kostrzewski, Andrew; Veeris, Christian; Nielsen, Thomas
2014-05-01
Digital Decision Generation (DDG) tools are important software sub-systems of Command and Control (C2) systems and technologies. In this paper, we present a special type of DDGs based on Bayesian Inference, related to adverse (hostile) networks, including such important applications as terrorism-related networks and organized crime ones.
Von Neumann Was Not a Quantum Bayesian
Stacey, Blake C
2014-01-01
Wikipedia has claimed for over two years now that John von Neumann was the "first quantum Bayesian." In context, this reads as stating that von Neumann inaugurated QBism, the approach to quantum theory promoted by Fuchs, Mermin and Schack. This essay explores how such a claim is, historically speaking, unsupported.
Bayesian calibration of car-following models
Van Hinsbergen, C.P.IJ.; Van Lint, H.W.C.; Hoogendoorn, S.P.; Van Zuylen, H.J.
2010-01-01
Recent research has revealed that there exist large inter-driver differences in car-following behavior such that different car-following models may apply to different drivers. This study applies Bayesian techniques to the calibration of car-following models, where prior distributions on each model p
Basics of Bayesian Learning - Basically Bayes
DEFF Research Database (Denmark)
Larsen, Jan
Tutorial presented at the IEEE Machine Learning for Signal Processing Workshop 2006, Maynooth, Ireland, September 8, 2006. The tutorial focuses on the basic elements of Bayesian learning and its relation to classical learning paradigms. This includes a critical discussion of the pros and cons...
On local optima in learning bayesian networks
DEFF Research Database (Denmark)
Dalgaard, Jens; Kocka, Tomas; Pena, Jose
2003-01-01
This paper proposes and evaluates the k-greedy equivalence search algorithm (KES) for learning Bayesian networks (BNs) from complete data. The main characteristic of KES is that it allows a trade-off between greediness and randomness, thus exploring different good local optima. When greediness...
Bayesian Estimation Supersedes the "t" Test
Kruschke, John K.
2013-01-01
Bayesian estimation for 2 groups provides complete distributions of credible values for the effect size, group means and their difference, standard deviations and their difference, and the normality of the data. The method handles outliers. The decision rule can accept the null value (unlike traditional "t" tests) when certainty in the estimate is…
Bayesian Estimation of Thermonuclear Reaction Rates
Iliadis, Christian; Coc, Alain; Timmes, Frank; Starrfield, Sumner
2016-01-01
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 in the past to this problem, 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 extra-solar planets, gravitational waves, and type Ia supernovae. However, nuclear physics, in particular, has been slow to adopt Bayesian methods. We present the first 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 d(p,$\\gamma$)$^3$He, $^3$He($^3$He,2p)$^4$He, and $^3$He($\\alpha$,$\\gamma$)$^7$Be reactions,...
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...
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...
Modelling crime linkage with Bayesian networks
J. de Zoete; M. Sjerps; D. Lagnado; N. Fenton
2015-01-01
When two or more crimes show specific similarities, such as a very distinct modus operandi, the probability that they were committed by the same offender becomes of interest. This probability depends on the degree of similarity and distinctiveness. We show how Bayesian networks can be used to model
A Bayesian approach to linear regression in astronomy
Sereno, Mauro
2015-01-01
Linear regression is common in astronomical analyses. I discuss a Bayesian hierarchical modeling of data with heteroscedastic and possibly correlated measurement errors and intrinsic scatter. The method fully accounts for time evolution. The slope, the normalization, and the intrinsic scatter of the relation can evolve with the redshift. The intrinsic distribution of the independent variable is approximated using a mixture of Gaussian distributions whose means and standard deviations depend on time. The method can address scatter in the measured independent variable (a kind of Eddington bias), selection effects in the response variable (Malmquist bias), and departure from linearity in form of a knee. I tested the method with toy models and simulations and quantified the effect of biases and inefficient modeling. The R-package LIRA (LInear Regression in Astronomy) is made available to perform the regression.
On Bayesian methods of exploring qualitative interactions for targeted treatment.
Chen, Wei; Ghosh, Debashis; Raghunathan, Trivellore E; Norkin, Maxim; Sargent, Daniel J; Bepler, Gerold
2012-12-10
Providing personalized treatments designed to maximize benefits and minimizing harms is of tremendous current medical interest. One problem in this area is the evaluation of the interaction between the treatment and other predictor variables. Treatment effects in subgroups having the same direction but different magnitudes are called quantitative interactions, whereas those having opposite directions in subgroups are called qualitative interactions (QIs). Identifying QIs is challenging because they are rare and usually unknown among many potential biomarkers. Meanwhile, subgroup analysis reduces the power of hypothesis testing and multiple subgroup analyses inflate the type I error rate. We propose a new Bayesian approach to search for QI in a multiple regression setting with adaptive decision rules. We consider various regression models for the outcome. We illustrate this method in two examples of phase III clinical trials. The algorithm is straightforward and easy to implement using existing software packages. We provide a sample code in Appendix A.
Petit, V.; Wade, G. A.
2011-01-01
In this paper we describe a Bayesian statistical method designed to infer the magnetic properties of stars observed using high-resolution circular spectropolarimetry in the context of large surveys. This approach is well suited for analysing stars for which the stellar rotation period is not known, and therefore the rotational phases of the observations are ambiguous. The model assumes that the magnetic observations correspond to a dipole oblique rotator, a situation commonly encountered in i...
Bayesian network as a modelling tool for risk management in agriculture
Svend Rasmussen; Madsen, Anders L.; Mogens Lund
2013-01-01
The importance of risk management increases as farmers become more exposed to risk. But risk management is a difficult topic because income risk is the result of the complex interaction of multiple risk factors combined with the effect of an increasing array of possible risk management tools. In this paper we use Bayesian networks as an integrated modelling approach for representing uncertainty and analysing risk management in agriculture. It is shown how historical farm account data may be e...
Computational statistics using the Bayesian Inference Engine
Weinberg, Martin D.
2013-09-01
This paper introduces the Bayesian Inference Engine (BIE), a general parallel, optimized software package for parameter inference and model selection. This package is motivated by the analysis needs of modern astronomical surveys and the need to organize and reuse expensive derived data. The BIE is the first platform for computational statistics designed explicitly to enable Bayesian update and model comparison for astronomical problems. Bayesian update is based on the representation of high-dimensional posterior distributions using metric-ball-tree based kernel density estimation. Among its algorithmic offerings, the BIE emphasizes hybrid tempered Markov chain Monte Carlo schemes that robustly sample multimodal posterior distributions in high-dimensional parameter spaces. Moreover, the BIE implements a full persistence or serialization system that stores the full byte-level image of the running inference and previously characterized posterior distributions for later use. Two new algorithms to compute the marginal likelihood from the posterior distribution, developed for and implemented in the BIE, enable model comparison for complex models and data sets. Finally, the BIE was designed to be a collaborative platform for applying Bayesian methodology to astronomy. It includes an extensible object-oriented and easily extended framework that implements every aspect of the Bayesian inference. By providing a variety of statistical algorithms for all phases of the inference problem, a scientist may explore a variety of approaches with a single model and data implementation. Additional technical details and download details are available from http://www.astro.umass.edu/bie. The BIE is distributed under the GNU General Public License.
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.
A Bayesian outlier criterion to detect SNPs under selection in large data sets.
Directory of Open Access Journals (Sweden)
Mathieu Gautier
Full Text Available BACKGROUND: The recent advent of high-throughput SNP genotyping technologies has opened new avenues of research for population genetics. In particular, a growing interest in the identification of footprints of selection, based on genome scans for adaptive differentiation, has emerged. METHODOLOGY/PRINCIPAL FINDINGS: The purpose of this study is to develop an efficient model-based approach to perform bayesian exploratory analyses for adaptive differentiation in very large SNP data sets. The basic idea is to start with a very simple model for neutral loci that is easy to implement under a bayesian framework and to identify selected loci as outliers via Posterior Predictive P-values (PPP-values. Applications of this strategy are considered using two different statistical models. The first one was initially interpreted in the context of populations evolving respectively under pure genetic drift from a common ancestral population while the second one relies on populations under migration-drift equilibrium. Robustness and power of the two resulting bayesian model-based approaches to detect SNP under selection are further evaluated through extensive simulations. An application to a cattle data set is also provided. CONCLUSIONS/SIGNIFICANCE: The procedure described turns out to be much faster than former bayesian approaches and also reasonably efficient especially to detect loci under positive selection.
Dynamic causal modelling of electrographic seizure activity using Bayesian belief updating.
Cooray, Gerald K; Sengupta, Biswa; Douglas, Pamela K; Friston, Karl
2016-01-15
Seizure activity in EEG recordings can persist for hours with seizure dynamics changing rapidly over time and space. To characterise the spatiotemporal evolution of seizure activity, large data sets often need to be analysed. Dynamic causal modelling (DCM) can be used to estimate the synaptic drivers of cortical dynamics during a seizure; however, the requisite (Bayesian) inversion procedure is computationally expensive. In this note, we describe a straightforward procedure, within the DCM framework, that provides efficient inversion of seizure activity measured with non-invasive and invasive physiological recordings; namely, EEG/ECoG. We describe the theoretical background behind a Bayesian belief updating scheme for DCM. The scheme is tested on simulated and empirical seizure activity (recorded both invasively and non-invasively) and compared with standard Bayesian inversion. We show that the Bayesian belief updating scheme provides similar estimates of time-varying synaptic parameters, compared to standard schemes, indicating no significant qualitative change in accuracy. The difference in variance explained was small (less than 5%). The updating method was substantially more efficient, taking approximately 5-10min compared to approximately 1-2h. Moreover, the setup of the model under the updating scheme allows for a clear specification of how neuronal variables fluctuate over separable timescales. This method now allows us to investigate the effect of fast (neuronal) activity on slow fluctuations in (synaptic) parameters, paving a way forward to understand how seizure activity is generated.
Universal Darwinism as a process of Bayesian inference
Campbell, John O
2016-01-01
Many of the mathematical frameworks describing natural selection are equivalent to Bayes Theorem, also known as Bayesian updating. By definition, a process of Bayesian Inference is one which involves a Bayesian update, so we may conclude that these frameworks describe natural selection as a process of Bayesian inference. Thus natural selection serves as a counter example to a widely-held interpretation that restricts Bayesian Inference to human mental processes (including the endeavors of statisticians). As Bayesian inference can always be cast in terms of (variational) free energy minimization, natural selection can be viewed as comprising two components: a generative model of an "experiment" in the external world environment, and the results of that "experiment" or the "surprise" entailed by predicted and actual outcomes of the "experiment". Minimization of free energy implies that the implicit measure of "surprise" experienced serves to update the generative model in a Bayesian manner. This description clo...
Ruane, Sara; Bryson, Robert W; Pyron, R Alexander; Burbrink, Frank T
2014-03-01
Both gene-tree discordance and unrecognized diversity are sources of error for accurate estimation of species trees, and can affect downstream diversification analyses by obscuring the correct number of nodes, their density, and the lengths of the branches subtending them. Although the theoretical impact of gene-tree discordance on evolutionary analyses has been examined previously, the effect of unsampled and cryptic diversity has not. Here, we examine how delimitation of previously unrecognized diversity in the milksnake (Lampropeltis triangulum) and use of a species-tree approach affects both estimation of the Lampropeltis phylogeny and comparative analyses with respect to the timing of diversification. Coalescent species delimitation indicates that L. triangulum is not monophyletic and that there are multiple species of milksnake, which increases the known species diversity in the genus Lampropeltis by 40%. Both genealogical and temporal discordance occurs between gene trees and the species tree, with evidence that mitochondrial DNA (mtDNA) introgression is a main factor. This discordance is further manifested in the preferred models of diversification, where the concatenated gene tree strongly supports an early burst of speciation during the Miocene, in contrast to species-tree estimates where diversification follows a birth-death model and speciation occurs mostly in the Pliocene and Pleistocene. This study highlights the crucial interaction among coalescent-based phylogeography and species delimitation, systematics, and species diversification analyses.
Bayesian network learning for natural hazard assessments
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
Bayesian multitask inverse reinforcement learning
Dimitrakakis, Christos
2011-01-01
We generalise the problem of inverse reinforcement learning to multiple tasks, from a set of demonstrations. Each demonstration may represent one expert trying to solve a different task. Alternatively, one may see each demonstration as given by a different expert trying to solve the same task. Our main technical contribution is to solve the problem by formalising it as statistical preference elicitation, via a number of structured priors, whose form captures our biases about the relatedness of different tasks or expert policies. We show that our methodology allows us not only to learn to efficiently from multiple experts but to also effectively differentiate between the goals of each. Possible applications include analysing the intrinsic motivations of subjects in behavioural experiments and imitation learning from multiple teachers.
Dembo, Mana; Radovčić, Davorka; Garvin, Heather M; Laird, Myra F; Schroeder, Lauren; Scott, Jill E; Brophy, Juliet; Ackermann, Rebecca R; Musiba, Chares M; de Ruiter, Darryl J; Mooers, Arne Ø; Collard, Mark
2016-08-01
Homo naledi is a recently discovered species of fossil hominin from South Africa. A considerable amount is already known about H. naledi but some important questions remain unanswered. Here we report a study that addressed two of them: "Where does H. naledi fit in the hominin evolutionary tree?" and "How old is it?" We used a large supermatrix of craniodental characters for both early and late hominin species and Bayesian phylogenetic techniques to carry out three analyses. First, we performed a dated Bayesian analysis to generate estimates of the evolutionary relationships of fossil hominins including H. naledi. Then we employed Bayes factor tests to compare the strength of support for hypotheses about the relationships of H. naledi suggested by the best-estimate trees. Lastly, we carried out a resampling analysis to assess the accuracy of the age estimate for H. naledi yielded by the dated Bayesian analysis. The analyses strongly supported the hypothesis that H. naledi forms a clade with the other Homo species and Australopithecus sediba. The analyses were more ambiguous regarding the position of H. naledi within the (Homo, Au. sediba) clade. A number of hypotheses were rejected, but several others were not. Based on the available craniodental data, Homo antecessor, Asian Homo erectus, Homo habilis, Homo floresiensis, Homo sapiens, and Au. sediba could all be the sister taxon of H. naledi. According to the dated Bayesian analysis, the most likely age for H. naledi is 912 ka. This age estimate was supported by the resampling analysis. Our findings have a number of implications. Most notably, they support the assignment of the new specimens to Homo, cast doubt on the claim that H. naledi is simply a variant of H. erectus, and suggest H. naledi is younger than has been previously proposed. PMID:27457542
Dembo, Mana; Radovčić, Davorka; Garvin, Heather M; Laird, Myra F; Schroeder, Lauren; Scott, Jill E; Brophy, Juliet; Ackermann, Rebecca R; Musiba, Chares M; de Ruiter, Darryl J; Mooers, Arne Ø; Collard, Mark
2016-08-01
Homo naledi is a recently discovered species of fossil hominin from South Africa. A considerable amount is already known about H. naledi but some important questions remain unanswered. Here we report a study that addressed two of them: "Where does H. naledi fit in the hominin evolutionary tree?" and "How old is it?" We used a large supermatrix of craniodental characters for both early and late hominin species and Bayesian phylogenetic techniques to carry out three analyses. First, we performed a dated Bayesian analysis to generate estimates of the evolutionary relationships of fossil hominins including H. naledi. Then we employed Bayes factor tests to compare the strength of support for hypotheses about the relationships of H. naledi suggested by the best-estimate trees. Lastly, we carried out a resampling analysis to assess the accuracy of the age estimate for H. naledi yielded by the dated Bayesian analysis. The analyses strongly supported the hypothesis that H. naledi forms a clade with the other Homo species and Australopithecus sediba. The analyses were more ambiguous regarding the position of H. naledi within the (Homo, Au. sediba) clade. A number of hypotheses were rejected, but several others were not. Based on the available craniodental data, Homo antecessor, Asian Homo erectus, Homo habilis, Homo floresiensis, Homo sapiens, and Au. sediba could all be the sister taxon of H. naledi. According to the dated Bayesian analysis, the most likely age for H. naledi is 912 ka. This age estimate was supported by the resampling analysis. Our findings have a number of implications. Most notably, they support the assignment of the new specimens to Homo, cast doubt on the claim that H. naledi is simply a variant of H. erectus, and suggest H. naledi is younger than has been previously proposed.
Bayesian parameter estimation for effective field theories
Wesolowski, S; Furnstahl, R J; Phillips, D R; Thapaliya, A
2015-01-01
We present procedures based on Bayesian statistics for effective field theory (EFT) parameter estimation from data. The extraction of low-energy constants (LECs) is guided by theoretical expectations that supplement such information in a quantifiable way through the specification of Bayesian priors. A prior for natural-sized LECs reduces the possibility of overfitting, and leads to a consistent accounting of different sources of uncertainty. A set of diagnostic tools are developed that analyze the fit and ensure that the priors do not bias the EFT parameter estimation. The procedures are illustrated using representative model problems and the extraction of LECs for the nucleon mass expansion in SU(2) chiral perturbation theory from synthetic lattice data.
Applications of Bayesian spectrum representation in acoustics
Botts, Jonathan M.
This dissertation utilizes a Bayesian inference framework to enhance the solution of inverse problems where the forward model maps to acoustic spectra. A Bayesian solution to filter design inverts a acoustic spectra to pole-zero locations of a discrete-time filter model. Spatial sound field analysis with a spherical microphone array is a data analysis problem that requires inversion of spatio-temporal spectra to directions of arrival. As with many inverse problems, a probabilistic analysis results in richer solutions than can be achieved with ad-hoc methods. In the filter design problem, the Bayesian inversion results in globally optimal coefficient estimates as well as an estimate the most concise filter capable of representing the given spectrum, within a single framework. This approach is demonstrated on synthetic spectra, head-related transfer function spectra, and measured acoustic reflection spectra. The Bayesian model-based analysis of spatial room impulse responses is presented as an analogous problem with equally rich solution. The model selection mechanism provides an estimate of the number of arrivals, which is necessary to properly infer the directions of simultaneous arrivals. Although, spectrum inversion problems are fairly ubiquitous, the scope of this dissertation has been limited to these two and derivative problems. The Bayesian approach to filter design is demonstrated on an artificial spectrum to illustrate the model comparison mechanism and then on measured head-related transfer functions to show the potential range of application. Coupled with sampling methods, the Bayesian approach is shown to outperform least-squares filter design methods commonly used in commercial software, confirming the need for a global search of the parameter space. The resulting designs are shown to be comparable to those that result from global optimization methods, but the Bayesian approach has the added advantage of a filter length estimate within the same unified
Narrowband interference parameterization for sparse Bayesian recovery
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.
Bayesian networks for enterprise risk assessment
Bonafede, C E
2006-01-01
According to different typologies of activity and priority, risks can assume diverse meanings and it can be assessed in different ways. In general risk is measured in terms of a probability combination of an event (frequency) and its consequence (impact). To estimate the frequency and the impact (severity) historical data or expert opinions (either qualitative or quantitative data) are used. Moreover qualitative data must be converted in numerical values to be used in the model. In the case of enterprise risk assessment the considered risks are, for instance, strategic, operational, legal and of image, which many times are difficult to be quantified. So in most cases only expert data, gathered by scorecard approaches, are available for risk analysis. The Bayesian Network is a useful tool to integrate different information and in particular to study the risk's joint distribution by using data collected from experts. In this paper we want to show a possible approach for building a Bayesian networks in the parti...
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.
QBism, the Perimeter of Quantum Bayesianism
Fuchs, Christopher A
2010-01-01
This article summarizes the Quantum Bayesian point of view of quantum mechanics, with special emphasis on the view's outer edges---dubbed QBism. QBism has its roots in personalist Bayesian probability theory, is crucially dependent upon the tools of quantum information theory, and most recently, has set out to investigate whether the physical world might be of a type sketched by some false-started philosophies of 100 years ago (pragmatism, pluralism, nonreductionism, and meliorism). Beyond conceptual issues, work at Perimeter Institute is focused on the hard technical problem of finding a good representation of quantum mechanics purely in terms of probabilities, without amplitudes or Hilbert-space operators. The best candidate representation involves a mysterious entity called a symmetric informationally complete quantum measurement. Contemplation of it gives a way of thinking of the Born Rule as an addition to the rules of probability theory, applicable when an agent considers gambling on the consequences of...
Distributed Bayesian Networks for User Modeling
DEFF Research Database (Denmark)
Tedesco, Roberto; Dolog, Peter; Nejdl, Wolfgang;
2006-01-01
The World Wide Web is a popular platform for providing eLearning applications to a wide spectrum of users. However – as users differ in their preferences, background, requirements, and goals – applications should provide personalization mechanisms. In the Web context, user models used...... by such adaptive applications are often partial fragments of an overall user model. The fragments have then to be collected and merged into a global user profile. In this paper we investigate and present algorithms able to cope with distributed, fragmented user models – based on Bayesian Networks – in the context...... of Web-based eLearning platforms. The scenario we are tackling assumes learners who use several systems over time, which are able to create partial Bayesian Networks for user models based on the local system context. In particular, we focus on how to merge these partial user models. Our merge mechanism...
Machine learning a Bayesian and optimization perspective
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...
Bayesian image reconstruction: Application to emission tomography
Energy Technology Data Exchange (ETDEWEB)
Nunez, J.; Llacer, J.
1989-02-01
In this paper we propose a Maximum a Posteriori (MAP) method of image reconstruction in the Bayesian framework for the Poisson noise case. We use entropy to define the prior probability and likelihood to define the conditional probability. The method uses sharpness parameters which can be theoretically computed or adjusted, allowing us to obtain MAP reconstructions without the problem of the grey'' reconstructions associated with the pre Bayesian reconstructions. We have developed several ways to solve the reconstruction problem and propose a new iterative algorithm which is stable, maintains positivity and converges to feasible images faster than the Maximum Likelihood Estimate method. We have successfully applied the new method to the case of Emission Tomography, both with simulated and real data. 41 refs., 4 figs., 1 tab.
The Bayesian Who Knew Too Much
Benétreau-Dupin, Yann
2014-01-01
In several papers, John Norton has argued that Bayesianism cannot handle ignorance adequately due to its inability to distinguish between neutral and disconfirming evidence. He argued that this inability sows confusion in, e.g., anthropic reasoning in cosmology or the Doomsday argument, by allowing one to draw unwarranted conclusions from a lack of knowledge. Norton has suggested criteria for a candidate for representation of neutral support. Imprecise credences (families of credal probability functions) constitute a Bayesian-friendly framework that allows us to avoid inadequate neutral priors and better handle ignorance. The imprecise model generally agrees with Norton's representation of ignorance but requires that his criterion of self-duality be reformulated or abandoned
Software Health Management with Bayesian Networks
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.
Learning Bayesian networks using genetic algorithm
Institute of Scientific and Technical Information of China (English)
Chen Fei; Wang Xiufeng; Rao Yimei
2007-01-01
A new method to evaluate the fitness of the Bayesian networks according to the observed data is provided. The main advantage of this criterion is that it is suitable for both the complete and incomplete cases while the others not.Moreover it facilitates the computation greatly. In order to reduce the search space, the notation of equivalent class proposed by David Chickering is adopted. Instead of using the method directly, the novel criterion, variable ordering, and equivalent class are combined,moreover the proposed mthod avoids some problems caused by the previous one. Later, the genetic algorithm which allows global convergence, lack in the most of the methods searching for Bayesian network is applied to search for a good model in thisspace. To speed up the convergence, the genetic algorithm is combined with the greedy algorithm. Finally, the simulation shows the validity of the proposed approach.
Bayesian Population Projections for the United Nations.
Raftery, Adrian E; Alkema, Leontine; Gerland, Patrick
2014-02-01
The United Nations regularly publishes projections of the populations of all the world's countries broken down by age and sex. These projections are the de facto standard and are widely used by international organizations, governments and researchers. Like almost all other population projections, they are produced using the standard deterministic cohort-component projection method and do not yield statements of uncertainty. We describe a Bayesian method for producing probabilistic population projections for most countries that the United Nations could use. It has at its core Bayesian hierarchical models for the total fertility rate and life expectancy at birth. We illustrate the method and show how it can be extended to address concerns about the UN's current assumptions about the long-term distribution of fertility. The method is implemented in the R packages bayesTFR, bayesLife, bayesPop and bayesDem.
Approximate Bayesian Computation: a nonparametric perspective
Blum, Michael
2010-01-01
Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing summary statistics s_obs from the data and simulating summary statistics for different values of the parameter theta. The posterior distribution is then approximated by an estimator of the conditional density g(theta|s_obs). In this paper, we derive the asymptotic bias and variance of the standard estimators of the posterior distribution which are based on rejection sampling and linear adjustment. Additionally, we introduce an original estimator of the posterior distribution based on quadratic adjustment and we show that its bias contains a fewer number of terms than the estimator with linear adjustment. Although we find that the estimators with adjustment are not universally superior to the estimator based on rejection sampling, we find that they can achieve better perfor...
Bayesian information fusion networks for biosurveillance applications.
Mnatsakanyan, Zaruhi R; Burkom, Howard S; Coberly, Jacqueline S; Lombardo, Joseph S
2009-01-01
This study introduces new information fusion algorithms to enhance disease surveillance systems with Bayesian decision support capabilities. A detection system was built and tested using chief complaints from emergency department visits, International Classification of Diseases Revision 9 (ICD-9) codes from records of outpatient visits to civilian and military facilities, and influenza surveillance data from health departments in the National Capital Region (NCR). Data anomalies were identified and distribution of time offsets between events in the multiple data streams were established. The Bayesian Network was built to fuse data from multiple sources and identify influenza-like epidemiologically relevant events. Results showed increased specificity compared with the alerts generated by temporal anomaly detection algorithms currently deployed by NCR health departments. Further research should be done to investigate correlations between data sources for efficient fusion of the collected data.
Bayesian Magnetohydrodynamic Seismology of Coronal Loops
Arregui, Inigo
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 inho...
A Bayesian nonparametric meta-analysis model.
Karabatsos, George; Talbott, Elizabeth; Walker, Stephen G
2015-03-01
In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal effect-size population distribution, conditionally on parameters and covariates. For estimating the mean overall effect size, such models may be adequate, but for prediction, they surely are not if the effect-size distribution exhibits non-normal behavior. To address this issue, we propose a Bayesian nonparametric meta-analysis model, which can describe a wider range of effect-size distributions, including unimodal symmetric distributions, as well as skewed and more multimodal distributions. We demonstrate our model through the analysis of real meta-analytic data arising from behavioral-genetic research. We compare the predictive performance of the Bayesian nonparametric model against various conventional and more modern normal fixed-effects and random-effects models.
Distributed Detection via Bayesian Updates and Consensus
Liu, Qipeng; Wang, Xiaofan
2014-01-01
In this paper, we discuss a class of distributed detection algorithms which can be viewed as implementations of Bayes' law in distributed settings. Some of the algorithms are proposed in the literature most recently, and others are first developed in this paper. The common feature of these algorithms is that they all combine (i) certain kinds of consensus protocols with (ii) Bayesian updates. They are different mainly in the aspect of the type of consensus protocol and the order of the two operations. After discussing their similarities and differences, we compare these distributed algorithms by numerical examples. We focus on the rate at which these algorithms detect the underlying true state of an object. We find that (a) The algorithms with consensus via geometric average is more efficient than that via arithmetic average; (b) The order of consensus aggregation and Bayesian update does not apparently influence the performance of the algorithms; (c) The existence of communication delay dramatically slows do...
Probabilistic forecasting and Bayesian data assimilation
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...
Bayesian Peak Picking for NMR Spectra
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.
A Bayesian approach to person perception.
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.
Bayesian parameter estimation for effective field theories
Wesolowski, S.; Klco, N.; Furnstahl, R. J.; Phillips, D. R.; Thapaliya, A.
2016-07-01
We present procedures based on Bayesian statistics for estimating, from data, the parameters of effective field theories (EFTs). The extraction of low-energy constants (LECs) is guided by theoretical expectations in a quantifiable way through the specification of Bayesian priors. A prior for natural-sized LECs reduces the possibility of overfitting, and leads to a consistent accounting of different sources of uncertainty. A set of diagnostic tools is developed that analyzes the fit and ensures that the priors do not bias the EFT parameter estimation. The procedures are illustrated using representative model problems, including the extraction of LECs for the nucleon-mass expansion in SU(2) chiral perturbation theory from synthetic lattice data.
BONNSAI: correlated stellar observables in Bayesian methods
Schneider, F R N; Fossati, L; Langer, N; de Koter, A
2016-01-01
In an era of large spectroscopic surveys of stars and big data, sophisticated statistical methods become more and more important in order to infer fundamental stellar parameters such as mass and age. Bayesian techniques are powerful methods because they can match all available observables simultaneously to stellar models while taking prior knowledge properly into account. However, in most cases it is assumed that observables are uncorrelated which is generally not the case. Here, we include correlations in the Bayesian code BONNSAI by incorporating the covariance matrix in the likelihood function. We derive a parametrisation of the covariance matrix that, in addition to classical uncertainties, only requires the specification of a correlation parameter that describes how observables co-vary. Our correlation parameter depends purely on the method with which observables have been determined and can be analytically derived in some cases. This approach therefore has the advantage that correlations can be accounte...
The Size-Weight Illusion is not anti-Bayesian after all: a unifying Bayesian account.
Peters, Megan A K; Ma, Wei Ji; Shams, Ladan
2016-01-01
When we lift two differently-sized but equally-weighted objects, we expect the larger to be heavier, but the smaller feels heavier. However, traditional Bayesian approaches with "larger is heavier" priors predict the smaller object should feel lighter; this Size-Weight Illusion (SWI) has thus been labeled "anti-Bayesian" and has stymied psychologists for generations. We propose that previous Bayesian approaches neglect the brain's inference process about density. In our Bayesian model, objects' perceived heaviness relationship is based on both their size and inferred density relationship: observers evaluate competing, categorical hypotheses about objects' relative densities, the inference about which is then used to produce the final estimate of weight. The model can qualitatively and quantitatively reproduce the SWI and explain other researchers' findings, and also makes a novel prediction, which we confirmed. This same computational mechanism accounts for other multisensory phenomena and illusions; that the SWI follows the same process suggests that competitive-prior Bayesian inference can explain human perception across many domains.
Bayesian nonparametric regression with varying residual density
Pati, Debdeep; Dunson, David B.
2013-01-01
We consider the problem of robust Bayesian inference on the mean regression function allowing the residual density to change flexibly with predictors. The proposed class of models is based on a Gaussian process prior for the mean regression function and mixtures of Gaussians for the collection of residual densities indexed by predictors. Initially considering the homoscedastic case, we propose priors for the residual density based on probit stick-breaking (PSB) scale mixtures and symmetrized ...
Towards Bayesian Deep Learning: A Survey
Wang, Hao; Yeung, Dit-Yan
2016-01-01
While perception tasks such as visual object recognition and text understanding play an important role in human intelligence, the subsequent tasks that involve inference, reasoning and planning require an even higher level of intelligence. The past few years have seen major advances in many perception tasks using deep learning models. For higher-level inference, however, probabilistic graphical models with their Bayesian nature are still more powerful and flexible. To achieve integrated intel...
Approximate Bayesian inference for complex ecosystems
Michael P H Stumpf
2014-01-01
Mathematical models have been central to ecology for nearly a century. Simple models of population dynamics have allowed us to understand fundamental aspects underlying the dynamics and stability of ecological systems. What has remained a challenge, however, is to meaningfully interpret experimental or observational data in light of mathematical models. Here, we review recent developments, notably in the growing field of approximate Bayesian computation (ABC), that allow us to calibrate mathe...
Forming Object Concept Using Bayesian Network
Nakamura, Tomoaki; Nagai, Takayuki
2010-01-01
This chapter hase discussed a novel framework for object understanding. Implementation of the proposed framework using Bayesian Network has been presented. Although the result given in this paper is preliminary one, we have shown that the system can form object concept by observing the performance by human hands. The on-line learning is left for the future works. Moreover the model should be extended so that it can represent the object usage and work objects.
Bayesian belief networks in business continuity.
Phillipson, Frank; Matthijssen, Edwin; Attema, Thomas
2014-01-01
Business continuity professionals aim to mitigate the various challenges to the continuity of their company. The goal is a coherent system of measures that encompass detection, prevention and recovery. Choices made in one part of the system affect other parts as well as the continuity risks of the company. In complex organisations, however, these relations are far from obvious. This paper proposes the use of Bayesian belief networks to expose these relations, and presents a modelling framework for this approach. PMID:25193453
Informed Source Separation: A Bayesian Tutorial
Knuth, Kevin
2013-01-01
Source separation problems are ubiquitous in the physical sciences; any situation where signals are superimposed calls for source separation to estimate the original signals. In this tutorial I will discuss the Bayesian approach to the source separation problem. This approach has a specific advantage in that it requires the designer to explicitly describe the signal model in addition to any other information or assumptions that go into the problem description. This leads naturally to the idea...
Market Segmentation Using Bayesian Model Based Clustering
Van Hattum, P.
2009-01-01
This dissertation deals with two basic problems in marketing, that are market segmentation, which is the grouping of persons who share common aspects, and market targeting, which is focusing your marketing efforts on one or more attractive market segments. For the grouping of persons who share common aspects a Bayesian model based clustering approach is proposed such that it can be applied to data sets that are specifically used for market segmentation. The cluster algorithm can handle very l...
Approximate Bayesian computation in population genetics.
Beaumont, Mark A; Zhang, Wenyang; Balding, David J.
2002-01-01
We propose a new method for approximate Bayesian statistical inference on the basis of summary statistics. The method is suited to complex problems that arise in population genetics, extending ideas developed in this setting by earlier authors. Properties of the posterior distribution of a parameter, such as its mean or density curve, are approximated without explicit likelihood calculations. This is achieved by fitting a local-linear regression of simulated parameter values on simulated summ...
Bayesian nonparametric duration model with censorship
Directory of Open Access Journals (Sweden)
Joseph Hakizamungu
2007-10-01
Full Text Available This paper is concerned with nonparametric i.i.d. durations models censored observations and we establish by a simple and unified approach the general structure of a bayesian nonparametric estimator for a survival function S. For Dirichlet prior distributions, we describe completely the structure of the posterior distribution of the survival function. These results are essentially supported by prior and posterior independence properties.
Bayesian modeling and classification of neural signals
Lewicki, Michael S.
1994-01-01
Signal processing and classification algorithms often have limited applicability resulting from an inaccurate model of the signal's underlying structure. We present here an efficient, Bayesian algorithm for modeling a signal composed of the superposition of brief, Poisson-distributed functions. This methodology is applied to the specific problem of modeling and classifying extracellular neural waveforms which are composed of a superposition of an unknown number of action potentials CAPs). ...
Bayesian Estimation and Inference Using Stochastic Electronics.
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. PMID:27047326
Bayesian biclustering of gene expression data
Liu Jun S; Gu Jiajun
2008-01-01
Abstract Background Biclustering of gene expression data searches for local patterns of gene expression. A bicluster (or a two-way cluster) is defined as a set of genes whose expression profiles are mutually similar within a subset of experimental conditions/samples. Although several biclustering algorithms have been studied, few are based on rigorous statistical models. Results We developed a Bayesian biclustering model (BBC), and implemented a Gibbs sampling procedure for its statistical in...
Nonparametric Bayesian Storyline Detection from Microtexts
Krishnan, Vinodh; Eisenstein, Jacob
2016-01-01
News events and social media are composed of evolving storylines, which capture public attention for a limited period of time. Identifying these storylines would enable many high-impact applications, such as tracking public interest and opinion in ongoing crisis events. However, this requires integrating temporal and linguistic information, and prior work takes a largely heuristic approach. We present a novel online non-parametric Bayesian framework for storyline detection, using the distance...
Dual Control for Approximate Bayesian Reinforcement Learning
Klenske, Edgar D.; Hennig, Philipp
2015-01-01
Control of non-episodic, finite-horizon dynamical systems with uncertain dynamics poses a tough and elementary case of the exploration-exploitation trade-off. Bayesian reinforcement learning, reasoning about the effect of actions and future observations, offers a principled solution, but is intractable. We review, then extend an old approximate approach from control theory---where the problem is known as dual control---in the context of modern regression methods, specifically generalized line...
A Bayesian framework for robotic programming
Lebeltel, Olivier; Diard, Julien; Bessiere, Pierre; Mazer, Emmanuel
2000-01-01
We propose an original method for programming robots based on Bayesian inference and learning. This method formally deals with problems of uncertainty and incomplete information that are inherent to the field. Indeed, the principal difficulties of robot programming comes from the unavoidable incompleteness of the models used. We present the formalism for describing a robotic task as well as the resolution methods. This formalism is inspired by the theory of probability, suggested by the physi...
Constrained bayesian inference of project performance models
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 ...
Bayesian Estimation and Inference Using Stochastic Electronics.
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.
Bayesian mixture models for Poisson astronomical images
Guglielmetti, Fabrizia; Fischer, Rainer; Dose, Volker
2012-01-01
Astronomical images in the Poisson regime are typically characterized by a spatially varying cosmic background, large variety of source morphologies and intensities, data incompleteness, steep gradients in the data, and few photon counts per pixel. The Background-Source separation technique is developed with the aim to detect faint and extended sources in astronomical images characterized by Poisson statistics. The technique employs Bayesian mixture models to reliably detect the background as...
Bayesian Variable Selection via Particle Stochastic Search.
Shi, Minghui; Dunson, David B
2011-02-01
We focus on Bayesian variable selection in regression models. One challenge is to search the huge model space adequately, while identifying high posterior probability regions. In the past decades, the main focus has been on the use of Markov chain Monte Carlo (MCMC) algorithms for these purposes. In this article, we propose a new computational approach based on sequential Monte Carlo (SMC), which we refer to as particle stochastic search (PSS). We illustrate PSS through applications to linear regression and probit models.
Bayesian Spatial Modelling with R-INLA
Finn Lindgren; Håvard Rue
2015-01-01
The principles behind the interface to continuous domain spatial models in the R- INLA software package for R are described. The integrated nested Laplace approximation (INLA) approach proposed by Rue, Martino, and Chopin (2009) is a computationally effective alternative to MCMC for Bayesian inference. INLA is designed for latent Gaussian models, a very wide and flexible class of models ranging from (generalized) linear mixed to spatial and spatio-temporal models. Combined with the stochastic...
Bayesian Predictive Distribution for the Magnitude of the Largest Aftershock
Shcherbakov, R.
2014-12-01
Aftershock sequences, which follow large earthquakes, last hundreds of days and are characterized by well defined frequency-magnitude and spatio-temporal distributions. The largest aftershocks in a sequence constitute significant hazard and can inflict additional damage to infrastructure. Therefore, the estimation of the magnitude of possible largest aftershocks in a sequence is of high importance. In this work, we propose a statistical model based on Bayesian analysis and extreme value statistics to describe the distribution of magnitudes of the largest aftershocks in a sequence. We derive an analytical expression for a Bayesian predictive distribution function for the magnitude of the largest expected aftershock and compute the corresponding confidence intervals. We assume that the occurrence of aftershocks can be modeled, to a good approximation, by a non-homogeneous Poisson process with a temporal event rate given by the modified Omori law. We also assume that the frequency-magnitude statistics of aftershocks can be approximated by Gutenberg-Richter scaling. We apply our analysis to 19 prominent aftershock sequences, which occurred in the last 30 years, in order to compute the Bayesian predictive distributions and the corresponding confidence intervals. In the analysis, we use the information of the early aftershocks in the sequences (in the first 1, 10, and 30 days after the main shock) to estimate retrospectively the confidence intervals for the magnitude of the expected largest aftershocks. We demonstrate by analysing 19 past sequences that in many cases we are able to constrain the magnitudes of the largest aftershocks. For example, this includes the analysis of the Darfield (Christchurch) aftershock sequence. The proposed analysis can be used for the earthquake hazard assessment and forecasting associated with the occurrence of large aftershocks. The improvement in instrumental data associated with early aftershocks can greatly enhance the analysis and
Sparse Bayesian learning in ISAR tomography imaging
Institute of Scientific and Technical Information of China (English)
SU Wu-ge; WANG Hong-qiang; DENG Bin; WANG Rui-jun; QIN Yu-liang
2015-01-01
Inverse synthetic aperture radar (ISAR) imaging can be regarded as a narrow-band version of the computer aided tomography (CT). The traditional CT imaging algorithms for ISAR, including the polar format algorithm (PFA) and the convolution back projection algorithm (CBP), usually suffer from the problem of the high sidelobe and the low resolution. The ISAR tomography image reconstruction within a sparse Bayesian framework is concerned. Firstly, the sparse ISAR tomography imaging model is established in light of the CT imaging theory. Then, by using the compressed sensing (CS) principle, a high resolution ISAR image can be achieved with limited number of pulses. Since the performance of existing CS-based ISAR imaging algorithms is sensitive to the user parameter, this makes the existing algorithms inconvenient to be used in practice. It is well known that the Bayesian formalism of recover algorithm named sparse Bayesian learning (SBL) acts as an effective tool in regression and classification, which uses an efficient expectation maximization procedure to estimate the necessary parameters, and retains a preferable property of thel0-norm diversity measure. Motivated by that, a fully automated ISAR tomography imaging algorithm based on SBL is proposed. Experimental results based on simulated and electromagnetic (EM) data illustrate the effectiveness and the superiority of the proposed algorithm over the existing algorithms.
Particle identification in ALICE: a Bayesian approach
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; Barbera, Roberto; Barile, Francesco; Barnafoldi, Gergely Gabor; Barnby, Lee Stuart; Ramillien Barret, Valerie; Bartalini, Paolo; Barth, Klaus; Bartke, Jerzy Gustaw; Bartsch, Esther; Basile, Maurizio; Bastid, Nicole; Basu, Sumit; Bathen, Bastian; Batigne, Guillaume; Batista Camejo, Arianna; Batyunya, Boris; Batzing, Paul Christoph; Bearden, Ian Gardner; Beck, Hans; Bedda, Cristina; Behera, Nirbhay Kumar; Belikov, Iouri; Bellini, Francesca; Bello Martinez, Hector; Bellwied, Rene; Belmont Iii, Ronald John; Belmont Moreno, Ernesto; Belyaev, Vladimir; Benacek, Pavel; Bencedi, Gyula; Beole, Stefania; Berceanu, Ionela; Bercuci, Alexandru; Berdnikov, Yaroslav; Berenyi, Daniel; Bertens, Redmer Alexander; Berzano, Dario; Betev, Latchezar; Bhasin, Anju; Bhat, Inayat Rasool; Bhati, Ashok Kumar; Bhattacharjee, Buddhadeb; Bhom, Jihyun; Bianchi, Livio; Bianchi, Nicola; Bianchin, Chiara; Bielcik, Jaroslav; Bielcikova, Jana; Bilandzic, Ante; Biro, Gabor; Biswas, Rathijit; Biswas, Saikat; Bjelogrlic, Sandro; Blair, Justin Thomas; Blau, Dmitry; Blume, Christoph; Bock, Friederike; Bogdanov, Alexey; Boggild, Hans; Boldizsar, Laszlo; Bombara, Marek; Book, Julian Heinz; Borel, Herve; Borissov, Alexander; Borri, Marcello; Bossu, Francesco; Botta, Elena; Bourjau, Christian; Braun-Munzinger, Peter; Bregant, Marco; Breitner, Timo Gunther; Broker, Theo Alexander; Browning, Tyler Allen; Broz, Michal; Brucken, Erik Jens; Bruna, Elena; Bruno, Giuseppe Eugenio; Budnikov, Dmitry; Buesching, Henner; Bufalino, Stefania; Buncic, Predrag; Busch, Oliver; Buthelezi, Edith Zinhle; Bashir Butt, Jamila; Buxton, Jesse Thomas; Cabala, Jan; Caffarri, Davide; Cai, Xu; Caines, Helen Louise; Calero Diaz, Liliet; Caliva, Alberto; Calvo Villar, Ernesto; Camerini, Paolo; Carena, Francesco; Carena, Wisla; Carnesecchi, Francesca; Castillo Castellanos, Javier Ernesto; Castro, Andrew John; Casula, Ester Anna Rita; Ceballos Sanchez, Cesar; Cepila, Jan; Cerello, Piergiorgio; Cerkala, Jakub; Chang, Beomsu; Chapeland, Sylvain; Chartier, Marielle; Charvet, Jean-Luc Fernand; Chattopadhyay, Subhasis; Chattopadhyay, Sukalyan; Chauvin, Alex; Chelnokov, Volodymyr; Cherney, Michael Gerard; Cheshkov, Cvetan Valeriev; Cheynis, Brigitte; Chibante Barroso, Vasco Miguel; Dobrigkeit Chinellato, David; Cho, Soyeon; Chochula, Peter; Choi, Kyungeon; Chojnacki, Marek; Choudhury, Subikash; Christakoglou, Panagiotis; Christensen, Christian Holm; Christiansen, Peter; Chujo, Tatsuya; Chung, Suh-Urk; Cicalo, Corrado; Cifarelli, Luisa; Cindolo, Federico; Cleymans, Jean Willy Andre; Colamaria, Fabio Filippo; Colella, Domenico; Collu, Alberto; Colocci, Manuel; Conesa Balbastre, Gustavo; Conesa Del Valle, Zaida; Connors, Megan Elizabeth; Contreras Nuno, Jesus Guillermo; Cormier, Thomas Michael; Corrales Morales, Yasser; Cortes Maldonado, Ismael; Cortese, Pietro; Cosentino, Mauro Rogerio; Costa, Filippo; Crochet, Philippe; Cruz Albino, Rigoberto; Cuautle Flores, Eleazar; Cunqueiro Mendez, Leticia; Dahms, Torsten; Dainese, Andrea; Danisch, Meike Charlotte; Danu, Andrea; Das, Debasish; Das, Indranil; Das, Supriya; Dash, Ajay Kumar; Dash, Sadhana; De, Sudipan; De Caro, Annalisa; De Cataldo, Giacinto; De Conti, Camila; De Cuveland, Jan; De Falco, Alessandro; De Gruttola, Daniele; De Marco, Nora; De Pasquale, Salvatore; Deisting, Alexander; Deloff, Andrzej; Denes, Ervin Sandor; Deplano, Caterina; Dhankher, Preeti; Di Bari, Domenico; Di Mauro, Antonio; Di Nezza, Pasquale; Diaz Corchero, Miguel Angel; Dietel, Thomas; Dillenseger, Pascal; Divia, Roberto; Djuvsland, Oeystein; Dobrin, Alexandru Florin; Domenicis Gimenez, Diogenes; Donigus, Benjamin; Dordic, Olja; Drozhzhova, Tatiana; Dubey, Anand Kumar; Dubla, Andrea; Ducroux, Laurent; Dupieux, Pascal; Ehlers Iii, Raymond James; Elia, Domenico; Endress, Eric; Engel, Heiko; Epple, Eliane; Erazmus, Barbara Ewa; Erdemir, Irem; Erhardt, Filip; Espagnon, Bruno; Estienne, Magali Danielle; Esumi, Shinichi; Eum, Jongsik; Evans, David; Evdokimov, Sergey; Eyyubova, Gyulnara; Fabbietti, Laura; Fabris, Daniela; Faivre, Julien; Fantoni, Alessandra; Fasel, Markus; Feldkamp, Linus; Feliciello, Alessandro; Feofilov, Grigorii; Ferencei, Jozef; Fernandez Tellez, Arturo; Gonzalez Ferreiro, Elena; Ferretti, Alessandro; Festanti, Andrea; Feuillard, Victor Jose Gaston; Figiel, Jan; Araujo Silva Figueredo, Marcel; Filchagin, Sergey; Finogeev, Dmitry; Fionda, Fiorella; Fiore, Enrichetta Maria; Fleck, Martin Gabriel; Floris, Michele; Foertsch, Siegfried Valentin; Foka, Panagiota; Fokin, Sergey; Fragiacomo, Enrico; Francescon, Andrea; Frankenfeld, Ulrich Michael; Fronze, Gabriele Gaetano; Fuchs, Ulrich; Furget, Christophe; Furs, Artur; Fusco Girard, Mario; Gaardhoeje, Jens Joergen; Gagliardi, Martino; Gago Medina, Alberto Martin; Gallio, Mauro; Gangadharan, Dhevan Raja; Ganoti, Paraskevi; Gao, Chaosong; Garabatos Cuadrado, Jose; Garcia-Solis, Edmundo Javier; Gargiulo, Corrado; Gasik, Piotr Jan; Gauger, Erin Frances; Germain, Marie; Gheata, Andrei George; Gheata, Mihaela; Ghosh, Premomoy; Ghosh, Sanjay Kumar; Gianotti, Paola; Giubellino, Paolo; Giubilato, Piero; Gladysz-Dziadus, Ewa; Glassel, Peter; Gomez Coral, Diego Mauricio; Gomez Ramirez, Andres; Sanchez Gonzalez, Andres; Gonzalez, Victor; Gonzalez Zamora, Pedro; Gorbunov, Sergey; Gorlich, Lidia Maria; Gotovac, Sven; Grabski, Varlen; Grachov, Oleg Anatolievich; Graczykowski, Lukasz Kamil; Graham, Katie Leanne; Grelli, Alessandro; Grigoras, Alina Gabriela; Grigoras, Costin; Grigoryev, Vladislav; Grigoryan, Ara; Grigoryan, Smbat; Grynyov, Borys; Grion, Nevio; Gronefeld, Julius Maximilian; Grosse-Oetringhaus, Jan Fiete; Grosso, Raffaele; Guber, Fedor; Guernane, Rachid; Guerzoni, Barbara; Gulbrandsen, Kristjan Herlache; Gunji, Taku; Gupta, Anik; Gupta, Ramni; Haake, Rudiger; Haaland, Oystein Senneset; Hadjidakis, Cynthia Marie; Haiduc, Maria; Hamagaki, Hideki; Hamar, Gergoe; Hamon, Julien Charles; Harris, John William; Harton, Austin Vincent; Hatzifotiadou, Despina; Hayashi, Shinichi; Heckel, Stefan Thomas; Hellbar, Ernst; Helstrup, Haavard; Herghelegiu, Andrei Ionut; Herrera Corral, Gerardo Antonio; Hess, Benjamin Andreas; Hetland, Kristin Fanebust; Hillemanns, Hartmut; Hippolyte, Boris; Horak, David; Hosokawa, Ritsuya; Hristov, Peter Zahariev; Humanic, Thomas; Hussain, Nur; Hussain, Tahir; Hutter, Dirk; Hwang, Dae Sung; Ilkaev, Radiy; Inaba, Motoi; Incani, Elisa; Ippolitov, Mikhail; Irfan, Muhammad; Ivanov, Marian; Ivanov, Vladimir; Izucheev, Vladimir; Jacazio, Nicolo; Jacobs, Peter Martin; Jadhav, Manoj Bhanudas; Jadlovska, Slavka; Jadlovsky, Jan; Jahnke, Cristiane; Jakubowska, Monika Joanna; Jang, Haeng Jin; Janik, Malgorzata Anna; Pahula Hewage, Sandun; Jena, Chitrasen; Jena, Satyajit; Jimenez Bustamante, Raul Tonatiuh; Jones, Peter Graham; Jusko, Anton; Kalinak, Peter; Kalweit, Alexander Philipp; Kamin, Jason Adrian; Kang, Ju Hwan; Kaplin, Vladimir; Kar, Somnath; Karasu Uysal, Ayben; Karavichev, Oleg; Karavicheva, Tatiana; Karayan, Lilit; Karpechev, Evgeny; Kebschull, Udo Wolfgang; Keidel, Ralf; Keijdener, Darius Laurens; Keil, Markus; Khan, Mohammed Mohisin; Khan, Palash; Khan, Shuaib Ahmad; Khanzadeev, Alexei; Kharlov, Yury; Kileng, Bjarte; Kim, Do Won; Kim, Dong Jo; Kim, Daehyeok; Kim, Hyeonjoong; Kim, Jinsook; Kim, Minwoo; Kim, Se Yong; Kim, Taesoo; Kirsch, Stefan; Kisel, Ivan; Kiselev, Sergey; Kisiel, Adam Ryszard; Kiss, Gabor; Klay, Jennifer Lynn; Klein, Carsten; Klein, Jochen; Klein-Boesing, Christian; Klewin, Sebastian; Kluge, Alexander; Knichel, Michael Linus; Knospe, Anders Garritt; Kobdaj, Chinorat; Kofarago, Monika; Kollegger, Thorsten; Kolozhvari, Anatoly; Kondratev, Valerii; Kondratyeva, Natalia; Kondratyuk, Evgeny; Konevskikh, Artem; Kopcik, Michal; Kostarakis, Panagiotis; Kour, Mandeep; Kouzinopoulos, Charalampos; Kovalenko, Oleksandr; Kovalenko, Vladimir; Kowalski, Marek; Koyithatta Meethaleveedu, Greeshma; Kralik, Ivan; Kravcakova, Adela; Krivda, Marian; Krizek, Filip; Kryshen, Evgeny; Krzewicki, Mikolaj; Kubera, Andrew Michael; Kucera, Vit; Kuhn, Christian Claude; Kuijer, Paulus Gerardus; Kumar, Ajay; Kumar, Jitendra; Kumar, Lokesh; Kumar, Shyam; Kurashvili, Podist; Kurepin, Alexander; Kurepin, Alexey; Kuryakin, Alexey; Kweon, Min Jung; Kwon, Youngil; La Pointe, Sarah Louise; La Rocca, Paola; Ladron De Guevara, Pedro; Lagana Fernandes, Caio; Lakomov, Igor; Langoy, Rune; Lara Martinez, Camilo Ernesto; Lardeux, Antoine Xavier; Lattuca, Alessandra; Laudi, Elisa; Lea, Ramona; Leardini, Lucia; Lee, Graham Richard; Lee, Seongjoo; Lehas, Fatiha; Lemmon, Roy Crawford; Lenti, Vito; Leogrande, Emilia; Leon Monzon, Ildefonso; Leon Vargas, Hermes; Leoncino, Marco; Levai, Peter; Li, Shuang; Li, Xiaomei; Lien, Jorgen Andre; Lietava, Roman; Lindal, Svein; Lindenstruth, Volker; Lippmann, Christian; Lisa, Michael Annan; Ljunggren, Hans Martin; Lodato, Davide Francesco; Lonne, Per-Ivar; Loginov, Vitaly; Loizides, Constantinos; Lopez, Xavier Bernard; Lopez Torres, Ernesto; Lowe, Andrew John; Luettig, Philipp Johannes; Lunardon, Marcello; Luparello, Grazia; Lutz, Tyler Harrison; Maevskaya, Alla; Mager, Magnus; Mahajan, Sanjay; Mahmood, Sohail Musa; Maire, Antonin; Majka, Richard Daniel; Malaev, Mikhail; Maldonado Cervantes, Ivonne Alicia; Malinina, Liudmila; Mal'Kevich, Dmitry; Malzacher, Peter; Mamonov, Alexander; Manko, Vladislav; Manso, Franck; Manzari, Vito; Marchisone, Massimiliano; Mares, Jiri; Margagliotti, Giacomo Vito; Margotti, Anselmo; Margutti, Jacopo; Marin, Ana Maria; Markert, Christina; Marquard, Marco; Martin, Nicole Alice; Martin Blanco, Javier; Martinengo, Paolo; Martinez Hernandez, Mario Ivan; Martinez-Garcia, Gines; Martinez Pedreira, Miguel; Mas, Alexis Jean-Michel; Masciocchi, Silvia; Masera, Massimo; Masoni, Alberto; Mastroserio, Annalisa; Matyja, Adam Tomasz; Mayer, Christoph; Mazer, Joel Anthony; Mazzoni, Alessandra Maria; Mcdonald, Daniel; Meddi, Franco; Melikyan, Yuri; Menchaca-Rocha, Arturo Alejandro; Meninno, Elisa; Mercado-Perez, Jorge; Meres, Michal; Miake, Yasuo; Mieskolainen, Matti Mikael; Mikhaylov, Konstantin; Milano, Leonardo; Milosevic, Jovan; Mischke, Andre; Mishra, Aditya Nath; Miskowiec, Dariusz Czeslaw; Mitra, Jubin; Mitu, Ciprian Mihai; Mohammadi, Naghmeh; Mohanty, Bedangadas; Molnar, Levente; Montano Zetina, Luis Manuel; Montes Prado, Esther; Moreira De Godoy, Denise Aparecida; Perez Moreno, Luis Alberto; Moretto, Sandra; Morreale, Astrid; Morsch, Andreas; Muccifora, Valeria; Mudnic, Eugen; Muhlheim, Daniel Michael; Muhuri, Sanjib; Mukherjee, Maitreyee; Mulligan, James Declan; Gameiro Munhoz, Marcelo; Munzer, Robert Helmut; Murakami, Hikari; Murray, Sean; Musa, Luciano; Musinsky, Jan; Naik, Bharati; Nair, Rahul; Nandi, Basanta Kumar; Nania, Rosario; Nappi, Eugenio; Naru, Muhammad Umair; Ferreira Natal Da Luz, Pedro Hugo; Nattrass, Christine; Rosado Navarro, Sebastian; Nayak, Kishora; Nayak, Ranjit; Nayak, Tapan Kumar; Nazarenko, Sergey; Nedosekin, Alexander; Nellen, Lukas; Ng, Fabian; Nicassio, Maria; Niculescu, Mihai; Niedziela, Jeremi; Nielsen, Borge Svane; Nikolaev, Sergey; Nikulin, Sergey; Nikulin, Vladimir; Noferini, Francesco; Nomokonov, Petr; Nooren, Gerardus; Cabanillas Noris, Juan Carlos; Norman, Jaime; Nyanin, Alexander; Nystrand, Joakim Ingemar; Oeschler, Helmut Oskar; Oh, Saehanseul; Oh, Sun Kun; Ohlson, Alice Elisabeth; Okatan, Ali; Okubo, Tsubasa; Olah, Laszlo; Oleniacz, Janusz; Oliveira Da Silva, Antonio Carlos; Oliver, Michael Henry; Onderwaater, Jacobus; Oppedisano, Chiara; Orava, Risto; Oravec, Matej; Ortiz Velasquez, Antonio; Oskarsson, Anders Nils Erik; Otwinowski, Jacek Tomasz; Oyama, Ken; Ozdemir, Mahmut; Pachmayer, Yvonne Chiara; Pagano, Davide; Pagano, Paola; Paic, Guy; Pal, Susanta Kumar; Pan, Jinjin; Pandey, Ashutosh Kumar; Papikyan, Vardanush; Pappalardo, Giuseppe; Pareek, Pooja; Park, Woojin; Parmar, Sonia; Passfeld, Annika; Paticchio, Vincenzo; Patra, Rajendra Nath; Paul, Biswarup; Pei, Hua; Peitzmann, Thomas; Pereira Da Costa, Hugo Denis Antonio; Peresunko, Dmitry Yurevich; Perez Lara, Carlos Eugenio; Perez Lezama, Edgar; Peskov, Vladimir; Pestov, Yury; Petracek, Vojtech; Petrov, Viacheslav; Petrovici, Mihai; Petta, Catia; Piano, Stefano; Pikna, Miroslav; Pillot, Philippe; Ozelin De Lima Pimentel, Lais; Pinazza, Ombretta; Pinsky, Lawrence; Piyarathna, Danthasinghe; Ploskon, Mateusz Andrzej; Planinic, Mirko; Pluta, Jan Marian; Pochybova, Sona; Podesta Lerma, Pedro Luis Manuel; Poghosyan, Martin; Polishchuk, Boris; Poljak, Nikola; Poonsawat, Wanchaloem; Pop, Amalia; Porteboeuf, Sarah Julie; Porter, R Jefferson; Pospisil, Jan; Prasad, Sidharth Kumar; Preghenella, Roberto; Prino, Francesco; Pruneau, Claude Andre; Pshenichnov, Igor; Puccio, Maximiliano; Puddu, Giovanna; Pujahari, Prabhat Ranjan; Punin, Valery; Putschke, Jorn Henning; Qvigstad, Henrik; Rachevski, Alexandre; Raha, Sibaji; Rajput, Sonia; Rak, Jan; Rakotozafindrabe, Andry Malala; Ramello, Luciano; Rami, Fouad; Raniwala, Rashmi; Raniwala, Sudhir; Rasanen, Sami Sakari; Rascanu, Bogdan Theodor; Rathee, Deepika; Read, Kenneth Francis; Redlich, Krzysztof; Reed, Rosi Jan; Rehman, Attiq Ur; Reichelt, Patrick Simon; Reidt, Felix; Ren, Xiaowen; Renfordt, Rainer Arno Ernst; Reolon, Anna Rita; Reshetin, Andrey; Reygers, Klaus Johannes; Riabov, Viktor; Ricci, Renato Angelo; Richert, Tuva Ora Herenui; Richter, Matthias Rudolph; Riedler, Petra; Riegler, Werner; Riggi, Francesco; Ristea, Catalin-Lucian; Rocco, Elena; Rodriguez Cahuantzi, Mario; Rodriguez Manso, Alis; Roeed, Ketil; Rogochaya, Elena; Rohr, David Michael; Roehrich, Dieter; Ronchetti, Federico; Ronflette, Lucile; Rosnet, Philippe; Rossi, Andrea; Roukoutakis, Filimon; Roy, Ankhi; Roy, Christelle Sophie; Roy, Pradip Kumar; Rubio Montero, Antonio Juan; Rui, Rinaldo; Russo, Riccardo; Ryabinkin, Evgeny; Ryabov, Yury; Rybicki, Andrzej; Saarinen, Sampo; Sadhu, Samrangy; Sadovskiy, Sergey; Safarik, Karel; Sahlmuller, Baldo; Sahoo, Pragati; Sahoo, Raghunath; Sahoo, Sarita; Sahu, Pradip Kumar; Saini, Jogender; Sakai, Shingo; Saleh, Mohammad Ahmad; Salzwedel, Jai Samuel Nielsen; Sambyal, Sanjeev Singh; Samsonov, Vladimir; Sandor, Ladislav; Sandoval, Andres; Sano, Masato; Sarkar, Debojit; Sarkar, Nachiketa; Sarma, Pranjal; Scapparone, Eugenio; Scarlassara, Fernando; Schiaua, Claudiu Cornel; Schicker, Rainer Martin; Schmidt, Christian Joachim; Schmidt, Hans Rudolf; Schuchmann, Simone; Schukraft, Jurgen; Schulc, Martin; Schutz, Yves Roland; Schwarz, Kilian Eberhard; Schweda, Kai Oliver; Scioli, Gilda; Scomparin, Enrico; Scott, Rebecca Michelle; Sefcik, Michal; Seger, Janet Elizabeth; Sekiguchi, Yuko; Sekihata, Daiki; Selyuzhenkov, Ilya; Senosi, Kgotlaesele; Senyukov, Serhiy; Serradilla Rodriguez, Eulogio; Sevcenco, Adrian; Shabanov, Arseniy; Shabetai, Alexandre; Shadura, Oksana; Shahoyan, Ruben; Shahzad, Muhammed Ikram; Shangaraev, Artem; Sharma, Ankita; Sharma, Mona; Sharma, Monika; Sharma, Natasha; Sheikh, Ashik Ikbal; Shigaki, Kenta; Shou, Qiye; Shtejer Diaz, Katherin; Sibiryak, Yury; Siddhanta, Sabyasachi; Sielewicz, Krzysztof Marek; Siemiarczuk, Teodor; Silvermyr, David Olle Rickard; Silvestre, Catherine Micaela; Simatovic, Goran; Simonetti, Giuseppe; Singaraju, Rama Narayana; Singh, Ranbir; Singha, Subhash; Singhal, Vikas; Sinha, Bikash; Sarkar - Sinha, Tinku; Sitar, Branislav; Sitta, Mario; Skaali, Bernhard; Slupecki, Maciej; Smirnov, Nikolai; Snellings, Raimond; Snellman, Tomas Wilhelm; Song, Jihye; Song, Myunggeun; Song, Zixuan; Soramel, Francesca; Sorensen, Soren Pontoppidan; Derradi De Souza, Rafael; Sozzi, Federica; Spacek, Michal; Spiriti, Eleuterio; Sputowska, Iwona Anna; Spyropoulou-Stassinaki, Martha; Stachel, Johanna; Stan, Ionel; Stankus, Paul; Stenlund, Evert Anders; Steyn, Gideon Francois; Stiller, Johannes Hendrik; Stocco, Diego; Strmen, Peter; Alarcon Do Passo Suaide, Alexandre; Sugitate, Toru; Suire, Christophe Pierre; Suleymanov, Mais Kazim Oglu; Suljic, Miljenko; Sultanov, Rishat; Sumbera, Michal; Sumowidagdo, Suharyo; Szabo, Alexander; Szanto De Toledo, Alejandro; Szarka, Imrich; Szczepankiewicz, Adam; Szymanski, Maciej Pawel; Tabassam, Uzma; Takahashi, Jun; Tambave, Ganesh Jagannath; Tanaka, Naoto; Tarhini, Mohamad; Tariq, Mohammad; Tarzila, Madalina-Gabriela; Tauro, Arturo; Tejeda Munoz, Guillermo; Telesca, Adriana; Terasaki, Kohei; Terrevoli, Cristina; Teyssier, Boris; Thaeder, Jochen Mathias; Thakur, Dhananjaya; Thomas, Deepa; Tieulent, Raphael Noel; Timmins, Anthony Robert; Toia, Alberica; Trogolo, Stefano; Trombetta, Giuseppe; Trubnikov, Victor; Trzaska, Wladyslaw Henryk; Tsuji, Tomoya; Tumkin, Alexandr; Turrisi, Rosario; Tveter, Trine Spedstad; Ullaland, Kjetil; Uras, Antonio; Usai, Gianluca; Utrobicic, Antonija; Vala, Martin; Valencia Palomo, Lizardo; Vallero, Sara; Van Der Maarel, Jasper; Van Hoorne, Jacobus Willem; Van Leeuwen, Marco; Vanat, Tomas; Vande Vyvre, Pierre; Varga, Dezso; Vargas Trevino, Aurora Diozcora; Vargyas, Marton; Varma, Raghava; Vasileiou, Maria; Vasiliev, Andrey; Vauthier, Astrid; Vechernin, Vladimir; Veen, Annelies Marianne; Veldhoen, Misha; Velure, Arild; Vercellin, Ermanno; Vergara Limon, Sergio; Vernet, Renaud; Verweij, Marta; Vickovic, Linda; Viesti, Giuseppe; Viinikainen, Jussi Samuli; Vilakazi, Zabulon; Villalobos Baillie, Orlando; Villatoro Tello, Abraham; Vinogradov, Alexander; Vinogradov, Leonid; Vinogradov, Yury; Virgili, Tiziano; Vislavicius, Vytautas; Viyogi, Yogendra; Vodopyanov, Alexander; Volkl, Martin Andreas; Voloshin, Kirill; Voloshin, Sergey; Volpe, Giacomo; Von Haller, Barthelemy; Vorobyev, Ivan; Vranic, Danilo; Vrlakova, Janka; Vulpescu, Bogdan; Wagner, Boris; Wagner, Jan; Wang, Hongkai; Wang, Mengliang; Watanabe, Daisuke; Watanabe, Yosuke; Weber, Michael; Weber, Steffen Georg; Weiser, Dennis Franz; Wessels, Johannes Peter; Westerhoff, Uwe; Whitehead, Andile Mothegi; Wiechula, Jens; Wikne, Jon; Wilk, Grzegorz Andrzej; Wilkinson, Jeremy John; Williams, Crispin; Windelband, Bernd Stefan; Winn, Michael Andreas; Yang, Hongyan; Yang, Ping; Yano, Satoshi; Yasin, Zafar; Yin, Zhongbao; Yokoyama, Hiroki; Yoo, In-Kwon; Yoon, Jin Hee; Yurchenko, Volodymyr; Yushmanov, Igor; Zaborowska, Anna; Zaccolo, Valentina; Zaman, Ali; Zampolli, Chiara; Correia Zanoli, Henrique Jose; Zaporozhets, Sergey; Zardoshti, Nima; Zarochentsev, Andrey; Zavada, Petr; Zavyalov, Nikolay; Zbroszczyk, Hanna Paulina; Zgura, Sorin Ion; Zhalov, Mikhail; Zhang, Haitao; Zhang, Xiaoming; Zhang, Yonghong; Chunhui, Zhang; Zhang, Zuman; Zhao, Chengxin; Zhigareva, Natalia; Zhou, Daicui; Zhou, You; Zhou, Zhuo; Zhu, Hongsheng; Zhu, Jianhui; Zichichi, Antonino; Zimmermann, Alice; Zimmermann, Markus Bernhard; Zinovjev, Gennady; Zyzak, Maksym
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 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...
Bayesian Recurrent Neural Network for Language Modeling.
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.
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.
Bayesian Methods for Radiation Detection and Dosimetry
International Nuclear Information System (INIS)
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
Bayesian and Dempster–Shafer fusion
Indian Academy of Sciences (India)
Subhash Challa; Don Koks
2004-04-01
The Kalman Filter is traditionally viewed as a prediction–correction ﬁltering algorithm. In this work we show that it can be viewed as a Bayesian fusion algorithm and derive it using Bayesian arguments. We begin with an outline of Bayes theory, using it to discuss well-known quantities such as priors, likelihood and posteriors, and we provide the basic Bayesian fusion equation. We derive the Kalman Filter from this equation using a novel method to evaluate the Chapman–Kolmogorov prediction integral. We then use the theory to fuse data from multiple sensors. Vying with this approach is the Dempster–Shafer theory, which deals with measures of “belief”, and is based on the nonclassical idea of “mass” as opposed to probability. Although these two measures look very similar, there are some differences. We point them out through outlining the ideas of the Dempster– Shafer theory and presenting the basic Dempster–Shafer fusion equation. Finally we compare the two methods, and discuss the relative merits and demerits using an illustrative example.
Sironi, Emanuele; Pinchi, Vilma; Taroni, Franco
2016-01-01
In the past few decades, the rise of criminal, civil and asylum cases involving young people lacking valid identification documents has generated an increase in the demand of age estimation. The chronological age or the probability that an individual is older or younger than a given age threshold are generally estimated by means of some statistical methods based on observations performed on specific physical attributes. Among these statistical methods, those developed in the Bayesian framework allow users to provide coherent and transparent assignments which fulfill forensic and medico-legal purposes. The application of the Bayesian approach is facilitated by using probabilistic graphical tools, such as Bayesian networks. The aim of this work is to test the performances of the Bayesian network for age estimation recently presented in scientific literature in classifying individuals as older or younger than 18 years of age. For these exploratory analyses, a sample related to the ossification status of the medial clavicular epiphysis available in scientific literature was used. Results obtained in the classification are promising: in the criminal context, the Bayesian network achieved, on the average, a rate of correct classifications of approximatively 97%, whilst in the civil context, the rate is, on the average, close to the 88%. These results encourage the continuation of the development and the testing of the method in order to support its practical application in casework.
Directory of Open Access Journals (Sweden)
David Lunn
Full Text Available The advantages of Bayesian statistical approaches, such as flexibility and the ability to acknowledge uncertainty in all parameters, have made them the prevailing method for analysing the spread of infectious diseases in human or animal populations. We introduce a Bayesian approach to experimental host-pathogen systems that shares these attractive features. Since uncertainty in all parameters is acknowledged, existing information can be accounted for through prior distributions, rather than through fixing some parameter values. The non-linear dynamics, multi-factorial design, multiple measurements of responses over time and sampling error that are typical features of experimental host-pathogen systems can also be naturally incorporated. We analyse the dynamics of the free-living protozoan Paramecium caudatum and its specialist bacterial parasite Holospora undulata. Our analysis provides strong evidence for a saturable infection function, and we were able to reproduce the two waves of infection apparent in the data by separating the initial inoculum from the parasites released after the first cycle of infection. In addition, the parameter estimates from the hierarchical model can be combined to infer variations in the parasite's basic reproductive ratio across experimental groups, enabling us to make predictions about the effect of resources and host genotype on the ability of the parasite to spread. Even though the high level of variability between replicates limited the resolution of the results, this Bayesian framework has strong potential to be used more widely in experimental ecology.
Directory of Open Access Journals (Sweden)
Yufei Huang
2007-06-01
Full Text Available Reverse engineering of genetic regulatory networks from time series microarray data are investigated. We propose a dynamic Bayesian networks (DBNs modeling and a full Bayesian learning scheme. The proposed DBN directly models the continuous expression levels and also is associated with parameters that indicate the degree as well as the type of regulations. To learn the network from data, we proposed a reversible jump Markov chain Monte Carlo (RJMCMC algorithm. The RJMCMC algorithm can provide not only more accurate inference results than the deterministic alternative algorithms but also an estimate of the a posteriori probabilities (APPs of the network topology. The estimated APPs provide useful information on the confidence of the inferred results and can also be used for efficient Bayesian data integration. The proposed approach is tested on yeast cell cycle microarray data and the results are compared with the KEGG pathway map.
Learning Local Components to Understand Large Bayesian Networks
DEFF Research Database (Denmark)
Zeng, Yifeng; Xiang, Yanping; Cordero, Jorge;
2009-01-01
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...... (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...... 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....
BAYESIAN ESTIMATION OF RELIABILITY IN TWOPARAMETER GEOMETRIC DISTRIBUTION
Directory of Open Access Journals (Sweden)
Sudhansu S. Maiti
2015-12-01
Full Text Available Bayesian estimation of reliability of a component, tR ( = P(X ≥ t, when X follows two-parameter geometric distribution, has been considered. Maximum Likelihood Estimator (MLE, an Unbiased Estimator and Bayesian Estimator have been compared. Bayesian estimation of component reliability R = P ( X ≤ Y , arising under stress-strength setup, when Y is assumed to follow independent two-parameter geometric distribution has also been discussed assuming independent priors for parameters under different loss functions.
Chain ladder method: Bayesian bootstrap versus classical bootstrap
Peters, Gareth W.; Mario V. W\\"uthrich; Shevchenko, Pavel V.
2010-01-01
The intention of this paper is to estimate a Bayesian distribution-free chain ladder (DFCL) model using approximate Bayesian computation (ABC) methodology. We demonstrate how to estimate quantities of interest in claims reserving and compare the estimates to those obtained from classical and credibility approaches. In this context, a novel numerical procedure utilising Markov chain Monte Carlo (MCMC), ABC and a Bayesian bootstrap procedure was developed in a truly distribution-free setting. T...
A tutorial introduction to Bayesian models of cognitive development
Perfors, Amy; Tenenbaum, Joshua B.; Griffiths, Thomas L.; Xu, Fei
2010-01-01
We present an introduction to Bayesian inference as it is used in probabilistic models of cognitive development. Our goal is to provide an intuitive and accessible guide to the what, the how, and the why of the Bayesian approach: what sorts of problems and data the framework is most relevant for, and how and why it may be useful for developmentalists. We emphasize a qualitative understanding of Bayesian inference, but also include information about additional resources for those interested in...
Bayesian just-so stories in psychology and neuroscience
Bowers, J.S.; Davis, Colin J
2012-01-01
According to Bayesian theories in psychology and neuroscience, minds and brains are (near) optimal in solving a wide range of tasks. We challenge this view and argue that more traditional, non-Bayesian approaches are more promising. We make three main arguments. First, we show that the empirical evidence for Bayesian theories in psychology is weak at best. This weakness relates to the many arbitrary ways that priors, likelihoods, and utility functions can be altered in order to account fo...
Bayesian just-so stories in cognitive psychology and neuroscience.
Bowers, J.S.; Davis, Colin J
2012-01-01
According to Bayesian theories in psychology and neuroscience, minds and brains are (near) optimal in solving a wide range of tasks. We challenge this view and argue that more traditional, non-Bayesian approaches are more promising. We make three main arguments. First, we show that the empirical evidence for Bayesian theories in psychology is weak at best. This weakness relates to the many arbitrary ways that priors, likelihoods, and utility functions can be altered in order to account fo...
The Bayesian Modelling Of Inflation Rate In Romania
Mihaela Simionescu
2014-01-01
Bayesian econometrics knew a considerable increase in popularity in the last years, joining the interests of various groups of researchers in economic sciences and additional ones as specialists in econometrics, commerce, industry, marketing, finance, micro-economy, macro-economy and other domains. The purpose of this research is to achieve an introduction in Bayesian approach applied in economics, starting with Bayes theorem. For the Bayesian linear regression models the methodology of estim...
Bayesian non- and semi-parametric methods and applications
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
Petit, V
2011-01-01
In this paper we describe a Bayesian statistical method designed to infer the magnetic properties of stars observed using high-resolution circular spectropolarimetry in the context of large surveys. This approach is well suited for analysing stars for which the stellar rotation period is not known, and therefore the rotational phases of the observations are ambiguous. The model assumes that the magnetic observations correspond to a dipole oblique rotator, a situation commonly encountered in intermediate and high-mass stars. Using reasonable assumptions regarding the model parameter prior probability density distributions, the Bayesian algorithm determines the posterior probability densities corresponding to the surface magnetic field geometry and strength by performing a comparison between the observed and computed Stokes V profiles. Based on the results of numerical simulations, we conclude that this method yields a useful estimate of the surface dipole field strength based on a small number (i.e. 1 or 2) of...
BGLS: A Bayesian formalism for the generalised Lomb-Scargle periodogram
Mortier, A; Correia, C M; Santerne, A; Santos, N C
2014-01-01
Context. Frequency analyses are very important in astronomy today, not least in the ever-growing field of exoplanets, where short-period signals in stellar radial velocity data are investigated. Periodograms are the main (and powerful) tools for this purpose. However, recovering the correct frequencies and assessing the probability of each frequency is not straightforward. Aims. We provide a formalism that is easy to implement in a code, to describe a Bayesian periodogram that includes weights and a constant offset in the data. The relative probability between peaks can be easily calculated with this formalism. We discuss the differences and agreements between the various periodogram formalisms with simulated examples. Methods. We used the Bayesian probability theory to describe the probability that a full sine function (including weights derived from the errors on the data values and a constant offset) with a specific frequency is present in the data. Results. From the expression for our Baysian generalised ...
The Power of Principled Bayesian Methods in the Study of Stellar Evolution
von Hippel, Ted; Stenning, David C; Robinson, Elliot; Jeffery, Elizabeth; Stein, Nathan; Jefferys, William H; O'Malley, Erin
2016-01-01
It takes years of effort employing the best telescopes and instruments to obtain high-quality stellar photometry, astrometry, and spectroscopy. Stellar evolution models contain the experience of lifetimes of theoretical calculations and testing. Yet most astronomers fit these valuable models to these precious datasets by eye. We show that a principled Bayesian approach to fitting models to stellar data yields substantially more information over a range of stellar astrophysics. We highlight advances in determining the ages of star clusters, mass ratios of binary stars, limitations in the accuracy of stellar models, post-main-sequence mass loss, and the ages of individual white dwarfs. We also outline a number of unsolved problems that would benefit from principled Bayesian analyses.
Moscoso del Prado Martín, Fermín
2013-12-01
I introduce the Bayesian assessment of scaling (BAS), a simple but powerful Bayesian hypothesis contrast methodology that can be used to test hypotheses on the scaling regime exhibited by a sequence of behavioral data. Rather than comparing parametric models, as typically done in previous approaches, the BAS offers a direct, nonparametric way to test whether a time series exhibits fractal scaling. The BAS provides a simpler and faster test than do previous methods, and the code for making the required computations is provided. The method also enables testing of finely specified hypotheses on the scaling indices, something that was not possible with the previously available methods. I then present 4 simulation studies showing that the BAS methodology outperforms the other methods used in the psychological literature. I conclude with a discussion of methodological issues on fractal analyses in experimental psychology. PMID:24417750
Feeney, Stephen M; McEwen, Jason D; Mortlock, Daniel J; Peiris, Hiranya V
2013-01-01
A number of theoretically well-motivated additions to the standard cosmological model predict weak signatures in the form of spatially localized sources embedded in the cosmic microwave background (CMB) fluctuations. We present a hierarchical Bayesian statistical formalism and a complete data analysis pipeline for testing such scenarios. We derive an accurate approximation to the full posterior probability distribution over the parameters defining any theory that predicts sources embedded in the CMB, and perform an extensive set of tests in order to establish its validity. The approximation is implemented using a modular algorithm, designed to avoid a posteriori selection effects, which combines a candidate-detection stage with a full Bayesian model-selection and parameter-estimation analysis. We apply this pipeline to theories that predict cosmic textures and bubble collisions, extending previous analyses by using: (1) adaptive-resolution techniques, allowing us to probe features of arbitrary size, and (2) o...
Moscoso del Prado Martín, Fermín
2013-12-01
I introduce the Bayesian assessment of scaling (BAS), a simple but powerful Bayesian hypothesis contrast methodology that can be used to test hypotheses on the scaling regime exhibited by a sequence of behavioral data. Rather than comparing parametric models, as typically done in previous approaches, the BAS offers a direct, nonparametric way to test whether a time series exhibits fractal scaling. The BAS provides a simpler and faster test than do previous methods, and the code for making the required computations is provided. The method also enables testing of finely specified hypotheses on the scaling indices, something that was not possible with the previously available methods. I then present 4 simulation studies showing that the BAS methodology outperforms the other methods used in the psychological literature. I conclude with a discussion of methodological issues on fractal analyses in experimental psychology.
Bayesian approaches to spatial inference: Modelling and computational challenges and solutions
Moores, Matthew; Mengersen, Kerrie
2014-12-01
We discuss a range of Bayesian modelling approaches for spatial data and investigate some of the associated computational challenges. This paper commences with a brief review of Bayesian mixture models and Markov random fields, with enabling computational algorithms including Markov chain Monte Carlo (MCMC) and integrated nested Laplace approximation (INLA). Following this, we focus on the Potts model as a canonical approach, and discuss the challenge of estimating the inverse temperature parameter that controls the degree of spatial smoothing. We compare three approaches to addressing the doubly intractable nature of the likelihood, namely pseudo-likelihood, path sampling and the exchange algorithm. These techniques are applied to satellite data used to analyse water quality in the Great Barrier Reef.
Doing bayesian data analysis a tutorial with R and BUGS
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
Bayesian missing data problems EM, data augmentation and noniterative computation
Tan, Ming T; Ng, Kai Wang
2009-01-01
Bayesian Missing Data Problems: EM, Data Augmentation and Noniterative Computation presents solutions to missing data problems through explicit or noniterative sampling calculation of Bayesian posteriors. The methods are based on the inverse Bayes formulae discovered by one of the author in 1995. Applying the Bayesian approach to important real-world problems, the authors focus on exact numerical solutions, a conditional sampling approach via data augmentation, and a noniterative sampling approach via EM-type algorithms. After introducing the missing data problems, Bayesian approach, and poste
Bayesian integer frequency offset estimator for MIMO-OFDM systems
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Carrier frequency offset (CFO) in MIMO-OFDM systems can be decoupled into two parts: fraction frequency offset (FFO) and integer frequency offset (IFO). The problem of IFO estimation is addressed and a new IFO estimator based on the Bayesian philosophy is proposed. Also, it is shown that the Bayesian IFO estimator is optimal among all the IFO estimators. Furthermore, the Bayesian estimator can take advantage of oversampling so that better performance can be obtained. Finally, numerical results show the optimality of the Bayesian estimator and validate the theoretical analysis.
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.
Bayesian Inference of the Evolution of HBV/E
Andernach, Iris E.; Hunewald, Oliver E.; Muller, Claude P.
2013-01-01
Despite its wide spread and high prevalence in sub-Saharan Africa, hepatitis B virus genotype E (HBV/E) has a surprisingly low genetic diversity, indicating an only recent emergence of this genotype in the general African population. Here, we performed extensive phylogeographic analyses, including Bayesian MCMC modeling. Our results indicate a mutation rate of 1.9×10−4 substitutions per site and year (s/s/y) and confirm a recent emergence of HBV/E, most likely within the last 130 years, and only after the transatlantic slave-trade had come to an end. Our analyses suggest that HBV/E originated from the area of Nigeria, before rapidly spreading throughout sub-Saharan Africa. Interestingly, viral strains found in Haiti seem to be the result of multiple introductions only in the second half of the 20th century, corroborating an absence of a significant number of HBV/E strains in West Africa several centuries ago. Our results confirm that the hyperendemicity of HBV(E) in today's Africa is a recent phenomenon and likely the result of dramatic changes in the routes of viral transmission in a relatively recent past. PMID:24312336
Whole-Genome Analyses of LUNG FUNCTION, HEIGHT and SMOKING
Janss, Luc; Sigsgaard, Torben; Sorensen, Daniel
2014-01-01
A joint analysis of FEV1 (Forced Expiratory Volume after one second) and height is reported using novel methodology, as well as a single-trait analysis of smoking status. A first goal of the study was to incorporate dense genetic marker information in a random regression (Bayesian) model to quantify the relative contributions of genomic and environmental factors to the relationship between FEV1 and height. Smoking status was analysed using a probit random regression model and a second goal of...
Shah, Abhik; Woolf, Peter
2009-06-01
In this paper, we introduce pebl, a Python library and application for learning Bayesian network structure from data and prior knowledge that provides features unmatched by alternative software packages: the ability to use interventional data, flexible specification of structural priors, modeling with hidden variables and exploitation of parallel processing. PMID:20161541
Bayesian inference tools for inverse problems
Mohammad-Djafari, Ali
2013-08-01
In this paper, first the basics of Bayesian inference with a parametric model of the data is presented. Then, the needed extensions are given when dealing with inverse problems and in particular the linear models such as Deconvolution or image reconstruction in Computed Tomography (CT). The main point to discuss then is the prior modeling of signals and images. A classification of these priors is presented, first in separable and Markovien models and then in simple or hierarchical with hidden variables. For practical applications, we need also to consider the estimation of the hyper parameters. Finally, we see that we have to infer simultaneously on the unknowns, the hidden variables and the hyper parameters. Very often, the expression of this joint posterior law is too complex to be handled directly. Indeed, rarely we can obtain analytical solutions to any point estimators such the Maximum A posteriori (MAP) or Posterior Mean (PM). Three main tools are then can be used: Laplace approximation (LAP), Markov Chain Monte Carlo (MCMC) and Bayesian Variational Approximations (BVA). To illustrate all these aspects, we will consider a deconvolution problem where we know that the input signal is sparse and propose to use a Student-t prior for that. Then, to handle the Bayesian computations with this model, we use the property of Student-t which is modelling it via an infinite mixture of Gaussians, introducing thus hidden variables which are the variances. Then, the expression of the joint posterior of the input signal samples, the hidden variables (which are here the inverse variances of those samples) and the hyper-parameters of the problem (for example the variance of the noise) is given. From this point, we will present the joint maximization by alternate optimization and the three possible approximation methods. Finally, the proposed methodology is applied in different applications such as mass spectrometry, spectrum estimation of quasi periodic biological signals and
Meteorological Data Assimilation by Adaptive Bayesian Optimization.
Purser, Robert James
1992-01-01
The principal aim of this research is the elucidation of the Bayesian statistical principles that underlie the theory of objective meteorological analysis. In particular, emphasis is given to aspects of data assimilation that can benefit from an iterative numerical strategy. Two such aspects that are given special consideration are statistical validation of the covariance profiles and nonlinear initialization. A new economic algorithm is presented, based on the imposition of a sparse matrix structure for all covariances and precisions held during the computations. It is shown that very large datasets may be accommodated using this structure and a good linear approximation to the analysis equations established without the need to unnaturally fragment the problem. Since the integrity of the system of analysis equations is preserved, it is a relatively straight-forward matter to extend the basic analysis algorithm to one that incorporates a check on the plausibility of the statistical model assumed for background errors--the so-called "validation" problem. Two methods of validation are described within the sparse matrix framework: the first is essentially a direct extension of the Bayesian principles to embrace, not only the regular analysis variables, but also the parameters that determine the precise form of the covariance functions; the second technique is the non-Bayesian method of generalized cross validation adapted for use within the sparse matrix framework. The later part of this study is concerned with the establishment of a consistent dynamical balance within a forecast model--the initialization problem. The formal principles of the modern theory of initialization are reviewed and a critical examination is made of the concept of the "slow manifold". It is demonstrated, in accordance with more complete nonlinear models, that even within a simple three-mode linearized system, the notion that a universal slow manifold exists is untenable. It is therefore argued
Personalized Audio Systems - a Bayesian Approach
DEFF Research Database (Denmark)
Nielsen, Jens Brehm; Jensen, Bjørn Sand; Hansen, Toke Jansen;
2013-01-01
Modern audio systems are typically equipped with several user-adjustable parameters unfamiliar to most users listening to the system. To obtain the best possible setting, the user is forced into multi-parameter optimization with respect to the users's own objective and preference. To address this......, the present paper presents a general inter-active framework for personalization of such audio systems. The framework builds on Bayesian Gaussian process regression in which a model of the users's objective function is updated sequentially. The parameter setting to be evaluated in a given trial is...
Recovery of shapes: hypermodels and Bayesian learning
International Nuclear Information System (INIS)
We discuss the problem of recovering an image from its blurred and noisy copy with the additional information that the image consists of simple shapes with sharp edges. An iterative algorithm is given, based on the idea of updating the Tikhonov type smoothness penalty on the basis of the previous estimate. This algorithm is discussed in the framework of Bayesian hypermodels and it is shown that the approach can be justified as a sequential iterative scheme for finding the mode of the posterior density. An effective numerical algorithm based on preconditioned Krylov subspace iterations is suggested and demonstrated with a computed example
Bayesian model selection in Gaussian regression
Abramovich, Felix
2009-01-01
We consider a Bayesian approach to model selection in Gaussian linear regression, where the number of predictors might be much larger than the number of observations. From a frequentist view, the proposed procedure results in the penalized least squares estimation with a complexity penalty associated with a prior on the model size. We investigate the optimality properties of the resulting estimator. We establish the oracle inequality and specify conditions on the prior that imply its asymptotic minimaxity within a wide range of sparse and dense settings for "nearly-orthogonal" and "multicollinear" designs.
Structure-based bayesian sparse reconstruction
Quadeer, Ahmed Abdul
2012-12-01
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 information (Gaussian or otherwise) to obtain near optimal estimates. In addition, we make use of the rich structure of the sensing matrix encountered in many signal processing applications to develop a fast sparse recovery algorithm. The computational complexity of the proposed algorithm is very low compared with the widely used convex relaxation methods as well as greedy matching pursuit techniques, especially at high sparsity. © 1991-2012 IEEE.
Radioactive Contraband Detection: A Bayesian Approach
Energy Technology Data Exchange (ETDEWEB)
Candy, J; Breitfeller, E; Guidry, B; Manatt, D; Sale, K; Chambers, D; Axelrod, M; Meyer, A
2009-03-16
Radionuclide emissions from nuclear contraband challenge both detection and measurement technologies to capture and record each event. The development of a sequential Bayesian processor incorporating both the physics of gamma-ray emissions and the measurement of photon energies offers a physics-based approach to attack this challenging problem. It is shown that a 'physics-based' structure can be used to develop an effective detection technique, but also motivates the implementation of this approach using or particle filters to enhance and extract the required information.
Confidence Biases and Learning among Intuitive Bayesians
Lévy-Garboua, Louis; Askari, Muniza; Gazel, Marco
2015-01-01
URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/cesdp2015.html Documents de travail du Centre d'Economie de la Sorbonne 2015.80 - ISSN : 1955-611X We design a double-or-quits game to compare the speed of learning one's specific ability with the speed of rising confidence as the task gets increasingly difficult. We find that people on average learn to be overconfident faster than they learn their true ability and we present a simple Bayesian model of confidence which integ...
Bayesian parameter estimation by continuous homodyne detection
DEFF Research Database (Denmark)
Kiilerich, Alexander Holm; Molmer, Klaus
2016-01-01
and we show that the ensuing transient evolution is more sensitive to system parameters than the steady state of the system. The parameter sensitivity can be quantified by the Fisher information, and we investigate numerically and analytically how the temporal noise correlations in the measurement signal......We simulate the process of continuous homodyne detection of the radiative emission from a quantum system, and we investigate how a Bayesian analysis can be employed to determine unknown parameters that govern the system evolution. Measurement backaction quenches the system dynamics at all times...
Bayesian approach to avoiding track seduction
Salmond, David J.; Everett, Nicholas O.
2002-08-01
The problem of maintaining track on a primary target in the presence spurious objects is addressed. Recursive and batch filtering approaches are developed. For the recursive approach, a Bayesian track splitting filter is derived which spawns candidate tracks if there is a possibility of measurement misassociation. The filter evaluates the probability of each candidate track being associated with the primary target. The batch filter is a Markov-chain Monte Carlo (MCMC) algorithm which fits the observed data sequence to models of target dynamics and measurement-track association. Simulation results are presented.
Low Complexity Bayesian Single Channel Source Separation
DEFF Research Database (Denmark)
Beierholm, Thomas; Pedersen, Brian Dam; Winther, Ole
2004-01-01
We propose a simple Bayesian model for performing single channel speech separation using factorized source priors in a sliding window linearly transformed domain. Using a one dimensional mixture of Gaussians to model each band source leads to fast tractable inference for the source signals...... can be estimated quite precisely using ML-II, but the estimation is quite sensitive to the accuracy of the priors as opposed to the source separation quality for known mixing coefficients, which is quite insensitive to the accuracy of the priors. Finally, we discuss how to improve our approach while...
Bayesian regression of piecewise homogeneous Poisson processes
Directory of Open Access Journals (Sweden)
Diego Sevilla
2015-12-01
Full Text Available In this paper, a Bayesian method for piecewise regression is adapted to handle counting processes data distributed as Poisson. A numerical code in Mathematica is developed and tested analyzing simulated data. The resulting method is valuable for detecting breaking points in the count rate of time series for Poisson processes. Received: 2 November 2015, Accepted: 27 November 2015; Edited by: R. Dickman; Reviewed by: M. Hutter, Australian National University, Canberra, Australia.; DOI: http://dx.doi.org/10.4279/PIP.070018 Cite as: D J R Sevilla, Papers in Physics 7, 070018 (2015
A Bayesian approach to earthquake source studies
Minson, Sarah
Bayesian sampling has several advantages over conventional optimization approaches to solving inverse problems. It produces the distribution of all possible models sampled proportionally to how much each model is consistent with the data and the specified prior information, and thus images the entire solution space, revealing the uncertainties and trade-offs in the model. Bayesian sampling is applicable to both linear and non-linear modeling, and the values of the model parameters being sampled can be constrained based on the physics of the process being studied and do not have to be regularized. However, these methods are computationally challenging for high-dimensional problems. Until now the computational expense of Bayesian sampling has been too great for it to be practicable for most geophysical problems. I present a new parallel sampling algorithm called CATMIP for Cascading Adaptive Tempered Metropolis In Parallel. This technique, based on Transitional Markov chain Monte Carlo, makes it possible to sample distributions in many hundreds of dimensions, if the forward model is fast, or to sample computationally expensive forward models in smaller numbers of dimensions. The design of the algorithm is independent of the model being sampled, so CATMIP can be applied to many areas of research. I use CATMIP to produce a finite fault source model for the 2007 Mw 7.7 Tocopilla, Chile earthquake. Surface displacements from the earthquake were recorded by six interferograms and twelve local high-rate GPS stations. Because of the wealth of near-fault data, the source process is well-constrained. I find that the near-field high-rate GPS data have significant resolving power above and beyond the slip distribution determined from static displacements. The location and magnitude of the maximum displacement are resolved. The rupture almost certainly propagated at sub-shear velocities. The full posterior distribution can be used not only to calculate source parameters but also
Bayesian logistic betting strategy against probability forecasting
Kumon, Masayuki; Takemura, Akimichi; Takeuchi, Kei
2012-01-01
We propose a betting strategy based on Bayesian logistic regression modeling for the probability forecasting game in the framework of game-theoretic probability by Shafer and Vovk (2001). We prove some results concerning the strong law of large numbers in the probability forecasting game with side information based on our strategy. We also apply our strategy for assessing the quality of probability forecasting by the Japan Meteorological Agency. We find that our strategy beats the agency by exploiting its tendency of avoiding clear-cut forecasts.
Email Spam Filter using Bayesian Neural Networks
Directory of Open Access Journals (Sweden)
Nibedita Chakraborty
2012-03-01
Full Text Available Nowadays, e-mail is widely becoming one of the fastest and most economical forms of communication but they are prone to be misused. One such misuse is the posting of unsolicited, unwanted e-mails known as spam or junk e-mails. This paper presents and discusses an implementation of a spam filtering system. The idea is to use a neural network which will be trained to recognize different forms of often used words in spam mails. The Bayesian ANN is trained with finite sample sizes to approximate the ideal observer. This strategy can provide improved filtering of Spam than existing Static Spam filters.
Reasons for (prior) belief in bayesian epistemology
Dietrich, Franz; List, Christian
2012-01-01
Bayesian epistemology tells us with great precision how we should move from prior to posterior beliefs in light of new evidence or information, but says little about where our prior beliefs come from. It o¤ers few resources to describe some prior beliefs as rational or well-justi�ed, and others as irrational or unreasonable. A di¤erent strand of epistemology takes the central epistemological question to be not how to change one�s beliefs in light of new evidence, but what reasons justify a gi...
Bayesian Estimation of a Mixture Model
Ilhem Merah; Assia Chadli
2015-01-01
We present the properties of a bathtub curve reliability model having both a sufficient adaptability and a minimal number of parameters introduced by Idée and Pierrat (2010). This one is a mixture of a Gamma distribution G(2, (1/θ)) and a new distribution L(θ). We are interesting by Bayesian estimation of the parameters and survival function of this model with a squared-error loss function and non-informative prior using the approximations of Lindley (1980) and Tierney and Kadane (1986). Usin...
Bayesian Network Based XP Process Modelling
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Mohamed Abouelela
2010-07-01
Full Text Available A Bayesian Network based mathematical model has been used for modelling Extreme Programmingsoftware development process. The model is capable of predicting the expected finish time and theexpected defect rate for each XP release. Therefore, it can be used to determine the success/failure of anyXP Project. The model takes into account the effect of three XP practices, namely: Pair Programming,Test Driven Development and Onsite Customer practices. The model’s predictions were validated againsttwo case studies. Results show the precision of our model especially in predicting the project finish time.
Multisnapshot Sparse Bayesian Learning for DOA
Gerstoft, Peter; Mecklenbrauker, Christoph F.; Xenaki, Angeliki; Nannuru, Santosh
2016-10-01
The directions of arrival (DOA) of plane waves are estimated from multi-snapshot sensor array data using Sparse Bayesian Learning (SBL). The prior source amplitudes is assumed independent zero-mean complex Gaussian distributed with hyperparameters the unknown variances (i.e. the source powers). For a complex Gaussian likelihood with hyperparameter the unknown noise variance, the corresponding Gaussian posterior distribution is derived. For a given number of DOAs, the hyperparameters are automatically selected by maximizing the evidence and promote sparse DOA estimates. The SBL scheme for DOA estimation is discussed and evaluated competitively against LASSO ($\\ell_1$-regularization), conventional beamforming, and MUSIC
Bayesian parameter estimation by continuous homodyne detection
Kiilerich, Alexander Holm; Mølmer, Klaus
2016-09-01
We simulate the process of continuous homodyne detection of the radiative emission from a quantum system, and we investigate how a Bayesian analysis can be employed to determine unknown parameters that govern the system evolution. Measurement backaction quenches the system dynamics at all times and we show that the ensuing transient evolution is more sensitive to system parameters than the steady state of the system. The parameter sensitivity can be quantified by the Fisher information, and we investigate numerically and analytically how the temporal noise correlations in the measurement signal contribute to the ultimate sensitivity limit of homodyne detection.
Bayesian global analysis of neutrino oscillation data
Bergstrom, Johannes; Maltoni, Michele; Schwetz, Thomas
2015-01-01
We perform a Bayesian analysis of current neutrino oscillation data. When estimating the oscillation parameters we find that the results generally agree with those of the $\\chi^2$ method, with some differences involving $s_{23}^2$ and CP-violating effects. We discuss the additional subtleties caused by the circular nature of the CP-violating phase, and how it is possible to obtain correlation coefficients with $s_{23}^2$. When performing model comparison, we find that there is no significant evidence for any mass ordering, any octant of $s_{23}^2$ or a deviation from maximal mixing, nor the presence of CP-violation.
A Bayesian Framework for Combining Valuation Estimates
Yee, Kenton K
2007-01-01
Obtaining more accurate equity value estimates is the starting point for stock selection, value-based indexing in a noisy market, and beating benchmark indices through tactical style rotation. Unfortunately, discounted cash flow, method of comparables, and fundamental analysis typically yield discrepant valuation estimates. Moreover, the valuation estimates typically disagree with market price. Can one form a superior valuation estimate by averaging over the individual estimates, including market price? This article suggests a Bayesian framework for combining two or more estimates into a superior valuation estimate. The framework justifies the common practice of averaging over several estimates to arrive at a final point estimate.
Directory of Open Access Journals (Sweden)
C Elizabeth McCarron
Full Text Available BACKGROUND: Bayesian hierarchical models have been proposed to combine evidence from different types of study designs. However, when combining evidence from randomised and non-randomised controlled studies, imbalances in patient characteristics between study arms may bias the results. The objective of this study was to assess the performance of a proposed Bayesian approach to adjust for imbalances in patient level covariates when combining evidence from both types of study designs. METHODOLOGY/PRINCIPAL FINDINGS: Simulation techniques, in which the truth is known, were used to generate sets of data for randomised and non-randomised studies. Covariate imbalances between study arms were introduced in the non-randomised studies. The performance of the Bayesian hierarchical model adjusted for imbalances was assessed in terms of bias. The data were also modelled using three other Bayesian approaches for synthesising evidence from randomised and non-randomised studies. The simulations considered six scenarios aimed at assessing the sensitivity of the results to changes in the impact of the imbalances and the relative number and size of studies of each type. For all six scenarios considered, the Bayesian hierarchical model adjusted for differences within studies gave results that were unbiased and closest to the true value compared to the other models. CONCLUSIONS/SIGNIFICANCE: Where informed health care decision making requires the synthesis of evidence from randomised and non-randomised study designs, the proposed hierarchical Bayesian method adjusted for differences in patient characteristics between study arms may facilitate the optimal use of all available evidence leading to unbiased results compared to unadjusted analyses.
Bayesian item selection in constrained adaptive testing using shadow tests
Veldkamp, Bernard P.
2010-01-01
Application of Bayesian item selection criteria in computerized adaptive testing might result in improvement of bias and MSE of the ability estimates. The question remains how to apply Bayesian item selection criteria in the context of constrained adaptive testing, where large numbers of specificati
Some Quantum Information Inequalities from a Quantum Bayesian Networks Perspective
Tucci, Robert R.
2012-01-01
This is primarily a pedagogical paper. The paper re-visits some well-known quantum information theory inequalities. It does this from a quantum Bayesian networks perspective. The paper illustrates some of the benefits of using quantum Bayesian networks to discuss quantum SIT (Shannon Information Theory).
Bayesian Compressed Sensing with Unknown Measurement Noise Level
DEFF Research Database (Denmark)
Hansen, Thomas Lundgaard; Jørgensen, Peter Bjørn; Pedersen, Niels Lovmand;
2013-01-01
In sparse Bayesian learning (SBL) approximate Bayesian inference is applied to find sparse estimates from observations corrupted by additive noise. Current literature only vaguely considers the case where the noise level is unknown a priori. We show that for most state-of-the-art reconstruction a...
Universal Darwinism As a Process of Bayesian Inference.
Campbell, John O
2016-01-01
Many of the mathematical frameworks describing natural selection are equivalent to Bayes' Theorem, also known as Bayesian updating. By definition, a process of Bayesian Inference is one which involves a Bayesian update, so we may conclude that these frameworks describe natural selection as a process of Bayesian inference. Thus, natural selection serves as a counter example to a widely-held interpretation that restricts Bayesian Inference to human mental processes (including the endeavors of statisticians). As Bayesian inference can always be cast in terms of (variational) free energy minimization, natural selection can be viewed as comprising two components: a generative model of an "experiment" in the external world environment, and the results of that "experiment" or the "surprise" entailed by predicted and actual outcomes of the "experiment." Minimization of free energy implies that the implicit measure of "surprise" experienced serves to update the generative model in a Bayesian manner. This description closely accords with the mechanisms of generalized Darwinian process proposed both by Dawkins, in terms of replicators and vehicles, and Campbell, in terms of inferential systems. Bayesian inference is an algorithm for the accumulation of evidence-based knowledge. This algorithm is now seen to operate over a wide range of evolutionary processes, including natural selection, the evolution of mental models and cultural evolutionary processes, notably including science itself. The variational principle of free energy minimization may thus serve as a unifying mathematical framework for universal Darwinism, the study of evolutionary processes operating throughout nature. PMID:27375438
A SEMIPARAMETRIC BAYESIAN MODEL FOR CIRCULAR-LINEAR REGRESSION
We present a Bayesian approach to regress a circular variable on a linear predictor. The regression coefficients are assumed to have a nonparametric distribution with a Dirichlet process prior. The semiparametric Bayesian approach gives added flexibility to the model and is usefu...
Non-homogeneous dynamic Bayesian networks for continuous data
Grzegorczyk, Marco; Husmeier, Dirk
2011-01-01
Classical dynamic Bayesian networks (DBNs) are based on the homogeneous Markov assumption and cannot deal with non-homogeneous temporal processes. Various approaches to relax the homogeneity assumption have recently been proposed. The present paper presents a combination of a Bayesian network with c
What Is the Probability You Are a Bayesian?
Wulff, Shaun S.; Robinson, Timothy J.
2014-01-01
Bayesian methodology continues to be widely used in statistical applications. As a result, it is increasingly important to introduce students to Bayesian thinking at early stages in their mathematics and statistics education. While many students in upper level probability courses can recite the differences in the Frequentist and Bayesian…
Universal Darwinism As a Process of Bayesian Inference.
Campbell, John O
2016-01-01
Many of the mathematical frameworks describing natural selection are equivalent to Bayes' Theorem, also known as Bayesian updating. By definition, a process of Bayesian Inference is one which involves a Bayesian update, so we may conclude that these frameworks describe natural selection as a process of Bayesian inference. Thus, natural selection serves as a counter example to a widely-held interpretation that restricts Bayesian Inference to human mental processes (including the endeavors of statisticians). As Bayesian inference can always be cast in terms of (variational) free energy minimization, natural selection can be viewed as comprising two components: a generative model of an "experiment" in the external world environment, and the results of that "experiment" or the "surprise" entailed by predicted and actual outcomes of the "experiment." Minimization of free energy implies that the implicit measure of "surprise" experienced serves to update the generative model in a Bayesian manner. This description closely accords with the mechanisms of generalized Darwinian process proposed both by Dawkins, in terms of replicators and vehicles, and Campbell, in terms of inferential systems. Bayesian inference is an algorithm for the accumulation of evidence-based knowledge. This algorithm is now seen to operate over a wide range of evolutionary processes, including natural selection, the evolution of mental models and cultural evolutionary processes, notably including science itself. The variational principle of free energy minimization may thus serve as a unifying mathematical framework for universal Darwinism, the study of evolutionary processes operating throughout nature.
Using Alien Coins to Test Whether Simple Inference Is Bayesian
Cassey, Peter; Hawkins, Guy E.; Donkin, Chris; Brown, Scott D.
2016-01-01
Reasoning and inference are well-studied aspects of basic cognition that have been explained as statistically optimal Bayesian inference. Using a simplified experimental design, we conducted quantitative comparisons between Bayesian inference and human inference at the level of individuals. In 3 experiments, with more than 13,000 participants, we…
Bayesian Data-Model Fit Assessment for Structural Equation Modeling
Levy, Roy
2011-01-01
Bayesian approaches to modeling are receiving an increasing amount of attention in the areas of model construction and estimation in factor analysis, structural equation modeling (SEM), and related latent variable models. However, model diagnostics and model criticism remain relatively understudied aspects of Bayesian SEM. This article describes…
Bayesian Item Selection in Constrained Adaptive Testing Using Shadow Tests
Veldkamp, Bernard P.
2010-01-01
Application of Bayesian item selection criteria in computerized adaptive testing might result in improvement of bias and MSE of the ability estimates. The question remains how to apply Bayesian item selection criteria in the context of constrained adaptive testing, where large numbers of specifications have to be taken into account in the item…
Bayesian Learning and the Psychology of Rule Induction
Endress, Ansgar D.
2013-01-01
In recent years, Bayesian learning models have been applied to an increasing variety of domains. While such models have been criticized on theoretical grounds, the underlying assumptions and predictions are rarely made concrete and tested experimentally. Here, I use Frank and Tenenbaum's (2011) Bayesian model of rule-learning as a case study to…
Universal Darwinism as a process of Bayesian inference
Directory of Open Access Journals (Sweden)
John Oberon Campbell
2016-06-01
Full Text Available Many of the mathematical frameworks describing natural selection are equivalent to Bayes’ Theorem, also known as Bayesian updating. By definition, a process of Bayesian Inference is one which involves a Bayesian update, so we may conclude that these frameworks describe natural selection as a process of Bayesian inference. Thus natural selection serves as a counter example to a widely-held interpretation that restricts Bayesian Inference to human mental processes (including the endeavors of statisticians. As Bayesian inference can always be cast in terms of (variational free energy minimization, natural selection can be viewed as comprising two components: a generative model of an ‘experiment’ in the external world environment, and the results of that 'experiment' or the 'surprise' entailed by predicted and actual outcomes of the ‘experiment’. Minimization of free energy implies that the implicit measure of 'surprise' experienced serves to update the generative model in a Bayesian manner. This description closely accords with the mechanisms of generalized Darwinian process proposed both by Dawkins, in terms of replicators and vehicles, and Campbell, in terms of inferential systems. Bayesian inference is an algorithm for the accumulation of evidence-based knowledge. This algorithm is now seen to operate over a wide range of evolutionary processes, including natural selection, the evolution of mental models and cultural evolutionary processes, notably including science itself. The variational principle of free energy minimization may thus serve as a unifying mathematical framework for universal Darwinism, the study of evolutionary processes operating throughout nature.
Statistical assignment of DNA sequences using Bayesian phylogenetics
DEFF Research Database (Denmark)
Terkelsen, Kasper Munch; Boomsma, Wouter Krogh; Huelsenbeck, John P;
2008-01-01
We provide a new automated statistical method for DNA barcoding based on a Bayesian phylogenetic analysis. The method is based on automated database sequence retrieval, alignment, and phylogenetic analysis using a custom-built program for Bayesian phylogenetic analysis. We show on real data that ...
Survey of Bayesian Models for Modelling of Stochastic Temporal Processes
Energy Technology Data Exchange (ETDEWEB)
Ng, B
2006-10-12
This survey gives an overview of popular generative models used in the modeling of stochastic temporal systems. In particular, this survey is organized into two parts. The first part discusses the discrete-time representations of dynamic Bayesian networks and dynamic relational probabilistic models, while the second part discusses the continuous-time representation of continuous-time Bayesian networks.
Bayesian Approach to Neuro-Rough Models for Modelling HIV
Marwala, Tshilidzi
2007-01-01
This paper proposes a new neuro-rough model for modelling the risk of HIV from demographic data. The model is formulated using Bayesian framework and trained using Markov Chain Monte Carlo method and Metropolis criterion. When the model was tested to estimate the risk of HIV infection given the demographic data it was found to give the accuracy of 62% as opposed to 58% obtained from a Bayesian formulated rough set model trained using Markov chain Monte Carlo method and 62% obtained from a Bayesian formulated multi-layered perceptron (MLP) model trained using hybrid Monte. The proposed model is able to combine the accuracy of the Bayesian MLP model and the transparency of Bayesian rough set model.
3-Layered Bayesian Model Using in Text Classification
Directory of Open Access Journals (Sweden)
Chang Jiayu
2013-01-01
Full Text Available Naive Bayesian is one of quite effective classification methods in all of the text disaggregated models. Usually, the computed result will be large deviation from normal, with the reason of attribute relevance and so on. This study embarked from the degree of correlation, defined the node’s degree as well as the relations between nodes, proposed a 3-layered Bayesian Model. According to the conditional probability recurrence formula, the theory support of the 3-layered Bayesian Model is obtained. According to the theory analysis and the empirical datum contrast to the Naive Bayesian, the model has better attribute collection and classify. It can be also promoted to the Multi-layer Bayesian Model using in text classification.
Application of Bayesian Network Learning Methods to Land Resource Evaluation
Institute of Scientific and Technical Information of China (English)
HUANG Jiejun; HE Xiaorong; WAN Youchuan
2006-01-01
Bayesian network has a powerful ability for reasoning and semantic representation, which combined with qualitative analysis and quantitative analysis, with prior knowledge and observed data, and provides an effective way to deal with prediction, classification and clustering. Firstly, this paper presented an overview of Bayesian network and its characteristics, and discussed how to learn a Bayesian network structure from given data, and then constructed a Bayesian network model for land resource evaluation with expert knowledge and the dataset. The experimental results based on the test dataset are that evaluation accuracy is 87.5%, and Kappa index is 0.826. All these prove the method is feasible and efficient, and indicate that Bayesian network is a promising approach for land resource evaluation.
Bayesian signal processing classical, modern, and particle filtering methods
Candy, James V
2016-01-01
This book aims to give readers a unified Bayesian treatment starting from the basics (Baye's rule) to the more advanced (Monte Carlo sampling), evolving to the next-generation model-based techniques (sequential Monte Carlo sampling). This next edition incorporates a new chapter on "Sequential Bayesian Detection," a new section on "Ensemble Kalman Filters" as well as an expansion of Case Studies that detail Bayesian solutions for a variety of applications. These studies illustrate Bayesian approaches to real-world problems incorporating detailed particle filter designs, adaptive particle filters and sequential Bayesian detectors. In addition to these major developments a variety of sections are expanded to "fill-in-the gaps" of the first edition. Here metrics for particle filter (PF) designs with emphasis on classical "sanity testing" lead to ensemble techniques as a basic requirement for performance analysis. The expansion of information theory metrics and their application to PF designs is fully developed an...
Approximation methods for efficient learning of Bayesian networks
Riggelsen, C
2008-01-01
This publication offers and investigates efficient Monte Carlo simulation methods in order to realize a Bayesian approach to approximate learning of Bayesian networks from both complete and incomplete data. For large amounts of incomplete data when Monte Carlo methods are inefficient, approximations are implemented, such that learning remains feasible, albeit non-Bayesian. The topics discussed are: basic concepts about probabilities, graph theory and conditional independence; Bayesian network learning from data; Monte Carlo simulation techniques; and, the concept of incomplete data. In order to provide a coherent treatment of matters, thereby helping the reader to gain a thorough understanding of the whole concept of learning Bayesian networks from (in)complete data, this publication combines in a clarifying way all the issues presented in the papers with previously unpublished work.
Two-player conflicting interest Bayesian games and Bell nonlocality
Situ, Haozhen
2016-01-01
Nonlocality, one of the most remarkable aspects of quantum mechanics, is closely related to Bayesian game theory. Quantum mechanics can offer advantages to some Bayesian games, if the payoff functions are related to Bell inequalities in some way, most of these Bayesian games that have been discussed are common interest games. Recently, the first conflicting interest Bayesian game is proposed in Phys. Rev. Lett. 114, 020401 (2015). In the present paper, we present three new conflicting interest Bayesian games where quantum mechanics offers advantages. The first game is linked with Cereceda inequalities, the second game is linked with a generalized Bell inequality with three possible measurement outcomes, and the third game is linked with a generalized Bell inequality with three possible measurement settings.
Bayesian Models of Graphs, Arrays and Other Exchangeable Random Structures.
Orbanz, Peter; Roy, Daniel M
2015-02-01
The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and many other parametric and nonparametric Bayesian models fall within the remit of this framework; many problems arising in modern data analysis do not. This article provides an introduction to Bayesian models of graphs, matrices, and other data that can be modeled by random structures. We describe results in probability theory that generalize de Finetti's theorem to such data and discuss their relevance to nonparametric Bayesian modeling. With the basic ideas in place, we survey example models available in the literature; applications of such models include collaborative filtering, link prediction, and graph and network analysis. We also highlight connections to recent developments in graph theory and probability, and sketch the more general mathematical foundation of Bayesian methods for other types of data beyond sequences and arrays. PMID:26353253
Semisupervised learning using Bayesian interpretation: application to LS-SVM.
Adankon, Mathias M; Cheriet, Mohamed; Biem, Alain
2011-04-01
Bayesian reasoning provides an ideal basis for representing and manipulating uncertain knowledge, with the result that many interesting algorithms in machine learning are based on Bayesian inference. In this paper, we use the Bayesian approach with one and two levels of inference to model the semisupervised learning problem and give its application to the successful kernel classifier support vector machine (SVM) and its variant least-squares SVM (LS-SVM). Taking advantage of Bayesian interpretation of LS-SVM, we develop a semisupervised learning algorithm for Bayesian LS-SVM using our approach based on two levels of inference. Experimental results on both artificial and real pattern recognition problems show the utility of our method.
Bayesian nonparametric regression with varying residual density.
Pati, Debdeep; Dunson, David B
2014-02-01
We consider the problem of robust Bayesian inference on the mean regression function allowing the residual density to change flexibly with predictors. The proposed class of models is based on a Gaussian process prior for the mean regression function and mixtures of Gaussians for the collection of residual densities indexed by predictors. Initially considering the homoscedastic case, we propose priors for the residual density based on probit stick-breaking (PSB) scale mixtures and symmetrized PSB (sPSB) location-scale mixtures. Both priors restrict the residual density to be symmetric about zero, with the sPSB prior more flexible in allowing multimodal densities. We provide sufficient conditions to ensure strong posterior consistency in estimating the regression function under the sPSB prior, generalizing existing theory focused on parametric residual distributions. The PSB and sPSB priors are generalized to allow residual densities to change nonparametrically with predictors through incorporating Gaussian processes in the stick-breaking components. This leads to a robust Bayesian regression procedure that automatically down-weights outliers and influential observations in a locally-adaptive manner. Posterior computation relies on an efficient data augmentation exact block Gibbs sampler. The methods are illustrated using simulated and real data applications. PMID:24465053
Fully Bayesian Experimental Design for Pharmacokinetic Studies
Directory of Open Access Journals (Sweden)
Elizabeth G. Ryan
2015-03-01
Full Text Available Utility functions in Bayesian experimental design are usually based on the posterior distribution. When the posterior is found by simulation, it must be sampled from for each future dataset drawn from the prior predictive distribution. Many thousands of posterior distributions are often required. A popular technique in the Bayesian experimental design literature, which rapidly obtains samples from the posterior, is importance sampling, using the prior as the importance distribution. However, importance sampling from the prior will tend to break down if there is a reasonable number of experimental observations. In this paper, we explore the use of Laplace approximations in the design setting to overcome this drawback. Furthermore, we consider using the Laplace approximation to form the importance distribution to obtain a more efficient importance distribution than the prior. The methodology is motivated by a pharmacokinetic study, which investigates the effect of extracorporeal membrane oxygenation on the pharmacokinetics of antibiotics in sheep. The design problem is to find 10 near optimal plasma sampling times that produce precise estimates of pharmacokinetic model parameters/measures of interest. We consider several different utility functions of interest in these studies, which involve the posterior distribution of parameter functions.
Bayesian Discovery of Linear Acyclic Causal Models
Hoyer, Patrik O
2012-01-01
Methods for automated discovery of causal relationships from non-interventional data have received much attention recently. A widely used and well understood model family is given by linear acyclic causal models (recursive structural equation models). For Gaussian data both constraint-based methods (Spirtes et al., 1993; Pearl, 2000) (which output a single equivalence class) and Bayesian score-based methods (Geiger and Heckerman, 1994) (which assign relative scores to the equivalence classes) are available. On the contrary, all current methods able to utilize non-Gaussianity in the data (Shimizu et al., 2006; Hoyer et al., 2008) always return only a single graph or a single equivalence class, and so are fundamentally unable to express the degree of certainty attached to that output. In this paper we develop a Bayesian score-based approach able to take advantage of non-Gaussianity when estimating linear acyclic causal models, and we empirically demonstrate that, at least on very modest size networks, its accur...
Bayesian Cosmic Web Reconstruction: BARCODE for Clusters
Patrick Bos, E. G.; van de Weygaert, Rien; Kitaura, Francisco; Cautun, Marius
2016-10-01
We describe the Bayesian \\barcode\\ formalism that has been designed towards the reconstruction of the Cosmic Web in a given volume on the basis of the sampled galaxy cluster distribution. Based on the realization that the massive compact clusters are responsible for the major share of the large scale tidal force field shaping the anisotropic and in particular filamentary features in the Cosmic Web. Given the nonlinearity of the constraints imposed by the cluster configurations, we resort to a state-of-the-art constrained reconstruction technique to find a proper statistically sampled realization of the original initial density and velocity field in the same cosmic region. Ultimately, the subsequent gravitational evolution of these initial conditions towards the implied Cosmic Web configuration can be followed on the basis of a proper analytical model or an N-body computer simulation. The BARCODE formalism includes an implicit treatment for redshift space distortions. This enables a direct reconstruction on the basis of observational data, without the need for a correction of redshift space artifacts. In this contribution we provide a general overview of the the Cosmic Web connection with clusters and a description of the Bayesian BARCODE formalism. We conclude with a presentation of its successful workings with respect to test runs based on a simulated large scale matter distribution, in physical space as well as in redshift space.
Bayesian Analysis of High Dimensional Classification
Mukhopadhyay, Subhadeep; Liang, Faming
2009-12-01
Modern data mining and bioinformatics have presented an important playground for statistical learning techniques, where the number of input variables is possibly much larger than the sample size of the training data. In supervised learning, logistic regression or probit regression can be used to model a binary output and form perceptron classification rules based on Bayesian inference. In these cases , there is a lot of interest in searching for sparse model in High Dimensional regression(/classification) setup. we first discuss two common challenges for analyzing high dimensional data. The first one is the curse of dimensionality. The complexity of many existing algorithms scale exponentially with the dimensionality of the space and by virtue of that algorithms soon become computationally intractable and therefore inapplicable in many real applications. secondly, multicollinearities among the predictors which severely slowdown the algorithm. In order to make Bayesian analysis operational in high dimension we propose a novel 'Hierarchical stochastic approximation monte carlo algorithm' (HSAMC), which overcomes the curse of dimensionality, multicollinearity of predictors in high dimension and also it possesses the self-adjusting mechanism to avoid the local minima separated by high energy barriers. Models and methods are illustrated by simulation inspired from from the feild of genomics. Numerical results indicate that HSAMC can work as a general model selection sampler in high dimensional complex model space.
Bayesian nonparametric adaptive control using Gaussian processes.
Chowdhary, Girish; Kingravi, Hassan A; How, Jonathan P; Vela, Patricio A
2015-03-01
Most current model reference adaptive control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element is radial basis function networks (RBFNs), with RBF centers preallocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become noneffective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semiglobal in nature. This paper investigates a Gaussian process-based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty. The GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed-loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning.
Bayesian Kinematic Finite Fault Source Models (Invited)
Minson, S. E.; Simons, M.; Beck, J. L.
2010-12-01
Finite fault earthquake source models are inherently under-determined: there is no unique solution to the inverse problem of determining the rupture history at depth as a function of time and space when our data are only limited observations at the Earth's surface. Traditional inverse techniques rely on model constraints and regularization to generate one model from the possibly broad space of all possible solutions. However, Bayesian methods allow us to determine the ensemble of all possible source models which are consistent with the data and our a priori assumptions about the physics of the earthquake source. Until now, Bayesian techniques have been of limited utility because they are computationally intractable for problems with as many free parameters as kinematic finite fault models. We have developed a methodology called Cascading Adaptive Tempered Metropolis In Parallel (CATMIP) which allows us to sample very high-dimensional problems in a parallel computing framework. The CATMIP algorithm combines elements of simulated annealing and genetic algorithms with the Metropolis algorithm to dynamically optimize the algorithm's efficiency as it runs. We will present synthetic performance tests of finite fault models made with this methodology as well as a kinematic source model for the 2007 Mw 7.7 Tocopilla, Chile earthquake. This earthquake was well recorded by multiple ascending and descending interferograms and a network of high-rate GPS stations whose records can be used as near-field seismograms.
A Hierarchical Bayesian Model for Crowd Emotions
Urizar, Oscar J.; Baig, Mirza S.; Barakova, Emilia I.; Regazzoni, Carlo S.; Marcenaro, Lucio; Rauterberg, Matthias
2016-01-01
Estimation of emotions is an essential aspect in developing intelligent systems intended for crowded environments. However, emotion estimation in crowds remains a challenging problem due to the complexity in which human emotions are manifested and the capability of a system to perceive them in such conditions. This paper proposes a hierarchical Bayesian model to learn in unsupervised manner the behavior of individuals and of the crowd as a single entity, and explore the relation between behavior and emotions to infer emotional states. Information about the motion patterns of individuals are described using a self-organizing map, and a hierarchical Bayesian network builds probabilistic models to identify behaviors and infer the emotional state of individuals and the crowd. This model is trained and tested using data produced from simulated scenarios that resemble real-life environments. The conducted experiments tested the efficiency of our method to learn, detect and associate behaviors with emotional states yielding accuracy levels of 74% for individuals and 81% for the crowd, similar in performance with existing methods for pedestrian behavior detection but with novel concepts regarding the analysis of crowds. PMID:27458366
Refining gene signatures: a Bayesian approach
Directory of Open Access Journals (Sweden)
Labbe Aurélie
2009-12-01
Full Text Available Abstract Background In high density arrays, the identification of relevant genes for disease classification is complicated by not only the curse of dimensionality but also the highly correlated nature of the array data. In this paper, we are interested in the question of how many and which genes should be selected for a disease class prediction. Our work consists of a Bayesian supervised statistical learning approach to refine gene signatures with a regularization which penalizes for the correlation between the variables selected. Results Our simulation results show that we can most often recover the correct subset of genes that predict the class as compared to other methods, even when accuracy and subset size remain the same. On real microarray datasets, we show that our approach can refine gene signatures to obtain either the same or better predictive performance than other existing methods with a smaller number of genes. Conclusions Our novel Bayesian approach includes a prior which penalizes highly correlated features in model selection and is able to extract key genes in the highly correlated context of microarray data. The methodology in the paper is described in the context of microarray data, but can be applied to any array data (such as micro RNA, for example as a first step towards predictive modeling of cancer pathways. A user-friendly software implementation of the method is available.
A Bayesian framework for active artificial perception.
Ferreira, João Filipe; Lobo, Jorge; Bessière, Pierre; Castelo-Branco, Miguel; Dias, Jorge
2013-04-01
In this paper, we present a Bayesian framework for the active multimodal perception of 3-D structure and motion. The design of this framework finds its inspiration in the role of the dorsal perceptual pathway of the human brain. Its composing models build upon a common egocentric spatial configuration that is naturally fitting for the integration of readings from multiple sensors using a Bayesian approach. In the process, we will contribute with efficient and robust probabilistic solutions for cyclopean geometry-based stereovision and auditory perception based only on binaural cues, modeled using a consistent formalization that allows their hierarchical use as building blocks for the multimodal sensor fusion framework. We will explicitly or implicitly address the most important challenges of sensor fusion using this framework, for vision, audition, and vestibular sensing. Moreover, interaction and navigation require maximal awareness of spatial surroundings, which, in turn, is obtained through active attentional and behavioral exploration of the environment. The computational models described in this paper will support the construction of a simultaneously flexible and powerful robotic implementation of multimodal active perception to be used in real-world applications, such as human-machine interaction or mobile robot navigation. PMID:23014760
A Bayesian framework for active artificial perception.
Ferreira, João Filipe; Lobo, Jorge; Bessière, Pierre; Castelo-Branco, Miguel; Dias, Jorge
2013-04-01
In this paper, we present a Bayesian framework for the active multimodal perception of 3-D structure and motion. The design of this framework finds its inspiration in the role of the dorsal perceptual pathway of the human brain. Its composing models build upon a common egocentric spatial configuration that is naturally fitting for the integration of readings from multiple sensors using a Bayesian approach. In the process, we will contribute with efficient and robust probabilistic solutions for cyclopean geometry-based stereovision and auditory perception based only on binaural cues, modeled using a consistent formalization that allows their hierarchical use as building blocks for the multimodal sensor fusion framework. We will explicitly or implicitly address the most important challenges of sensor fusion using this framework, for vision, audition, and vestibular sensing. Moreover, interaction and navigation require maximal awareness of spatial surroundings, which, in turn, is obtained through active attentional and behavioral exploration of the environment. The computational models described in this paper will support the construction of a simultaneously flexible and powerful robotic implementation of multimodal active perception to be used in real-world applications, such as human-machine interaction or mobile robot navigation.
Bayesian Integration of multiscale environmental data
Energy Technology Data Exchange (ETDEWEB)
2016-08-22
The software is designed for efficiently integrating large-size of multi-scale environmental data using the Bayesian framework. Suppose we need to estimate the spatial distribution of variable X with high spatial resolution. The available data include (1) direct measurements Z of the unknowns with high resolution in a subset of the spatial domain (small spatial coverage), (2) measurements C of the unknowns at the median scale, and (3) measurements A of the unknowns at the coarsest scale but with large spatial coverage. The goal is to estimate the unknowns at the fine grids by conditioning to all the available data. We first consider all the unknowns as random variables and estimate conditional probability distribution of those variables by conditioning to the limited high-resolution observations (Z). We then treat the estimated probability distribution as the prior distribution. Within the Bayesian framework, we combine the median and large-scale measurements (C and A) through likelihood functions. Since we assume that all the relevant multivariate distributions are Gaussian, the resulting posterior distribution is a multivariate Gaussian distribution. The developed software provides numerical solutions of the posterior probability distribution. The software can be extended in several different ways to solve more general multi-scale data integration problems.
Bayesian estimation of isotopic age differences
International Nuclear Information System (INIS)
Isotopic dating is subject to uncertainties arising from counting statistics and experimental errors. These uncertainties are additive when an isotopic age difference is calculated. If large, they can lead to no significant age difference by classical statistics. In many cases, relative ages are known because of stratigraphic order or other clues. Such information can be used to establish a Bayes estimate of age difference which will include prior knowledge of age order. Age measurement errors are assumed to be log-normal and a noninformative but constrained bivariate prior for two true ages in known order is adopted. True-age ratio is distributed as a truncated log-normal variate. Its expected value gives an age-ratio estimate, and its variance provides credible intervals. Bayesian estimates of ages are different and in correct order even if measured ages are identical or reversed in order. For example, age measurements on two samples might both yield 100 ka with coefficients of variation of 0.2. Bayesian estimates are 22.7 ka for age difference with a 75% credible interval of [4.4, 43.7] ka
Bayesian estimation of isotopic age differences
Energy Technology Data Exchange (ETDEWEB)
Curl, R.L.
1988-08-01
Isotopic dating is subject to uncertainties arising from counting statistics and experimental errors. These uncertainties are additive when an isotopic age difference is calculated. If large, they can lead to no significant age difference by classical statistics. In many cases, relative ages are known because of stratigraphic order or other clues. Such information can be used to establish a Bayes estimate of age difference which will include prior knowledge of age order. Age measurement errors are assumed to be log-normal and a noninformative but constrained bivariate prior for two true ages in known order is adopted. True-age ratio is distributed as a truncated log-normal variate. Its expected value gives an age-ratio estimate, and its variance provides credible intervals. Bayesian estimates of ages are different and in correct order even if measured ages are identical or reversed in order. For example, age measurements on two samples might both yield 100 ka with coefficients of variation of 0.2. Bayesian estimates are 22.7 ka for age difference with a 75% credible interval of (4.4, 43.7) ka.
Measure Transformer Semantics for Bayesian Machine Learning
Borgström, Johannes; Gordon, Andrew D.; Greenberg, Michael; Margetson, James; van Gael, Jurgen
The Bayesian approach to machine learning amounts to inferring posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables. There is a trend in machine learning towards expressing Bayesian models as probabilistic programs. As a foundation for this kind of programming, we propose a core functional calculus with primitives for sampling prior distributions and observing variables. We define combinators for measure transformers, based on theorems in measure theory, and use these to give a rigorous semantics to our core calculus. The original features of our semantics include its support for discrete, continuous, and hybrid measures, and, in particular, for observations of zero-probability events. We compile our core language to a small imperative language that has a straightforward semantics via factor graphs, data structures that enable many efficient inference algorithms. We use an existing inference engine for efficient approximate inference of posterior marginal distributions, treating thousands of observations per second for large instances of realistic models.
Application of Bayesian graphs to SN Ia data analysis and compression
Ma, Con; Bassett, Bruce A
2016-01-01
Bayesian graphical models are an efficient tool for modelling complex data and derive self-consistent expressions of the posterior distribution of model parameters. We apply Bayesian graphs to perform statistical analyses of Type Ia supernova (SN Ia) luminosity distance measurements from the Joint Light-curve Analysis (JLA) dataset (Betoule et al. 2014, arXiv:1401.4064). In contrast to the $\\chi^2$ approach used in previous studies, the Bayesian inference allows us to fully account for the standard-candle parameter dependence of the data covariance matrix. Comparing with $\\chi^2$ analysis results we find a systematic offset of the marginal model parameter bounds. We demonstrate that the bias is statistically significant in the case of the SN Ia standardization parameters with a maximal $6\\sigma$ shift of the SN light-curve colour correction. In addition, we find that the evidence for a host galaxy correction is now only $2.4\\sigma$. Systematic offsets on the cosmological parameters remain small, but may incre...
Statistical modelling of railway track geometry degradation using Hierarchical Bayesian models
International Nuclear Information System (INIS)
Railway maintenance planners require a predictive model that can assess the railway track geometry degradation. The present paper uses a Hierarchical Bayesian model as a tool to model the main two quality indicators related to railway track geometry degradation: the standard deviation of longitudinal level defects and the standard deviation of horizontal alignment defects. Hierarchical Bayesian Models (HBM) are flexible statistical models that allow specifying different spatially correlated components between consecutive track sections, namely for the deterioration rates and the initial qualities parameters. HBM are developed for both quality indicators, conducting an extensive comparison between candidate models and a sensitivity analysis on prior distributions. HBM is applied to provide an overall assessment of the degradation of railway track geometry, for the main Portuguese railway line Lisbon–Oporto. - Highlights: • Rail track geometry degradation is analysed using Hierarchical Bayesian models. • A Gibbs sampling strategy is put forward to estimate the HBM. • Model comparison and sensitivity analysis find the most suitable model. • We applied the most suitable model to all the segments of the main Portuguese line. • Tackling spatial correlations using CAR structures lead to a better model fit
bspmma: An R Package for Bayesian Semiparametric Models for Meta-Analysis
Directory of Open Access Journals (Sweden)
Deborah Burr
2012-07-01
Full Text Available We introduce an R package, bspmma, which implements a Dirichlet-based random effects model specific to meta-analysis. In meta-analysis, when combining effect estimates from several heterogeneous studies, it is common to use a random-effects model. The usual frequentist or Bayesian models specify a normal distribution for the true effects. However, in many situations, the effect distribution is not normal, e.g., it can have thick tails, be skewed, or be multi-modal. A Bayesian nonparametric model based on mixtures of Dirichlet process priors has been proposed in the literature, for the purpose of accommodating the non-normality. We review this model and then describe a competitor, a semiparametric version which has the feature that it allows for a well-defined centrality parameter convenient for determining whether the overall effect is significant. This second Bayesian model is based on a different version of the Dirichlet process prior, and we call it the "conditional Dirichlet model". The package contains functions to carry out analyses based on either the ordinary or the conditional Dirichlet model, functions for calculating certain Bayes factors that provide a check on the appropriateness of the conditional Dirichlet model, and functions that enable an empirical Bayes selection of the precision parameter of the Dirichlet process. We illustrate the use of the package on two examples, and give an interpretation of the results in these two different scenarios.
cudaBayesreg: Parallel Implementation of a Bayesian Multilevel Model for fMRI Data Analysis
Directory of Open Access Journals (Sweden)
Adelino R. Ferreira da Silva
2011-10-01
Full Text Available Graphic processing units (GPUs are rapidly gaining maturity as powerful general parallel computing devices. A key feature in the development of modern GPUs has been the advancement of the programming model and programming tools. Compute Unified Device Architecture (CUDA is a software platform for massively parallel high-performance computing on Nvidia many-core GPUs. In functional magnetic resonance imaging (fMRI, the volume of the data to be processed, and the type of statistical analysis to perform call for high-performance computing strategies. In this work, we present the main features of the R-CUDA package cudaBayesreg which implements in CUDA the core of a Bayesian multilevel model for the analysis of brain fMRI data. The statistical model implements a Gibbs sampler for multilevel/hierarchical linear models with a normal prior. The main contribution for the increased performance comes from the use of separate threads for fitting the linear regression model at each voxel in parallel. The R-CUDA implementation of the Bayesian model proposed here has been able to reduce significantly the run-time processing of Markov chain Monte Carlo (MCMC simulations used in Bayesian fMRI data analyses. Presently, cudaBayesreg is only configured for Linux systems with Nvidia CUDA support.
A Genomic Bayesian Multi-trait and Multi-environment Model.
Montesinos-López, Osval A; Montesinos-López, Abelardo; Crossa, José; Toledo, Fernando H; Pérez-Hernández, Oscar; Eskridge, Kent M; Rutkoski, Jessica
2016-09-08
When information on multiple genotypes evaluated in multiple environments is recorded, a multi-environment single trait model for assessing genotype × environment interaction (G × E) is usually employed. Comprehensive models that simultaneously take into account the correlated traits and trait × genotype × environment interaction (T × G × E) are lacking. In this research, we propose a Bayesian model for analyzing multiple traits and multiple environments for whole-genome prediction (WGP) model. For this model, we used Half-[Formula: see text] priors on each standard deviation term and uniform priors on each correlation of the covariance matrix. These priors were not informative and led to posterior inferences that were insensitive to the choice of hyper-parameters. We also developed a computationally efficient Markov Chain Monte Carlo (MCMC) under the above priors, which allowed us to obtain all required full conditional distributions of the parameters leading to an exact Gibbs sampling for the posterior distribution. We used two real data sets to implement and evaluate the proposed Bayesian method and found that when the correlation between traits was high (>0.5), the proposed model (with unstructured variance-covariance) improved prediction accuracy compared to the model with diagonal and standard variance-covariance structures. The R-software package Bayesian Multi-Trait and Multi-Environment (BMTME) offers optimized C++ routines to efficiently perform the analyses.
Using consensus bayesian network to model the reactive oxygen species regulatory pathway.
Directory of Open Access Journals (Sweden)
Liangdong Hu
Full Text Available Bayesian network is one of the most successful graph models for representing the reactive oxygen species regulatory pathway. With the increasing number of microarray measurements, it is possible to construct the bayesian network from microarray data directly. Although large numbers of bayesian network learning algorithms have been developed, when applying them to learn bayesian networks from microarray data, the accuracies are low due to that the databases they used to learn bayesian networks contain too few microarray data. In this paper, we propose a consensus bayesian network which is constructed by combining bayesian networks from relevant literatures and bayesian networks learned from microarray data. It would have a higher accuracy than the bayesian networks learned from one database. In the experiment, we validated the bayesian network combination algorithm on several classic machine learning databases and used the consensus bayesian network to model the Escherichia coli's ROS pathway.
Revisiting Isotherm Analyses Using R: Comparison of Linear, Non-linear, and Bayesian Techniques
Extensive adsorption isotherm data exist for an array of chemicals of concern on a variety of engineered and natural sorbents. Several isotherm models exist that can accurately describe these data from which the resultant fitting parameters may subsequently be used in numerical ...
Puncher, M; Birchall, A; Bull, R K
2014-12-01
In Bayesian inference, the initial knowledge regarding the value of a parameter, before additional data are considered, is represented as a prior probability distribution. This paper describes the derivation of a prior distribution of intake that was used for the Bayesian analysis of plutonium and uranium worker doses in a recent epidemiology study. The chosen distribution is log-normal with a geometric standard deviation of 6 and a median value that is derived for each worker based on the duration of the work history and the number of reported acute intakes. The median value is a function of the work history and a constant related to activity in air concentration, M, which is derived separately for uranium and plutonium. The value of M is based primarily on measurements of plutonium and uranium in air derived from historical personal air sampler (PAS) data. However, there is significant uncertainty on the value of M that results from paucity of PAS data and from extrapolating these measurements to actual intakes. This paper compares posterior and prior distributions of intake and investigates the sensitivity of the Bayesian analyses to the assumed value of M. It is found that varying M by a factor of 10 results in a much smaller factor of 2 variation in mean intake and lung dose for both plutonium and uranium. It is concluded that if a log-normal distribution is considered to adequately represent worker intakes, then the Bayesian posterior distribution of dose is relatively insensitive to the value assumed of M. PMID:24191121
Application of Bayesian graphs to SN Ia data analysis and compression
Ma, Cong; Corasaniti, Pier-Stefano; Bassett, Bruce A.
2016-08-01
Bayesian graphical models are an efficient tool for modelling complex data and derive self-consistent expressions of the posterior distribution of model parameters. We apply Bayesian graphs to perform statistical analyses of Type Ia supernova (SN Ia) luminosity distance measurements from the Joint Light-curve Analysis (JLA) dataset (Betoule et al. 2014). In contrast to the χ2 approach used in previous studies, the Bayesian inference allows us to fully account for the standard-candle parameter dependence of the data covariance matrix. Comparing with χ2 analysis results we find a systematic offset of the marginal model parameter bounds. We demonstrate that the bias is statistically significant in the case of the SN Ia standardization parameters with a maximal 6σ shift of the SN light-curve colour correction. In addition, we find that the evidence for a host galaxy correction is now only 2.4σ. Systematic offsets on the cosmological parameters remain small, but may increase by combining constraints from complementary cosmological probes. The bias of the χ2 analysis is due to neglecting the parameter-dependent log-determinant of the data covariance, which gives more statistical weight to larger values of the standardization parameters. We find a similar effect on compressed distance modulus data. To this end we implement a fully consistent compression method of the JLA dataset that uses a Gaussian approximation of the posterior distribution for fast generation of compressed data. Overall, the results of our analysis emphasize the need for a fully consistent Bayesian statistical approach in the analysis of future large SN Ia datasets.
Applying Bayesian ideas to the development of medical guidelines.
Landrum, M B; Normand, S L
1999-01-30
Measurements of the quality of health care, in particular the underuse and overuse of medical therapies and diagnostic tests, often involve employment of medical practice guidelines to assess the appropriateness of treatments. This paper presents a case study of a Bayesian analysis for the development of medical guidelines based on expert opinion, using ordinal categorical rater data. We develop guidelines for the use of coronary angiography following an acute myocardial infarction (AMI) for 890 clinical indications using statistical models fit to appropriateness ratings obtained from a nine-member expert panel. The main foci of our analyses were on the estimation of an appropriateness score for each of the clinical indications, an associated measure of precision, and functions of the underlying score. We considered two classes of models that assume the ratings are either in the form of grouped normal data or are ungrouped variables arising from a normal distribution, while permitting rater effects and indication heterogeneity in both. We estimated models using Markov chain Monte Carlo methods and constructed indices quantifying appropriateness based on posterior probabilities of selected model parameters. We compared our model-based approach to the standard approach currently employed in medical guideline development and found that the standard approach correctly identified 99 per cent of the appropriate indications while overestimating appropriateness 18 per cent of the time compared to our model-based approach. PMID:10028134
Bayesian inference for identifying interaction rules in moving animal groups.
Mann, Richard P
2011-01-01
The emergence of similar collective patterns from different self-propelled particle models of animal groups points to a restricted set of "universal" classes for these patterns. While universality is interesting, it is often the fine details of animal interactions that are of biological importance. Universality thus presents a challenge to inferring such interactions from macroscopic group dynamics since these can be consistent with many underlying interaction models. We present a Bayesian framework for learning animal interaction rules from fine scale recordings of animal movements in swarms. We apply these techniques to the inverse problem of inferring interaction rules from simulation models, showing that parameters can often be inferred from a small number of observations. Our methodology allows us to quantify our confidence in parameter fitting. For example, we show that attraction and alignment terms can be reliably estimated when animals are milling in a torus shape, while interaction radius cannot be reliably measured in such a situation. We assess the importance of rate of data collection and show how to test different models, such as topological and metric neighbourhood models. Taken together our results both inform the design of experiments on animal interactions and suggest how these data should be best analysed. PMID:21829657
Bayesian inference for identifying interaction rules in moving animal groups.
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Richard P Mann
Full Text Available The emergence of similar collective patterns from different self-propelled particle models of animal groups points to a restricted set of "universal" classes for these patterns. While universality is interesting, it is often the fine details of animal interactions that are of biological importance. Universality thus presents a challenge to inferring such interactions from macroscopic group dynamics since these can be consistent with many underlying interaction models. We present a Bayesian framework for learning animal interaction rules from fine scale recordings of animal movements in swarms. We apply these techniques to the inverse problem of inferring interaction rules from simulation models, showing that parameters can often be inferred from a small number of observations. Our methodology allows us to quantify our confidence in parameter fitting. For example, we show that attraction and alignment terms can be reliably estimated when animals are milling in a torus shape, while interaction radius cannot be reliably measured in such a situation. We assess the importance of rate of data collection and show how to test different models, such as topological and metric neighbourhood models. Taken together our results both inform the design of experiments on animal interactions and suggest how these data should be best analysed.
A Bayesian Semiparametric Model for Radiation Dose-Response Estimation.
Furukawa, Kyoji; Misumi, Munechika; Cologne, John B; Cullings, Harry M
2016-06-01
In evaluating the risk of exposure to health hazards, characterizing the dose-response relationship and estimating acceptable exposure levels are the primary goals. In analyses of health risks associated with exposure to ionizing radiation, while there is a clear agreement that moderate to high radiation doses cause harmful effects in humans, little has been known about the possible biological effects at low doses, for example, below 0.1 Gy, which is the dose range relevant to most radiation exposures of concern today. A conventional approach to radiation dose-response estimation based on simple parametric forms, such as the linear nonthreshold model, can be misleading in evaluating the risk and, in particular, its uncertainty at low doses. As an alternative approach, we consider a Bayesian semiparametric model that has a connected piece-wise-linear dose-response function with prior distributions having an autoregressive structure among the random slope coefficients defined over closely spaced dose categories. With a simulation study and application to analysis of cancer incidence data among Japanese atomic bomb survivors, we show that this approach can produce smooth and flexible dose-response estimation while reasonably handling the risk uncertainty at low doses and elsewhere. With relatively few assumptions and modeling options to be made by the analyst, the method can be particularly useful in assessing risks associated with low-dose radiation exposures. PMID:26581473
ENERGY AWARE NETWORK: BAYESIAN BELIEF NETWORKS BASED DECISION MANAGEMENT SYSTEM
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Santosh Kumar Chaudhari
2011-06-01
Full Text Available A Network Management System (NMS plays a very important role in managing an ever-evolving telecommunication network. Generally an NMS monitors & maintains the health of network elements. The growing size of the network warrants extra functionalities from the NMS. An NMS provides all kinds of information about networks which can be used for other purposes apart from monitoring & maintaining networks like improving QoS & saving energy in the network. In this paper, we add another dimension to NMS services, namely, making an NMS energy aware. We propose a Decision Management System (DMS framework which uses a machine learning technique called Bayesian Belief Networks (BBN, to make the NMS energy aware. The DMS is capable of analysing and making control decisions based on network traffic. We factor in the cost of rerouting and power saving per port. Simulations are performed on standard network topologies, namely, ARPANet and IndiaNet. It is found that ~2.5-6.5% power can be saved.
A Bayesian model of category-specific emotional brain responses.
Wager, Tor D; Kang, Jian; Johnson, Timothy D; Nichols, Thomas E; Satpute, Ajay B; Barrett, Lisa Feldman
2015-04-01
Understanding emotion is critical for a science of healthy and disordered brain function, but the neurophysiological basis of emotional experience is still poorly understood. We analyzed human brain activity patterns from 148 studies of emotion categories (2159 total participants) using a novel hierarchical Bayesian model. The model allowed us to classify which of five categories--fear, anger, disgust, sadness, or happiness--is engaged by a study with 66% accuracy (43-86% across categories). Analyses of the activity patterns encoded in the model revealed that each emotion category is associated with unique, prototypical patterns of activity across multiple brain systems including the cortex, thalamus, amygdala, and other structures. The results indicate that emotion categories are not contained within any one region or system, but are represented as configurations across multiple brain networks. The model provides a precise summary of the prototypical patterns for each emotion category, and demonstrates that a sufficient characterization of emotion categories relies on (a) differential patterns of involvement in neocortical systems that differ between humans and other species, and (b) distinctive patterns of cortical-subcortical interactions. Thus, these findings are incompatible with several contemporary theories of emotion, including those that emphasize emotion-dedicated brain systems and those that propose emotion is localized primarily in subcortical activity. They are consistent with componential and constructionist views, which propose that emotions are differentiated by a combination of perceptual, mnemonic, prospective, and motivational elements. Such brain-based models of emotion provide a foundation for new translational and clinical approaches. PMID:25853490
A Bayesian decision approach to rainfall thresholds based flood warning
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M. L. V. Martina
2006-01-01
Full Text Available Operational real time flood forecasting systems generally require a hydrological model to run in real time as well as a series of hydro-informatics tools to transform the flood forecast into relatively simple and clear messages to the decision makers involved in flood defense. The scope of this paper is to set forth the possibility of providing flood warnings at given river sections based on the direct comparison of the quantitative precipitation forecast with critical rainfall threshold values, without the need of an on-line real time forecasting system. This approach leads to an extremely simplified alert system to be used by non technical stakeholders and could also be used to supplement the traditional flood forecasting systems in case of system failures. The critical rainfall threshold values, incorporating the soil moisture initial conditions, result from statistical analyses using long hydrological time series combined with a Bayesian utility function minimization. In the paper, results of an application of the proposed methodology to the Sieve river, a tributary of the Arno river in Italy, are given to exemplify its practical applicability.
A new Bayesian approach to the reconstruction of spectral functions
Burnier, Yannis
2013-01-01
We present a novel approach for the reconstruction of spectra from Euclidean correlator data that makes close contact to modern Bayesian concepts. It is based upon an axiomatically justified dimensionless prior distribution, which in the case of constant prior function $m(\\omega)$ only imprints smoothness on the reconstructed spectrum. In addition we are able to analytically integrate out the only relevant overall hyper-parameter $\\alpha$ in the prior, removing the necessity for Gaussian approximations found e.g. in the Maximum Entropy Method. Using a quasi-Newton minimizer and high-precision arithmetic, we are then able to find the unique global extremum of $P[\\rho|D]$ in the full $N_\\omega\\gg N_\\tau$ dimensional search space. The method actually yields gradually improving reconstruction results if the quality of the supplied input data increases, without introducing artificial peak structures, often encountered in the MEM. To support these statements we present mock data analyses for the case of zero width ...
A Bayesian Shrinkage Approach for AMMI Models.
da Silva, Carlos Pereira; de Oliveira, Luciano Antonio; Nuvunga, Joel Jorge; Pamplona, Andrezza Kéllen Alves; Balestre, Marcio
2015-01-01
Linear-bilinear models, especially the additive main effects and multiplicative interaction (AMMI) model, are widely applicable to genotype-by-environment interaction (GEI) studies in plant breeding programs. These models allow a parsimonious modeling of GE interactions, retaining a small number of principal components in the analysis. However, one aspect of the AMMI model that is still debated is the selection criteria for determining the number of multiplicative terms required to describe the GE interaction pattern. Shrinkage estimators have been proposed as selection criteria for the GE interaction components. In this study, a Bayesian approach was combined with the AMMI model with shrinkage estimators for the principal components. A total of 55 maize genotypes were evaluated in nine different environments using a complete blocks design with three replicates. The results show that the traditional Bayesian AMMI model produces low shrinkage of singular values but avoids the usual pitfalls in determining the credible intervals in the biplot. On the other hand, Bayesian shrinkage AMMI models have difficulty with the credible interval for model parameters, but produce stronger shrinkage of the principal components, converging to GE matrices that have more shrinkage than those obtained using mixed models. This characteristic allowed more parsimonious models to be chosen, and resulted in models being selected that were similar to those obtained by the Cornelius F-test (α = 0.05) in traditional AMMI models and cross validation based on leave-one-out. This characteristic allowed more parsimonious models to be chosen and more GEI pattern retained on the first two components. The resulting model chosen by posterior distribution of singular value was also similar to those produced by the cross-validation approach in traditional AMMI models. Our method enables the estimation of credible interval for AMMI biplot plus the choice of AMMI model based on direct posterior
A Bayesian Shrinkage Approach for AMMI Models.
Directory of Open Access Journals (Sweden)
Carlos Pereira da Silva
Full Text Available Linear-bilinear models, especially the additive main effects and multiplicative interaction (AMMI model, are widely applicable to genotype-by-environment interaction (GEI studies in plant breeding programs. These models allow a parsimonious modeling of GE interactions, retaining a small number of principal components in the analysis. However, one aspect of the AMMI model that is still debated is the selection criteria for determining the number of multiplicative terms required to describe the GE interaction pattern. Shrinkage estimators have been proposed as selection criteria for the GE interaction components. In this study, a Bayesian approach was combined with the AMMI model with shrinkage estimators for the principal components. A total of 55 maize genotypes were evaluated in nine different environments using a complete blocks design with three replicates. The results show that the traditional Bayesian AMMI model produces low shrinkage of singular values but avoids the usual pitfalls in determining the credible intervals in the biplot. On the other hand, Bayesian shrinkage AMMI models have difficulty with the credible interval for model parameters, but produce stronger shrinkage of the principal components, converging to GE matrices that have more shrinkage than those obtained using mixed models. This characteristic allowed more parsimonious models to be chosen, and resulted in models being selected that were similar to those obtained by the Cornelius F-test (α = 0.05 in traditional AMMI models and cross validation based on leave-one-out. This characteristic allowed more parsimonious models to be chosen and more GEI pattern retained on the first two components. The resulting model chosen by posterior distribution of singular value was also similar to those produced by the cross-validation approach in traditional AMMI models. Our method enables the estimation of credible interval for AMMI biplot plus the choice of AMMI model based on direct
Andrade, Daniel
2012-01-01
We present a new method to propagate lower bounds on conditional probability distributions in conventional Bayesian networks. Our method guarantees to provide outer approximations of the exact lower bounds. A key advantage is that we can use any available algorithms and tools for Bayesian networks in order to represent and infer lower bounds. This new method yields results that are provable exact for trees with binary variables, and results which are competitive to existing approximations in credal networks for all other network structures. Our method is not limited to a specific kind of network structure. Basically, it is also not restricted to a specific kind of inference, but we restrict our analysis to prognostic inference in this article. The computational complexity is superior to that of other existing approaches.
A Bayesian observer model constrained by efficient coding can explain 'anti-Bayesian' percepts.
Wei, Xue-Xin; Stocker, Alan A
2015-10-01
Bayesian observer models provide a principled account of the fact that our perception of the world rarely matches physical reality. The standard explanation is that our percepts are biased toward our prior beliefs. However, reported psychophysical data suggest that this view may be simplistic. We propose a new model formulation based on efficient coding that is fully specified for any given natural stimulus distribution. The model makes two new and seemingly anti-Bayesian predictions. First, it predicts that perception is often biased away from an observer's prior beliefs. Second, it predicts that stimulus uncertainty differentially affects perceptual bias depending on whether the uncertainty is induced by internal or external noise. We found that both model predictions match reported perceptual biases in perceived visual orientation and spatial frequency, and were able to explain data that have not been explained before. The model is general and should prove applicable to other perceptual variables and tasks. PMID:26343249
Analysing weak orbital signals in Gaia data
Lucy, L B
2014-01-01
Anomalous orbits are found when minimum-chi^{2} estimation is applied to synthetic Gaia data for weak orbital signals - i.e., orbits whose astrometric signatures are comparable to the single-scan measurement error (Pourbaix 2002). These orbits are nearly parabolic, edge-on, and their major axes align with the line-of-sight to the observer. Such orbits violate the Copernican principle (CPr) and as such could be rejected. However, the preferred alternative is to develop a statistical technique that incorporates the CPr as a fundamental postulate. This can be achieved in the context of Bayesian estimation by defining a Copernican prior. With this development, Pourbaix's anomalous orbits no longer arise. Instead, orbits with a somewhat higher chi^{2} but which do not violate the CPr are selected. Other areas of astronomy where the investigator must analyse data from 'imperfect experiments' might similarly benefit from appropriately- defined Copernican priors.
Wu, Yuefeng; Hooker, Giles
2013-01-01
This paper introduces a hierarchical framework to incorporate Hellinger distance methods into Bayesian analysis. We propose to modify a prior over non-parametric densities with the exponential of twice the Hellinger distance between a candidate and a parametric density. By incorporating a prior over the parameters of the second density, we arrive at a hierarchical model in which a non-parametric model is placed between parameters and the data. The parameters of the family can then be estimate...
Bayesian ensemble refinement by replica simulations and reweighting
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.
Bayesian ensemble refinement by replica simulations and reweighting.
Hummer, Gerhard; Köfinger, Jürgen
2015-12-28
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.
Directory of Open Access Journals (Sweden)
Canty Angelo
2007-09-01
Full Text Available Abstract Background This study compares the Bayesian and frequentist (non-Bayesian approaches in the modelling of the association between the risk of preterm birth and maternal proximity to hazardous waste and pollution from the Sydney Tar Pond site in Nova Scotia, Canada. Methods The data includes 1604 observed cases of preterm birth out of a total population of 17559 at risk of preterm birth from 144 enumeration districts in the Cape Breton Regional Municipality. Other covariates include the distance from the Tar Pond; the rate of unemployment to population; the proportion of persons who are separated, divorced or widowed; the proportion of persons who have no high school diploma; the proportion of persons living alone; the proportion of single parent families and average income. Bayesian hierarchical Poisson regression, quasi-likelihood Poisson regression and weighted linear regression models were fitted to the data. Results The results of the analyses were compared together with their limitations. Conclusion The results of the weighted linear regression and the quasi-likelihood Poisson regression agrees with the result from the Bayesian hierarchical modelling which incorporates the spatial effects.
Bayesian multivariate mixed-scale density estimation
Canale, Antonio
2011-01-01
Although univariate continuous density estimation has received abundant attention in the Bayesian nonparametrics literature, there is essentially no theory on multivariate mixed scale density estimation. In this article, we consider a general framework to jointly model continuous, count and categorical variables under a nonparametric prior, which is induced through rounding latent variables having an unknown density with respect to Lesbesgue measure. For the proposed class of priors, we provide sufficient conditions for large support, strong consistency and rates of posterior contraction. These conditions, which primarily relate to the prior on the latent variable density and heaviness of the tails for the observed continuous variables, allow one to convert sufficient conditions obtained in the setting of multivariate continuous density estimation to the mixed scale case. We provide new results in the multivariate continuous density estimation case, showing the Kullback-Leibler property and strong consistency...
Option Pricing Using Bayesian Neural Networks
Pires, Michael Maio
2007-01-01
Options have provided a field of much study because of the complexity involved in pricing them. The Black-Scholes equations were developed to price options but they are only valid for European styled options. There is added complexity when trying to price American styled options and this is why the use of neural networks has been proposed. Neural Networks are able to predict outcomes based on past data. The inputs to the networks here are stock volatility, strike price and time to maturity with the output of the network being the call option price. There are two techniques for Bayesian neural networks used. One is Automatic Relevance Determination (for Gaussian Approximation) and one is a Hybrid Monte Carlo method, both used with Multi-Layer Perceptrons.
Learning Bayesian network structure with immune algorithm
Institute of Scientific and Technical Information of China (English)
Zhiqiang Cai; Shubin Si; Shudong Sun; Hongyan Dui
2015-01-01
Finding out reasonable structures from bulky data is one of the difficulties in modeling of Bayesian network (BN), which is also necessary in promoting the application of BN. This pa-per proposes an immune algorithm based method (BN-IA) for the learning of the BN structure with the idea of vaccination. Further-more, the methods on how to extract the effective vaccines from local optimal structure and root nodes are also described in details. Final y, the simulation studies are implemented with the helicopter convertor BN model and the car start BN model. The comparison results show that the proposed vaccines and the BN-IA can learn the BN structure effectively and efficiently.
Bayesian Stratified Sampling to Assess Corpus Utility
Hochberg, J; Thomas, T; Hall, S; Hochberg, Judith; Scovel, Clint; Thomas, Timothy; Hall, Sam
1998-01-01
This paper describes a method for asking statistical questions about a large text corpus. We exemplify the method by addressing the question, "What percentage of Federal Register documents are real documents, of possible interest to a text researcher or analyst?" We estimate an answer to this question by evaluating 200 documents selected from a corpus of 45,820 Federal Register documents. Stratified sampling is used to reduce the sampling uncertainty of the estimate from over 3100 documents to fewer than 1000. The stratification is based on observed characteristics of real documents, while the sampling procedure incorporates a Bayesian version of Neyman allocation. A possible application of the method is to establish baseline statistics used to estimate recall rates for information retrieval systems.
Bayesian Spatial Modelling with R-INLA
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Finn Lindgren
2015-02-01
Full Text Available The principles behind the interface to continuous domain spatial models in the R- INLA software package for R are described. The integrated nested Laplace approximation (INLA approach proposed by Rue, Martino, and Chopin (2009 is a computationally effective alternative to MCMC for Bayesian inference. INLA is designed for latent Gaussian models, a very wide and flexible class of models ranging from (generalized linear mixed to spatial and spatio-temporal models. Combined with the stochastic partial differential equation approach (SPDE, Lindgren, Rue, and Lindstrm 2011, one can accommodate all kinds of geographically referenced data, including areal and geostatistical ones, as well as spatial point process data. The implementation interface covers stationary spatial mod- els, non-stationary spatial models, and also spatio-temporal models, and is applicable in epidemiology, ecology, environmental risk assessment, as well as general geostatistics.
Bayesian model comparison with intractable likelihoods
Everitt, Richard G; Rowing, Ellen; Evdemon-Hogan, Melina
2015-01-01
Markov random field models are used widely in computer science, statistical physics and spatial statistics and network analysis. However, Bayesian analysis of these models using standard Monte Carlo methods is not possible due to their intractable likelihood functions. Several methods have been developed that permit exact, or close to exact, simulation from the posterior distribution. However, estimating the evidence and Bayes' factors (BFs) for these models remains challenging in general. This paper describes new random weight importance sampling and sequential Monte Carlo methods for estimating BFs that use simulation to circumvent the evaluation of the intractable likelihood, and compares them to existing methods. In some cases we observe an advantage in the use of biased weight estimates; an initial investigation into the theoretical and empirical properties of this class of methods is presented.
Bayesian individualization via sampling-based methods.
Wakefield, J
1996-02-01
We consider the situation where we wish to adjust the dosage regimen of a patient based on (in general) sparse concentration measurements taken on-line. A Bayesian decision theory approach is taken which requires the specification of an appropriate prior distribution and loss function. A simple method for obtaining samples from the posterior distribution of the pharmacokinetic parameters of the patient is described. In general, these samples are used to obtain a Monte Carlo estimate of the expected loss which is then minimized with respect to the dosage regimen. Some special cases which yield analytic solutions are described. When the prior distribution is based on a population analysis then a method of accounting for the uncertainty in the population parameters is described. Two simulation studies showing how the methods work in practice are presented. PMID:8827585
A Nonparametric Bayesian Model for Nested Clustering.
Lee, Juhee; Müller, Peter; Zhu, Yitan; Ji, Yuan
2016-01-01
We propose a nonparametric Bayesian model for clustering where clusters of experimental units are determined by a shared pattern of clustering another set of experimental units. The proposed model is motivated by the analysis of protein activation data, where we cluster proteins such that all proteins in one cluster give rise to the same clustering of patients. That is, we define clusters of proteins by the way that patients group with respect to the corresponding protein activations. This is in contrast to (almost) all currently available models that use shared parameters in the sampling model to define clusters. This includes in particular model based clustering, Dirichlet process mixtures, product partition models, and more. We show results for two typical biostatistical inference problems that give rise to clustering. PMID:26519174
For whom will the Bayesian agents vote?
Caticha, Nestor; Vicente, Renato
2015-01-01
Within an agent-based model where moral classifications are socially learned, we ask if a population of agents behaves in a way that may be compared with conservative or liberal positions in the real political spectrum. We assume that agents first experience a formative period, in which they adjust their learning style acting as supervised Bayesian adaptive learners. The formative phase is followed by a period of social influence by reinforcement learning. By comparing data generated by the agents with data from a sample of 15000 Moral Foundation questionnaires we found the following. 1. The number of information exchanges in the formative phase correlates positively with statistics identifying liberals in the social influence phase. This is consistent with recent evidence that connects the dopamine receptor D4-7R gene, political orientation and early age social clique size. 2. The learning algorithms that result from the formative phase vary in the way they treat novelty and corroborative information with mo...
Bayesian network learning with cutting planes
Cussens, James
2012-01-01
The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which maximises log marginal likelihood (BDe score). Integer programming, specifically the SCIP framework, is used to solve this optimisation problem. Acyclicity constraints are added to the integer program (IP) during solving in the form of cutting planes. Finding good cutting planes is the key to the success of the approach -the search for such cutting planes is effected using a sub-IP. Results show that this is a particularly fast method for exact BN learning.
Exploration vs Exploitation in Bayesian Optimization
Jalali, Ali; Fern, Xiaoli
2012-01-01
The problem of optimizing unknown costly-to-evaluate functions has been studied for a long time in the context of Bayesian Optimization. Algorithms in this field aim to find the optimizer of the function by asking only a few function evaluations at locations carefully selected based on a posterior model. In this paper, we assume the unknown function is Lipschitz continuous. Leveraging the Lipschitz property, we propose an algorithm with a distinct exploration phase followed by an exploitation phase. The exploration phase aims to select samples that shrink the search space as much as possible. The exploitation phase then focuses on the reduced search space and selects samples closest to the optimizer. Considering the Expected Improvement (EI) as a baseline, we empirically show that the proposed algorithm significantly outperforms EI.
Bayesian Estimation of a Mixture Model
Directory of Open Access Journals (Sweden)
Ilhem Merah
2015-05-01
Full Text Available We present the properties of a bathtub curve reliability model having both a sufficient adaptability and a minimal number of parameters introduced by Idée and Pierrat (2010. This one is a mixture of a Gamma distribution G(2, (1/θ and a new distribution L(θ. We are interesting by Bayesian estimation of the parameters and survival function of this model with a squared-error loss function and non-informative prior using the approximations of Lindley (1980 and Tierney and Kadane (1986. Using a statistical sample of 60 failure data relative to a technical device, we illustrate the results derived. Based on a simulation study, comparisons are made between these two methods and the maximum likelihood method of this two parameters model.
Improving randomness characterization through Bayesian model selection
R., Rafael Díaz-H; Martínez, Alí M Angulo; U'Ren, Alfred B; Hirsch, Jorge G; Marsili, Matteo; Castillo, Isaac Pérez
2016-01-01
Nowadays random number generation plays an essential role in technology with important applications in areas ranging from cryptography, which lies at the core of current communication protocols, to Monte Carlo methods, and other probabilistic algorithms. In this context, a crucial scientific endeavour is to develop effective methods that allow the characterization of random number generators. However, commonly employed methods either lack formality (e.g. the NIST test suite), or are inapplicable in principle (e.g. the characterization derived from the Algorithmic Theory of Information (ATI)). In this letter we present a novel method based on Bayesian model selection, which is both rigorous and effective, for characterizing randomness in a bit sequence. We derive analytic expressions for a model's likelihood which is then used to compute its posterior probability distribution. Our method proves to be more rigorous than NIST's suite and the Borel-Normality criterion and its implementation is straightforward. We...
Bayesian hypothesis testing for key comparisons
Wübbeler, Gerd; Bodnar, Olha; Elster, Clemens
2016-08-01
Unilateral degrees of equivalence are the key result in the analysis of key comparison data and they are used to approve, or disapprove, calibration and measurement capabilities of the participating laboratories. To this end, it is checked whether a degree of equivalence differs significantly from zero. Proceeding in such a way can be viewed as carrying out a classical hypothesis test. We develop a Bayesian counterpart to this approach which has the advantage that it can include prior assessment of the corresponding Consultative Committee about the calibration and measurement capabilities of the participating laboratories. Simple expressions are derived and their implementation is provided in terms of MATLAB® and R programs. The novel procedure is illustrated by its application to two recent key comparisons CCL-K1 and CCM.FF-K4.1.2011.
Logistic regression against a divergent Bayesian network
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Noel Antonio Sánchez Trujillo
2015-01-01
Full Text Available This article is a discussion about two statistical tools used for prediction and causality assessment: logistic regression and Bayesian networks. Using data of a simulated example from a study assessing factors that might predict pulmonary emphysema (where fingertip pigmentation and smoking are considered; we posed the following questions. Is pigmentation a confounding, causal or predictive factor? Is there perhaps another factor, like smoking, that confounds? Is there a synergy between pigmentation and smoking? The results, in terms of prediction, are similar with the two techniques; regarding causation, differences arise. We conclude that, in decision-making, the sum of both: a statistical tool, used with common sense, and previous evidence, taking years or even centuries to develop; is better than the automatic and exclusive use of statistical resources.
Modeling Social Annotation: a Bayesian Approach
Plangprasopchok, Anon
2008-01-01
Collaborative tagging systems, such as del.icio.us, CiteULike, and others, allow users to annotate objects, e.g., Web pages or scientific papers, with descriptive labels called tags. The social annotations, contributed by thousands of users, can potentially be used to infer categorical knowledge, classify documents or recommend new relevant information. Traditional text inference methods do not make best use of socially-generated data, since they do not take into account variations in individual users' perspectives and vocabulary. In a previous work, we introduced a simple probabilistic model that takes interests of individual annotators into account in order to find hidden topics of annotated objects. Unfortunately, our proposed approach had a number of shortcomings, including overfitting, local maxima and the requirement to specify values for some parameters. In this paper we address these shortcomings in two ways. First, we extend the model to a fully Bayesian framework. Second, we describe an infinite ver...
Bayesian segmentation of brainstem structures in MRI
DEFF Research Database (Denmark)
Iglesias, Juan Eugenio; Van Leemput, Koen; Bhatt, Priyanka;
2015-01-01
In this paper we present a method to segment four brainstem structures (midbrain, pons, medulla oblongata and superior cerebellar peduncle) from 3D brain MRI scans. The segmentation method relies on a probabilistic atlas of the brainstem and its neighboring brain structures. To build the atlas, we...... combined a dataset of 39 scans with already existing manual delineations of the whole brainstem and a dataset of 10 scans in which the brainstem structures were manually labeled with a protocol that was specifically designed for this study. The resulting atlas can be used in a Bayesian framework to segment...... the brainstem structures in novel scans. Thanks to the generative nature of the scheme, the segmentation method is robust to changes in MRI contrast or acquisition hardware. Using cross validation, we show that the algorithm can segment the structures in previously unseen T1 and FLAIR scans with great accuracy...
Bayesian Cosmic Web Reconstruction: BARCODE for Clusters
Bos, E G Patrick; Kitaura, Francisco; Cautun, Marius
2016-01-01
We describe the Bayesian BARCODE formalism that has been designed towards the reconstruction of the Cosmic Web in a given volume on the basis of the sampled galaxy cluster distribution. Based on the realization that the massive compact clusters are responsible for the major share of the large scale tidal force field shaping the anisotropic and in particular filamentary features in the Cosmic Web. Given the nonlinearity of the constraints imposed by the cluster configurations, we resort to a state-of-the-art constrained reconstruction technique to find a proper statistically sampled realization of the original initial density and velocity field in the same cosmic region. Ultimately, the subsequent gravitational evolution of these initial conditions towards the implied Cosmic Web configuration can be followed on the basis of a proper analytical model or an N-body computer simulation. The BARCODE formalism includes an implicit treatment for redshift space distortions. This enables a direct reconstruction on the ...
Entropic Priors and Bayesian Model Selection
Brewer, Brendon J
2009-01-01
We demonstrate that the principle of maximum relative entropy (ME), used judiciously, can ease the specification of priors in model selection problems. The resulting effect is that models that make sharp predictions are disfavoured, weakening the usual Bayesian "Occam's Razor". This is illustrated with a simple example involving what Jaynes called a "sure thing" hypothesis. Jaynes' resolution of the situation involved introducing a large number of alternative "sure thing" hypotheses that were possible before we observed the data. However, in more complex situations, it may not be possible to explicitly enumerate large numbers of alternatives. The entropic priors formalism produces the desired result without modifying the hypothesis space or requiring explicit enumeration of alternatives; all that is required is a good model for the prior predictive distribution for the data. This idea is illustrated with a simple rigged-lottery example, and we outline how this idea may help to resolve a recent debate amongst ...
Bayesian variable selection with spherically symmetric priors
De Kock, M B
2014-01-01
We propose that Bayesian variable selection for linear parametrisations with Gaussian iid likelihoods be based on the spherical symmetry of the diagonalised parameter space. This reduces the multidimensional parameter space problem to one dimension without the need for conjugate priors. Combining this likelihood with what we call the r-prior results in a framework in which we can derive closed forms for the evidence, posterior and characteristic function for four different r-priors, including the hyper-g prior and the Zellner-Siow prior, which are shown to be special cases of our r-prior. Two scenarios of a single variable dispersion parameter and of fixed dispersion are studied separately, and asymptotic forms comparable to the traditional information criteria are derived. In a simple simulation exercise, we find that model comparison based on our uniform r-prior appears to fare better than the current model comparison schemes.
Bayesian Overlapping Community Detection in Dynamic Networks
Ghorbani, Mahsa; Khodadadi, Ali
2016-01-01
Detecting community structures in social networks has gained considerable attention in recent years. However, lack of prior knowledge about the number of communities, and their overlapping nature have made community detection a challenging problem. Moreover, many of the existing methods only consider static networks, while most of real world networks are dynamic and evolve over time. Hence, finding consistent overlapping communities in dynamic networks without any prior knowledge about the number of communities is still an interesting open research problem. In this paper, we present an overlapping community detection method for dynamic networks called Dynamic Bayesian Overlapping Community Detector (DBOCD). DBOCD assumes that in every snapshot of network, overlapping parts of communities are dense areas and utilizes link communities instead of common node communities. Using Recurrent Chinese Restaurant Process and community structure of the network in the last snapshot, DBOCD simultaneously extracts the numbe...
Human collective intelligence as distributed Bayesian inference
Krafft, Peter M; Pan, Wei; Della Penna, Nicolás; Altshuler, Yaniv; Shmueli, Erez; Tenenbaum, Joshua B; Pentland, Alex
2016-01-01
Collective intelligence is believed to underly the remarkable success of human society. The formation of accurate shared beliefs is one of the key components of human collective intelligence. How are accurate shared beliefs formed in groups of fallible individuals? Answering this question requires a multiscale analysis. We must understand both the individual decision mechanisms people use, and the properties and dynamics of those mechanisms in the aggregate. As of yet, mathematical tools for such an approach have been lacking. To address this gap, we introduce a new analytical framework: We propose that groups arrive at accurate shared beliefs via distributed Bayesian inference. Distributed inference occurs through information processing at the individual level, and yields rational belief formation at the group level. We instantiate this framework in a new model of human social decision-making, which we validate using a dataset we collected of over 50,000 users of an online social trading platform where inves...
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...... complex prior representation achieve improved sparsity representations in low signalto- noise ratio as opposed to state-of-the-art sparse estimators. This result is of particular importance for the applicability of the algorithms in the field of channel estimation. We then derive various iterative...... and computational complexity. We also analyze the impact of transceiver filters on the sparseness of the channel response, and propose a dictionary design that permits the deployment of sparse inference methods in conditions of low bandwidth....
Bayesian isochrone fitting and stellar ages
Valls-Gabaud, D
2016-01-01
Stellar evolution theory has been extraordinarily successful at explaining the different phases under which stars form, evolve and die. While the strongest constraints have traditionally come from binary stars, the advent of asteroseismology is bringing unique measures in well-characterised stars. For stellar populations in general, however, only photometric measures are usually available, and the comparison with the predictions of stellar evolution theory have mostly been qualitative. For instance, the geometrical shapes of isochrones have been used to infer ages of coeval populations, but without any proper statistical basis. In this chapter we provide a pedagogical review on a Bayesian formalism to make quantitative inferences on the properties of single, binary and small ensembles of stars, including unresolved populations. As an example, we show how stellar evolution theory can be used in a rigorous way as a prior information to measure the ages of stars between the ZAMS and the Helium flash, and their u...
A guide to Bayesian model selection for ecologists
Hooten, Mevin B.; Hobbs, N.T.
2015-01-01
The steady upward trend in the use of model selection and Bayesian methods in ecological research has made it clear that both approaches to inference are important for modern analysis of models and data. However, in teaching Bayesian methods and in working with our research colleagues, we have noticed a general dissatisfaction with the available literature on Bayesian model selection and multimodel inference. Students and researchers new to Bayesian methods quickly find that the published advice on model selection is often preferential in its treatment of options for analysis, frequently advocating one particular method above others. The recent appearance of many articles and textbooks on Bayesian modeling has provided welcome background on relevant approaches to model selection in the Bayesian framework, but most of these are either very narrowly focused in scope or inaccessible to ecologists. Moreover, the methodological details of Bayesian model selection approaches are spread thinly throughout the literature, appearing in journals from many different fields. Our aim with this guide is to condense the large body of literature on Bayesian approaches to model selection and multimodel inference and present it specifically for quantitative ecologists as neutrally as possible. We also bring to light a few important and fundamental concepts relating directly to model selection that seem to have gone unnoticed in the ecological literature. Throughout, we provide only a minimal discussion of philosophy, preferring instead to examine the breadth of approaches as well as their practical advantages and disadvantages. This guide serves as a reference for ecologists using Bayesian methods, so that they can better understand their options and can make an informed choice that is best aligned with their goals for inference.
Study of Online Bayesian Networks Learning in a Multi-Agent System
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Yonghui Cao
2013-01-01
Full Text Available This paper introduces online Bayesian network learning in detail. The structural and parametric learning abilities of the online Bayesian network learning are explored. The paper starts with revisiting the multi-agent self-organization problem and the proposed solution. Then, we explain the proposed Bayesian network learning, three scoring functions, namely Log-Likelihood, Minimum description length, and Bayesian scores.
Bayesian exploration for intelligent identification of textures.
Fishel, Jeremy A; Loeb, Gerald E
2012-01-01
In order to endow robots with human-like abilities to characterize and identify objects, they must be provided with tactile sensors and intelligent algorithms to select, control, and interpret data from useful exploratory movements. Humans make informed decisions on the sequence of exploratory movements that would yield the most information for the task, depending on what the object may be and prior knowledge of what to expect from possible exploratory movements. This study is focused on texture discrimination, a subset of a much larger group of exploratory movements and percepts that humans use to discriminate, characterize, and identify objects. Using a testbed equipped with a biologically inspired tactile sensor (the BioTac), we produced sliding movements similar to those that humans make when exploring textures. Measurement of tactile vibrations and reaction forces when exploring textures were used to extract measures of textural properties inspired from psychophysical literature (traction, roughness, and fineness). Different combinations of normal force and velocity were identified to be useful for each of these three properties. A total of 117 textures were explored with these three movements to create a database of prior experience to use for identifying these same textures in future encounters. When exploring a texture, the discrimination algorithm adaptively selects the optimal movement to make and property to measure based on previous experience to differentiate the texture from a set of plausible candidates, a process we call Bayesian exploration. Performance of 99.6% in correctly discriminating pairs of similar textures was found to exceed human capabilities. Absolute classification from the entire set of 117 textures generally required a small number of well-chosen exploratory movements (median = 5) and yielded a 95.4% success rate. The method of Bayesian exploration developed and tested in this paper may generalize well to other cognitive problems.
Bayesian exploration for intelligent identification of textures
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Jeremy A. Fishel
2012-06-01
Full Text Available In order to endow robots with humanlike abilities to characterize and identify objects, they must be provided with tactile sensors and intelligent algorithms to select, control and interpret data from useful exploratory movements. Humans make informed decisions on the sequence of exploratory movements that would yield the most information for the task, depending on what the object may be and prior knowledge of what to expect from possible exploratory movements. This study is focused on texture discrimination, a subset of a much larger group of exploratory movements and percepts that humans use to discriminate, characterize, and identify objects. Using a testbed equipped with a biologically inspired tactile sensor (the BioTac® we produced sliding movements similar to those that humans make when exploring textures. Measurement of tactile vibrations and reaction forces when exploring textures were used to extract measures of textural properties inspired from psychophysical literature (traction, roughness, and fineness. Different combinations of normal force and velocity were identified to be useful for each of these three properties. A total of 117 textures were explored with these three movements to create a database of prior experience to use for identifying these same textures in future encounters. When exploring a texture, the discrimination algorithm adaptively selects the optimal movement to make and property to measure based on previous experience to differentiate the texture from a set of plausible candidates, a process we call Bayesian exploration. Performance of 99.6% in correctly discriminating pairs of similar textures was found to exceed human capabilities. Absolute classification from the entire set of 117 textures generally required a small number of well-chosen exploratory movements (median=5 and yielded a 95.4% success rate. The method of Bayesian exploration developed and tested in this paper may generalize well to other
A Bayesian Framework for SNP Identification
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Webb-Robertson, Bobbie-Jo M.; Havre, Susan L.; Payne, Deborah A.
2005-07-01
Current proteomics techniques, such as mass spectrometry, focus on protein identification, usually ignoring most types of modifications beyond post-translational modifications, with the assumption that only a small number of peptides have to be matched to a protein for a positive identification. However, not all proteins are being identified with current techniques and improved methods to locate points of mutation are becoming a necessity. In the case when single-nucleotide polymorphisms (SNPs) are observed, brute force is the most common method to locate them, quickly becoming computationally unattractive as the size of the database associated with the model organism grows. We have developed a Bayesian model for SNPs, BSNP, incorporating evolutionary information at both the nucleotide and amino acid levels. Formulating SNPs as a Bayesian inference problem allows probabilities of interest to be easily obtained, for example the probability of a specific SNP or specific type of mutation over a gene or entire genome. Three SNP databases were observed in the evaluation of the BSNP model; the first SNP database is a disease specific gene in human, hemoglobin, the second is also a disease specific gene in human, p53, and the third is a more general SNP database for multiple genes in mouse. We validate that the BSNP model assigns higher posterior probabilities to the SNPs defined in all three separate databases than can be attributed to chance under specific evolutionary information, for example the amino acid model described by Majewski and Ott in conjunction with either the four-parameter nucleotide model by Bulmer or seven-parameter nucleotide model by Majewski and Ott.
MERGING DIGITAL SURFACE MODELS IMPLEMENTING BAYESIAN APPROACHES
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H. Sadeq
2016-06-01
Full Text Available In this research different DSMs from different sources have been merged. The merging is based on a probabilistic model using a Bayesian Approach. The implemented data have been sourced from very high resolution satellite imagery sensors (e.g. WorldView-1 and Pleiades. It is deemed preferable to use a Bayesian Approach when the data obtained from the sensors are limited and it is difficult to obtain many measurements or it would be very costly, thus the problem of the lack of data can be solved by introducing a priori estimations of data. To infer the prior data, it is assumed that the roofs of the buildings are specified as smooth, and for that purpose local entropy has been implemented. In addition to the a priori estimations, GNSS RTK measurements have been collected in the field which are used as check points to assess the quality of the DSMs and to validate the merging result. The model has been applied in the West-End of Glasgow containing different kinds of buildings, such as flat roofed and hipped roofed buildings. Both quantitative and qualitative methods have been employed to validate the merged DSM. The validation results have shown that the model was successfully able to improve the quality of the DSMs and improving some characteristics such as the roof surfaces, which consequently led to better representations. In addition to that, the developed model has been compared with the well established Maximum Likelihood model and showed similar quantitative statistical results and better qualitative results. Although the proposed model has been applied on DSMs that were derived from satellite imagery, it can be applied to any other sourced DSMs.