A Bayesian Markov geostatistical model for estimation of hydrogeological properties
International Nuclear Information System (INIS)
A geostatistical methodology based on Markov-chain analysis and Bayesian statistics was developed for probability estimations of hydrogeological and geological properties in the siting process of a nuclear waste repository. The probability estimates have practical use in decision-making on issues such as siting, investigation programs, and construction design. The methodology is nonparametric which makes it possible to handle information that does not exhibit standard statistical distributions, as is often the case for classified information. Data do not need to meet the requirements on additivity and normality as with the geostatistical methods based on regionalized variable theory, e.g., kriging. The methodology also has a formal way for incorporating professional judgments through the use of Bayesian statistics, which allows for updating of prior estimates to posterior probabilities each time new information becomes available. A Bayesian Markov Geostatistical Model (BayMar) software was developed for implementation of the methodology in two and three dimensions. This paper gives (1) a theoretical description of the Bayesian Markov Geostatistical Model; (2) a short description of the BayMar software; and (3) an example of application of the model for estimating the suitability for repository establishment with respect to the three parameters of lithology, hydraulic conductivity, and rock quality designation index (RQD) at 400--500 meters below ground surface in an area around the Aespoe Hard Rock Laboratory in southeastern Sweden
Bayesian Geostatistical Design
DEFF Research Database (Denmark)
Diggle, Peter; Lophaven, Søren Nymand
2006-01-01
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...
Bayesian Analysis of Geostatistical Models With an Auxiliary Lattice
Park, Jincheol
2012-04-01
The Gaussian geostatistical model has been widely used for modeling spatial data. However, this model suffers from a severe difficulty in computation: it requires users to invert a large covariance matrix. This is infeasible when the number of observations is large. In this article, we propose an auxiliary lattice-based approach for tackling this difficulty. By introducing an auxiliary lattice to the space of observations and defining a Gaussian Markov random field on the auxiliary lattice, our model completely avoids the requirement of matrix inversion. It is remarkable that the computational complexity of our method is only O(n), where n is the number of observations. Hence, our method can be applied to very large datasets with reasonable computational (CPU) times. The numerical results indicate that our model can approximate Gaussian random fields very well in terms of predictions, even for those with long correlation lengths. For real data examples, our model can generally outperform conventional Gaussian random field models in both prediction errors and CPU times. Supplemental materials for the article are available online. © 2012 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.
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...
A Bayesian spatio-temporal geostatistical model with an auxiliary lattice for large datasets
Xu, Ganggang
2015-01-01
When spatio-temporal datasets are large, the computational burden can lead to failures in the implementation of traditional geostatistical tools. In this paper, we propose a computationally efficient Bayesian hierarchical spatio-temporal model in which the spatial dependence is approximated by a Gaussian Markov random field (GMRF) while the temporal correlation is described using a vector autoregressive model. By introducing an auxiliary lattice on the spatial region of interest, the proposed method is not only able to handle irregularly spaced observations in the spatial domain, but it is also able to bypass the missing data problem in a spatio-temporal process. Because the computational complexity of the proposed Markov chain Monte Carlo algorithm is of the order O(n) with n the total number of observations in space and time, our method can be used to handle very large spatio-temporal datasets with reasonable CPU times. The performance of the proposed model is illustrated using simulation studies and a dataset of precipitation data from the coterminous United States.
Predictive risk mapping of schistosomiasis in Brazil using Bayesian geostatistical models.
Scholte, Ronaldo G C; Gosoniu, Laura; Malone, John B; Chammartin, Frédérique; Utzinger, Jürg; Vounatsou, Penelope
2014-04-01
Schistosomiasis is one of the most common parasitic diseases in tropical and subtropical areas, including Brazil. A national control programme was initiated in Brazil in the mid-1970s and proved successful in terms of morbidity control, as the number of cases with hepato-splenic involvement was reduced significantly. To consolidate control and move towards elimination, there is a need for reliable maps on the spatial distribution of schistosomiasis, so that interventions can target communities at highest risk. The purpose of this study was to map the distribution of Schistosoma mansoni in Brazil. We utilized readily available prevalence data from the national schistosomiasis control programme for the years 2005-2009, derived remotely sensed climatic and environmental data and obtained socioeconomic data from various sources. Data were collated into a geographical information system and Bayesian geostatistical models were developed. Model-based maps identified important risk factors related to the transmission of S. mansoni and confirmed that environmental variables are closely associated with indices of poverty. Our smoothed predictive risk map, including uncertainty, highlights priority areas for intervention, namely the northern parts of North and Southeast regions and the eastern part of Northeast region. Our predictive risk map provides a useful tool for to strengthen existing surveillance-response mechanisms. PMID:24361640
Diggle, Peter J
2007-01-01
Model-based geostatistics refers to the application of general statistical principles of modeling and inference to geostatistical problems. This volume provides a treatment of model-based geostatistics and emphasizes on statistical methods and applications. It also features analyses of datasets from a range of scientific contexts.
Energy Technology Data Exchange (ETDEWEB)
Kara G. Eby
2010-08-01
At the Idaho National Laboratory (INL) Cs-137 concentrations above the U.S. Environmental Protection Agency risk-based threshold of 0.23 pCi/g may increase the risk of human mortality due to cancer. As a leader in nuclear research, the INL has been conducting nuclear activities for decades. Elevated anthropogenic radionuclide levels including Cs-137 are a result of atmospheric weapons testing, the Chernobyl accident, and nuclear activities occurring at the INL site. Therefore environmental monitoring and long-term surveillance of Cs-137 is required to evaluate risk. However, due to the large land area involved, frequent and comprehensive monitoring is limited. Developing a spatial model that predicts Cs-137 concentrations at unsampled locations will enhance the spatial characterization of Cs-137 in surface soils, provide guidance for an efficient monitoring program, and pinpoint areas requiring mitigation strategies. The predictive model presented herein is based on applied geostatistics using a Bayesian analysis of environmental characteristics across the INL site, which provides kriging spatial maps of both Cs-137 estimates and prediction errors. Comparisons are presented of two different kriging methods, showing that the use of secondary information (i.e., environmental characteristics) can provide improved prediction performance in some areas of the INL site.
Archie C.A. Clements; MOYEED, RANA; Brooker, Simon
2006-01-01
A Bayesian geostatistical model was developed to predict the intensity of infection with Schistosoma mansoni in East Africa. Epidemiological data from purposively-designed and standardized surveys were available for 31,458 schoolchildren (90% aged between 6-16 years) from 459 locations across the region and used in combination with remote sensing environmental data to identify factors associated with spatial variation in infection patterns. The geostatistical model explicitly takes into accou...
Geostatistical models for air pollution
International Nuclear Information System (INIS)
The objective of this paper is to present geostatistical models applied to the spatial characterisation of air pollution phenomena. A concise presentation of the geostatistical methodologies is illustrated with practical examples. The case study was conducted in an underground copper-mine located on the southern of Portugal, where a biomonitoring program using lichens has been implemented. Given the characteristics of lichens as indicators of air pollution it was possible to gather a great amount of data in space, which enabled the development and application of geostatistical methodologies. The advantages of using geostatistical models compared with deterministic models, as environmental control tools, are highlighted. (author)
An interactive Bayesian geostatistical inverse protocol for hydraulic tomography
Fienen, Michael N.; Clemo, Tom; Kitanidis, Peter K.
2008-01-01
Hydraulic tomography is a powerful technique for characterizing heterogeneous hydrogeologic parameters. An explicit trade-off between characterization based on measurement misfit and subjective characterization using prior information is presented. We apply a Bayesian geostatistical inverse approach that is well suited to accommodate a flexible model with the level of complexity driven by the data and explicitly considering uncertainty. Prior information is incorporated through the selection of a parameter covariance model characterizing continuity and providing stability. Often, discontinuities in the parameter field, typically caused by geologic contacts between contrasting lithologic units, necessitate subdivision into zones across which there is no correlation among hydraulic parameters. We propose an interactive protocol in which zonation candidates are implied from the data and are evaluated using cross validation and expert knowledge. Uncertainty introduced by limited knowledge of dynamic regional conditions is mitigated by using drawdown rather than native head values. An adjoint state formulation of MODFLOW-2000 is used to calculate sensitivities which are used both for the solution to the inverse problem and to guide protocol decisions. The protocol is tested using synthetic two-dimensional steady state examples in which the wells are located at the edge of the region of interest.
Geostatistical Modeling of Pore Velocity
Energy Technology Data Exchange (ETDEWEB)
Devary, J.L.; Doctor, P.G.
1981-06-01
A significant part of evaluating a geologic formation as a nuclear waste repository involves the modeling of contaminant transport in the surrounding media in the event the repository is breached. The commonly used contaminant transport models are deterministic. However, the spatial variability of hydrologic field parameters introduces uncertainties into contaminant transport predictions. This paper discusses the application of geostatistical techniques to the modeling of spatially varying hydrologic field parameters required as input to contaminant transport analyses. Kriging estimation techniques were applied to Hanford Reservation field data to calculate hydraulic conductivity and the ground-water potential gradients. These quantities were statistically combined to estimate the groundwater pore velocity and to characterize the pore velocity estimation error. Combining geostatistical modeling techniques with product error propagation techniques results in an effective stochastic characterization of groundwater pore velocity, a hydrologic parameter required for contaminant transport analyses.
Troldborg, M.; Nowak, W.; Binning, P. J.; Bjerg, P. L.
2012-12-01
Estimates of mass discharge (mass/time) are increasingly being used when assessing risks of groundwater contamination and designing remedial systems at contaminated sites. Mass discharge estimates are, however, prone to rather large uncertainties as they integrate uncertain spatial distributions of both concentration and groundwater flow velocities. For risk assessments or any other decisions that are being based on mass discharge estimates, it is essential to address these uncertainties. We present a novel Bayesian geostatistical approach for quantifying the uncertainty of the mass discharge across a multilevel control plane. The method decouples the flow and transport simulation and has the advantage of avoiding the heavy computational burden of three-dimensional numerical flow and transport simulation coupled with geostatistical inversion. It may therefore be of practical relevance to practitioners compared to existing methods that are either too simple or computationally demanding. The method is based on conditional geostatistical simulation and accounts for i) heterogeneity of both the flow field and the concentration distribution through Bayesian geostatistics (including the uncertainty in covariance functions), ii) measurement uncertainty, and iii) uncertain source zone geometry and transport parameters. The method generates multiple equally likely realizations of the spatial flow and concentration distribution, which all honour the measured data at the control plane. The flow realizations are generated by analytical co-simulation of the hydraulic conductivity and the hydraulic gradient across the control plane. These realizations are made consistent with measurements of both hydraulic conductivity and head at the site. An analytical macro-dispersive transport solution is employed to simulate the mean concentration distribution across the control plane, and a geostatistical model of the Box-Cox transformed concentration data is used to simulate observed
Boysen, Courtney; Davis, Elizabeth G.; Beard, Laurie A.; Lubbers, Brian V.; Raghavan, Ram K.
2015-01-01
Kansas witnessed an unprecedented outbreak in Corynebacterium pseudotuberculosis infection among horses, a disease commonly referred to as pigeon fever during fall 2012. Bayesian geostatistical models were developed to identify key environmental and climatic risk factors associated with C. pseudotuberculosis infection in horses. Positive infection status among horses (cases) was determined by positive test results for characteristic abscess formation, positive bacterial culture on purulent material obtained from a lanced abscess (n = 82), or positive serologic evidence of exposure to organism (≥1:512)(n = 11). Horses negative for these tests (n = 172)(controls) were considered free of infection. Information pertaining to horse demographics and stabled location were obtained through review of medical records and/or contact with horse owners via telephone. Covariate information for environmental and climatic determinants were obtained from USDA (soil attributes), USGS (land use/land cover), and NASA MODIS and NASA Prediction of Worldwide Renewable Resources (climate). Candidate covariates were screened using univariate regression models followed by Bayesian geostatistical models with and without covariates. The best performing model indicated a protective effect for higher soil moisture content (OR = 0.53, 95% CrI = 0.25, 0.71), and detrimental effects for higher land surface temperature (≥35°C) (OR = 2.81, 95% CrI = 2.21, 3.85) and habitat fragmentation (OR = 1.31, 95% CrI = 1.27, 2.22) for C. pseudotuberculosis infection status in horses, while age, gender and breed had no effect. Preventative and ecoclimatic significance of these findings are discussed. PMID:26473728
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...... 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...
Uncertainty of mass discharge estimates from contaminated sites using a fully Bayesian framework
DEFF Research Database (Denmark)
Troldborg, Mads; Nowak, Wolfgang; Binning, Philip John; Bjerg, Poul Løgstrup; Helmig, Rainer
plane. The method accounts for: (1) conceptual model uncertainty through Bayesian model averaging, (2) heterogeneity through Bayesian geostatistics with an uncertain geostatistical model, and (3) measurement uncertainty. An ensemble of unconditional steady-state plume realizations is generated through...
DEFF Research Database (Denmark)
Troldborg, Mads; Nowak, Wolfgang; Binning, Philip John;
multilevel control plane. The method decouples the flow and transport simulation and has the advantage of avoiding the heavy computational burden of three-dimensional numerical flow and transport simulation coupled with geostatistical inversion. It may therefore be of practical relevance to practitioners...... hydraulic gradient across the control plane and are consistent with measurements of both hydraulic conductivity and head at the site. An analytical macro-dispersive transport solution is employed to simulate the mean concentration distribution across the control plane, and a geostatistical model of the Box-Cox...
Reservoir Modeling Combining Geostatistics with Markov Chain Monte Carlo Inversion
DEFF Research Database (Denmark)
Zunino, Andrea; Lange, Katrine; Melnikova, Yulia;
2014-01-01
geostatistics. The geostatistical algorithm learns the multiple-point statistics from prototype models, then generates proposal models which are tested by a Metropolis sampler. The solution of the inverse problem is finally represented by a collection of reservoir models in terms of facies and porosity, which...
Geostatistical methods applied to field model residuals
DEFF Research Database (Denmark)
Maule, Fox; Mosegaard, K.; Olsen, Nils
The geomagnetic field varies on a variety of time- and length scales, which are only rudimentary considered in most present field models. The part of the observed field that can not be explained by a given model, the model residuals, is often considered as an estimate of the data uncertainty (which...... consists of measurement errors and unmodelled signal), and is typically assumed to be uncorrelated and Gaussian distributed. We have applied geostatistical methods to analyse the residuals of the Oersted(09d/04) field model [http://www.dsri.dk/Oersted/Field_models/IGRF_2005_candidates/], which is based...... on 5 years of Ørsted and CHAMP data, and includes secular variation and acceleration, as well as low-degree external (magnetospheric) and induced fields. The analysis is done in order to find the statistical behaviour of the space-time structure of the residuals, as a proxy for the data covariances...
Bayesian Spatial Modelling with R-INLA
Directory of Open Access Journals (Sweden)
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.
International Nuclear Information System (INIS)
The use of statistical methodology in the Hydrogeochemical and Stream Sediment Reconnaissance Program of the National Uranium Resource Evaluation (NURE) Program is useful in identifying local and regional trends related to uranium provinces and districts. Additionally, appropriate statistical summarization of the data is important in any subsequent evaluation. Since as many as 190,000 samples are to be collected during the Oak Ridge Program, it is necessary to computerize most statistical procedures to enable timely release of the data. These automated procedures are developed through the interaction of geologists, statisticians, and computer personnel. This team effort is designed to efficiently produce meaningful geologic results that are statistically sound. The following discussion will present a brief explanation of the regional technique of weighted sum contouring and a localized technique of cluster analysis. In both of these methods, the geologist constructs a geochemical model by selecting appropriate uranium related parameters and assigning the relative importance to each parameter in the model. The model can then be evaluated by relating the patterns defined by the analysis to the geologic formations and any known uranium mineralization
Bayesian default probability models
Andrlíková, Petra
2014-01-01
This paper proposes a methodology for default probability estimation for low default portfolios, where the statistical inference may become troublesome. The author suggests using logistic regression models with the Bayesian estimation of parameters. The piecewise logistic regression model and Box-Cox transformation of credit risk score is used to derive the estimates of probability of default, which extends the work by Neagu et al. (2009). The paper shows that the Bayesian models are more acc...
Institute of Scientific and Technical Information of China (English)
ZHANG Jingxiong; LI Deren
2005-01-01
This paper seeks a synthesis of Bayesian and geostatistical approaches to combining categorical data in the context of remote sensing classification.By experiment with aerial photographs and Landsat TM data, accuracy of spectral, spatial, and combined classification results was evaluated.It was confirmed that the incorporation of spatial information in spectral classification increases accuracy significantly.Secondly, through test with a 5-class and a 3-class classification schemes, it was revealed that setting a proper semantic framework for classification is fundamental to any endeavors of categorical mapping and the most important factor affecting accuracy.Lastly, this paper promotes non-parametric methods for both definition of class membership profiling based on band-specific histograms of image intensities and derivation of spatial probability via indicator kriging, a non-parametric geostatistical technique.
Geostatistical analysis using K-splines in the geoadditive model
Vandendijck, Yannick; Faes, Christel; Hens, Niel
2015-01-01
In geostatistics, both kriging and smoothing splines are commonly used to predict a quantity of interest. The geoadditive model proposed by Kammann and Wand (2003) represents a fusion of kriging and penalized spline additive models. The fact that the underlying spatial covariance structure is poorly estimated using geoadditive models is a drawback. We describe K-splines, an extension of geoadditive models such that estimation of the underlying spatial process parameters and predictions ...
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
Fractal and geostatistical methods for modeling of a fracture network
International Nuclear Information System (INIS)
The modeling of fracture networks is useful for fluid flow and rock mechanics studies. About 6600 fracture traces were recorded on drifts of a uranium mine in a granite massif. The traces have an extension of 0.20-20 m. The network was studied by fractal and by geostatistical methods but can be considered neither as a fractal with a constant dimension nor a set of purely randomly located fractures. Two kinds of generalization of conventional models can still provide more flexibility for the characterization of the network: (a) a nonscaling fractal model with variable similarity dimension (for a 2-D network of traces, the dimension varying from 2 for the 10-m scale to 1 for the centimeter scale, (b) a parent-daughter model with a regionalized density; the geostatistical study allows a 3-D model to be established where: fractures are assumed to be discs; fractures are grouped in clusters or swarms; and fracturation density is regionalized (with two ranges at about 30 and 300 m). The fractal model is easy to fit and to simulate along a line, but 2-D and 3-D simulations are more difficult. The geostatistical model is more complex, but easy to simulate, even in 3-D
Fractal and geostatistical methods for modeling of a fracture network
Energy Technology Data Exchange (ETDEWEB)
Chiles, J.P.
1988-08-01
The modeling of fracture networks is useful for fluid flow and rock mechanics studies. About 6600 fracture traces were recorded on drifts of a uranium mine in a granite massif. The traces have an extension of 0.20-20 m. The network was studied by fractal and by geostatistical methods but can be considered neither as a fractal with a constant dimension nor a set of purely randomly located fractures. Two kinds of generalization of conventional models can still provide more flexibility for the characterization of the network: (a) a nonscaling fractal model with variable similarity dimension (for a 2-D network of traces, the dimension varying from 2 for the 10-m scale to 1 for the centimeter scale, (b) a parent-daughter model with a regionalized density; the geostatistical study allows a 3-D model to be established where: fractures are assumed to be discs; fractures are grouped in clusters or swarms; and fracturation density is regionalized (with two ranges at about 30 and 300 m). The fractal model is easy to fit and to simulate along a line, but 2-D and 3-D simulations are more difficult. The geostatistical model is more complex, but easy to simulate, even in 3-D.
Stochastic Local Interaction (SLI) model: Bridging machine learning and geostatistics
Hristopulos, Dionissios T.
2015-12-01
Machine learning and geostatistics are powerful mathematical frameworks for modeling spatial data. Both approaches, however, suffer from poor scaling of the required computational resources for large data applications. We present the Stochastic Local Interaction (SLI) model, which employs a local representation to improve computational efficiency. SLI combines geostatistics and machine learning with ideas from statistical physics and computational geometry. It is based on a joint probability density function defined by an energy functional which involves local interactions implemented by means of kernel functions with adaptive local kernel bandwidths. SLI is expressed in terms of an explicit, typically sparse, precision (inverse covariance) matrix. This representation leads to a semi-analytical expression for interpolation (prediction), which is valid in any number of dimensions and avoids the computationally costly covariance matrix inversion.
Chen, Xingyuan; Murakami, Haruko; Hahn, Melanie S.; Hammond, Glenn E.; Rockhold, Mark L.; Zachara, John M.; Rubin, Yoram
2012-06-01
Tracer tests performed under natural or forced gradient flow conditions can provide useful information for characterizing subsurface properties, through monitoring, modeling, and interpretation of the tracer plume migration in an aquifer. Nonreactive tracer experiments were conducted at the Hanford 300 Area, along with constant-rate injection tests and electromagnetic borehole flowmeter tests. A Bayesian data assimilation technique, the method of anchored distributions (MAD) (Rubin et al., 2010), was applied to assimilate the experimental tracer test data with the other types of data and to infer the three-dimensional heterogeneous structure of the hydraulic conductivity in the saturated zone of the Hanford formation.In this study, the Bayesian prior information on the underlying random hydraulic conductivity field was obtained from previous field characterization efforts using constant-rate injection and borehole flowmeter test data. The posterior distribution of the conductivity field was obtained by further conditioning the field on the temporal moments of tracer breakthrough curves at various observation wells. MAD was implemented with the massively parallel three-dimensional flow and transport code PFLOTRAN to cope with the highly transient flow boundary conditions at the site and to meet the computational demands of MAD. A synthetic study proved that the proposed method could effectively invert tracer test data to capture the essential spatial heterogeneity of the three-dimensional hydraulic conductivity field. Application of MAD to actual field tracer data at the Hanford 300 Area demonstrates that inverting for spatial heterogeneity of hydraulic conductivity under transient flow conditions is challenging and more work is needed.
Arshia Amiri; Ulf-G Gerdtham
2012-01-01
This paper introduces a new way of investigating linear and nonlinear Granger causality between exports, imports and economic growth in France over the period 1961_2006 with using geostatistical models (kiriging and Inverse distance weighting). Geostatistical methods are the ordinary methods for forecasting the locatins and making map in water engineerig, environment, environmental pollution, mining, ecology, geology and geography. Although, this is the first time which geostatistics knowledg...
Slater, Hannah; Michael, Edwin
2013-01-01
There is increasing interest to control or eradicate the major neglected tropical diseases. Accurate modelling of the geographic distributions of parasitic infections will be crucial to this endeavour. We used 664 community level infection prevalence data collated from the published literature in conjunction with eight environmental variables, altitude and population density, and a multivariate Bayesian generalized linear spatial model that allows explicit accounting for spatial autocorrelation and incorporation of uncertainty in input data and model parameters, to construct the first spatially-explicit map describing LF prevalence distribution in Africa. We also ran the best-fit model against predictions made by the HADCM3 and CCCMA climate models for 2050 to predict the likely distributions of LF under future climate and population changes. We show that LF prevalence is strongly influenced by spatial autocorrelation between locations but is only weakly associated with environmental covariates. Infection prevalence, however, is found to be related to variations in population density. All associations with key environmental/demographic variables appear to be complex and non-linear. LF prevalence is predicted to be highly heterogenous across Africa, with high prevalences (>20%) estimated to occur primarily along coastal West and East Africa, and lowest prevalences predicted for the central part of the continent. Error maps, however, indicate a need for further surveys to overcome problems with data scarcity in the latter and other regions. Analysis of future changes in prevalence indicates that population growth rather than climate change per se will represent the dominant factor in the predicted increase/decrease and spread of LF on the continent. We indicate that these results could play an important role in aiding the development of strategies that are best able to achieve the goals of parasite elimination locally and globally in a manner that may also account
Model-Based Geostatistical Mapping of the Prevalence of Onchocerca volvulus in West Africa
O’Hanlon, Simon J.; Slater, Hannah C.; Cheke, Robert A.; Boatin, Boakye A.; Coffeng, Luc E.; Pion, Sébastien D. S.; Boussinesq, Michel; Zouré, Honorat G. M.; Stolk, Wilma A.; Basáñez, María-Gloria
2016-01-01
Background The initial endemicity (pre-control prevalence) of onchocerciasis has been shown to be an important determinant of the feasibility of elimination by mass ivermectin distribution. We present the first geostatistical map of microfilarial prevalence in the former Onchocerciasis Control Programme in West Africa (OCP) before commencement of antivectorial and antiparasitic interventions. Methods and Findings Pre-control microfilarial prevalence data from 737 villages across the 11 constituent countries in the OCP epidemiological database were used as ground-truth data. These 737 data points, plus a set of statistically selected environmental covariates, were used in a Bayesian model-based geostatistical (B-MBG) approach to generate a continuous surface (at pixel resolution of 5 km x 5km) of microfilarial prevalence in West Africa prior to the commencement of the OCP. Uncertainty in model predictions was measured using a suite of validation statistics, performed on bootstrap samples of held-out validation data. The mean Pearson’s correlation between observed and estimated prevalence at validation locations was 0.693; the mean prediction error (average difference between observed and estimated values) was 0.77%, and the mean absolute prediction error (average magnitude of difference between observed and estimated values) was 12.2%. Within OCP boundaries, 17.8 million people were deemed to have been at risk, 7.55 million to have been infected, and mean microfilarial prevalence to have been 45% (range: 2–90%) in 1975. Conclusions and Significance This is the first map of initial onchocerciasis prevalence in West Africa using B-MBG. Important environmental predictors of infection prevalence were identified and used in a model out-performing those without spatial random effects or environmental covariates. Results may be compared with recent epidemiological mapping efforts to find areas of persisting transmission. These methods may be extended to areas where
Model-Based Geostatistical Mapping of the Prevalence of Onchocerca volvulus in West Africa.
Directory of Open Access Journals (Sweden)
Simon J O'Hanlon
2016-01-01
Full Text Available The initial endemicity (pre-control prevalence of onchocerciasis has been shown to be an important determinant of the feasibility of elimination by mass ivermectin distribution. We present the first geostatistical map of microfilarial prevalence in the former Onchocerciasis Control Programme in West Africa (OCP before commencement of antivectorial and antiparasitic interventions.Pre-control microfilarial prevalence data from 737 villages across the 11 constituent countries in the OCP epidemiological database were used as ground-truth data. These 737 data points, plus a set of statistically selected environmental covariates, were used in a Bayesian model-based geostatistical (B-MBG approach to generate a continuous surface (at pixel resolution of 5 km x 5km of microfilarial prevalence in West Africa prior to the commencement of the OCP. Uncertainty in model predictions was measured using a suite of validation statistics, performed on bootstrap samples of held-out validation data. The mean Pearson's correlation between observed and estimated prevalence at validation locations was 0.693; the mean prediction error (average difference between observed and estimated values was 0.77%, and the mean absolute prediction error (average magnitude of difference between observed and estimated values was 12.2%. Within OCP boundaries, 17.8 million people were deemed to have been at risk, 7.55 million to have been infected, and mean microfilarial prevalence to have been 45% (range: 2-90% in 1975.This is the first map of initial onchocerciasis prevalence in West Africa using B-MBG. Important environmental predictors of infection prevalence were identified and used in a model out-performing those without spatial random effects or environmental covariates. Results may be compared with recent epidemiological mapping efforts to find areas of persisting transmission. These methods may be extended to areas where data are sparse, and may be used to help inform the
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…
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 ...
Study on geological environment model using geostatistics method
International Nuclear Information System (INIS)
The purpose of this study is to develop the geostatistical procedure for modeling geological environments and to evaluate the quantitative relationship between the amount of information and the reliability of the model using the data sets obtained in the surface-based investigation phase (Phase 1) of the Horonobe Underground Research Laboratory Project. This study lasts for three years from FY2004 to FY2006 and this report includes the research in FY2005 as the second year of three-year study. In FY2005 research, the hydrogeological model was built as well as FY2004 research using the data obtained from the deep boreholes (HDB-6, 7 and 8) and the ground magnetotelluric (AMT) survey which were executed in FY2004 in addition to the data sets used in the first year of study. Above all, the relationship between the amount of information and the reliability of the model was demonstrated through a comparison of the models at each step which corresponds to the investigation stage in each FY. Furthermore, the statistical test was applied for detecting the difference of basic statistics of various data due to geological features with a view to taking the geological information into the modeling procedures. (author)
3D Geostatistical Modeling and Uncertainty Analysis in a Carbonate Reservoir, SW Iran
Mohammad Reza Kamali; Azadeh Omidvar; Ezatallah Kazemzadeh
2013-01-01
The aim of geostatistical reservoir characterization is to utilize wide variety of data, in different scales and accuracies, to construct reservoir models which are able to represent geological heterogeneities and also quantifying uncertainties by producing numbers of equiprobable models. Since all geostatistical methods used in estimation of reservoir parameters are inaccurate, modeling of “estimation error” in form of uncertainty analysis is very important. In this paper, the definition of ...
Development of Bayesian Geostatistical Models with Applications in Malaria Epidemiology
Gosoniu, Laura
2008-01-01
Plasmodium falciparum malaria is a leading infectious disease and a major cause of morbidity and mortality in large areas of the developing world, especially Africa. Accurate estimates of the burden of the disease are useful for planning and implementing malaria control interventions and for monitoring the impact of prevention and control activities. Information on the population at risk of malaria can be compared to existing levels of service provision to identify underserved ...
Geostatistical interpolation for modelling SPT data in northern Izmir
Indian Academy of Sciences (India)
Selim Altun; A Burak Göktepe; Alper Sezer
2013-12-01
In this study, it was aimed to map the corrected Standard Penetration Test(SPT) values in Karşıyaka city center by kriging approach. Six maps were prepared by this geostatistical approach at depths of 3, 6, 9, 13.5, 18 and 25.5m. Borehole test results obtained from 388 boreholes in central Karşıyaka were used to model the spatial variation of $(\\text{N}_1)_{\\text{60cs}}$ values in an area of 5.5 km2. Corrections were made for depth, hammer energy, rod length, sampler, borehole diameter and fines content, to the data in hand. At various depths, prepared variograms and the kriging method were used together to model the variation of corrected SPT data in the region, which enabled the estimation of missing data in the region. The results revealed that the estimation ability of the models were acceptable, which were validated by a number of parameters as well as the comparisons of the actual and estimated data. Outcomes of this study can be used in microzonation studies, site response analyses, calculation of bearing capacity of subsoils in the region and producing a number of parameters which are empirically related to corrected SPT number as well.
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
Unified Geostatistical Modeling for Data Fusion and Spatial Heteroskedasticity with R Package ramps
Directory of Open Access Journals (Sweden)
Brian J. Smith
2008-03-01
Full Text Available This article illustrates usage of the ramps R package, which implements the reparameterized and marginalized posterior sampling (RAMPS algorithm for complex Bayesian geostatistical models. The RAMPS methodology allows joint modeling of areal and point-source data arising from the same underlying spatial process. A reparametrization of variance parameters facilitates slice sampling based on simplexes, which can be useful in general when multiple variances are present. Prediction at arbitrary points can be made, which is critical in applications where maps are needed. Our implementation takes advantage of sparse matrix operations in the Matrix package and can provide substantial savings in computing time for large datasets. A user-friendly interface, similar to the nlme mixed effects models package, enables users to analyze datasets with little programming effort. Support is provided for numerous spatial and spatiotemporal correlation structures, user-defined correlation structures, and non-spatial random effects. The package features are illustrated via a synthetic dataset of spatially correlated observation distributed across the state of Iowa, USA.
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...
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 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
Nonparametric Bayesian Modeling of Complex Networks
DEFF Research Database (Denmark)
Schmidt, Mikkel Nørgaard; Mørup, Morten
2013-01-01
Modeling structure in complex networks using Bayesian nonparametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This article provides a gentle introduction to nonparametric Bayesian modeling of complex networks: Using...... for complex networks can be derived and point out relevant literature....
Amiri, Arshia; Gerdtham, Ulf-G
2011-01-01
This paper introduces a new way of investigating linear and nonlinear Granger causality between exports, imports and economic growth in France over the period 1961-2006 with using geostatistical models (kiriging and inverse distance weighting). Geostatistical methods are the ordinary methods for forecasting the locations and making map in water engineerig, environment, environmental pollution, mining, ecology, geology and geography. Although, this is the first time which geostatistics knowle...
Sacchi, Q.; Borello, E.S.; Weltje, G.J.; Dalman, R.
2016-01-01
Current static reservoir models are created by quantitative integration of interpreted well and seismic data through geostatistical tools. In these models, equiprobable realizations of structural settings and property distributions can be generated by stochastic simulation techniques. The integratio
Directory of Open Access Journals (Sweden)
Federica Giardina
2015-11-01
Full Text Available The study of malaria spatial epidemiology has benefited from recent advances in geographic information system and geostatistical modelling. Significant progress in earth observation technologies has led to the development of moderate, high and very high resolution imagery. Extensive literature exists on the relationship between malaria and environmental/climatic factors in different geographical areas, but few studies have linked human malaria parasitemia survey data with remote sensing-derived land cover/land use variables and very few have used Earth Observation products. Comparison among the different resolution products to model parasitemia has not yet been investigated. In this study, we probe a proximity measure to incorporate different land cover classes and assess the effect of the spatial resolution of remotely sensed land cover and elevation on malaria risk estimation in Mozambique after adjusting for other environmental factors at a fixed spatial resolution. We used data from the Demographic and Health survey carried out in 2011, which collected malaria parasitemia data on children from 0 to 5 years old, analysing them with a Bayesian geostatistical model. We compared the risk predicted using land cover and elevation at moderate resolution with the risk obtained employing the same variables at high resolution. We used elevation data at moderate and high resolution and the land cover layer from the Moderate Resolution Imaging Spectroradiometer as well as the one produced by MALAREO, a project covering part of Mozambique during 2010-2012 that was funded by the European Union’s 7th Framework Program. Moreover, the number of infected children was predicted at different spatial resolutions using AFRIPOP population data and the enhanced population data generated by the MALAREO project for comparison of estimates. The Bayesian geostatistical model showed that the main determinants of malaria presence are precipitation and day temperature
Use of geostatistical modeling to capture complex geology in finite-element analyses
International Nuclear Information System (INIS)
This paper summarizes a number of transient thermal analyses performed for a representative two-dimensional cross section of volcanic tuffs at Yucca Mountain using the finite element, nonlinear heat-conduction code COYOTE-II. In addition to conventional design analyses, in which material properties are formulated as a uniform single material and as horizontally layered, internally uniform matters, an attempt was made to increase the resemblance of the thermal property field to the actual geology by creating two fairly complex, geologically realistic models. The first model was created by digitizing an existing two-dimensional geologic cross section of Yucca Mountain. The second model was created using conditional geostatistical simulation. Direct mapping of geostatistically generated material property fields onto finite element computational meshes was demonstrated to yield temperature fields approximately equivalent to those generated through more conventional procedures. However, the ability to use the geostatistical models offers a means of simplifying the physical-process analyses
Kosack, Christian; Vogt, Christian; Rath, Volker; Marquart, Gabriele
2010-05-01
The knowledge of the permeability distribution at depth is of primary concern for any geothermal reservoir engineering. However, permeability might change over orders of magnitude even for a single rock type and is additionally controlled by tectonic or engineered fracturing of the rocks. During reservoir exploration pumping tests are regularly performed where tracer marked water is pumped in one borehole and retrieved at one or a few others. At the European Enhanced Geothermal System (EGS) test site at Soultz-sous-Forêts three wells had been drilled in the granitic bedrock down to 4 to 5 km and were hydraulically stimulated to enhance the hydraulic connectivity between the wells. In July 2005, a tracer circulation test was carried out in order to estimate the changes of the hydraulic properties. Therefore a tracer was injected into the well GPK3 for 19 hours at a rate of 0.015 m3 s-1 and a concentration of 0.389 mol m-3. Tracer concentration was measured in the production wells over the following 5 months, while the produced water was re-injected into GPK3. This experiment demonstrated a good hydraulic connection between GPK3 and one of the production wells, GPK2, while a very low connectivity was observed in the other one, GPK4. We tested three different approaches simulating the pumping experiment with the numerical simulator shemat_suite in a simplified 3D model of the site in order to study their respective potential to estimate a reliable permeability distribution for the Soultz reservoir: A full-physics gradient-based Bayesian inversion, a massive Monte Carlo approach with geostatistic analysis, and an Ensemble-Kalman-Filter (EnKF) assimilation. A common feature in all models is a high permeability zone which acts as main flow area and transports most of the tracer. It is assumed to be associated with the fault zone cutting through the boreholes GPK2 and GPK3. With the Bayesian Inversion we were able to estimate a parameter set consisting of porosity
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
Yan, Hongxiang; Moradkhani, Hamid
2016-08-01
Assimilation of satellite soil moisture and streamflow data into a distributed hydrologic model has received increasing attention over the past few years. This study provides a detailed analysis of the joint and separate assimilation of streamflow and Advanced Scatterometer (ASCAT) surface soil moisture into a distributed Sacramento Soil Moisture Accounting (SAC-SMA) model, with the use of recently developed particle filter-Markov chain Monte Carlo (PF-MCMC) method. Performance is assessed over the Salt River Watershed in Arizona, which is one of the watersheds without anthropogenic effects in Model Parameter Estimation Experiment (MOPEX). A total of five data assimilation (DA) scenarios are designed and the effects of the locations of streamflow gauges and the ASCAT soil moisture on the predictions of soil moisture and streamflow are assessed. In addition, a geostatistical model is introduced to overcome the significantly biased satellite soil moisture and also discontinuity issue. The results indicate that: (1) solely assimilating outlet streamflow can lead to biased soil moisture estimation; (2) when the study area can only be partially covered by the satellite data, the geostatistical approach can estimate the soil moisture for those uncovered grid cells; (3) joint assimilation of streamflow and soil moisture from geostatistical modeling can further improve the surface soil moisture prediction. This study recommends that the geostatistical model is a helpful tool to aid the remote sensing technique and the hydrologic DA study.
Computational methods for Bayesian model choice
Robert, Christian P.; Wraith, Darren
2009-01-01
In this note, we shortly survey some recent approaches on the approximation of the Bayes factor used in Bayesian hypothesis testing and in Bayesian model choice. In particular, we reassess importance sampling, harmonic mean sampling, and nested sampling from a unified perspective.
Methodology and applications in non-linear model-based geostatistics
DEFF Research Database (Denmark)
Christensen, Ole Fredslund
Today geostatistics is used in a number of research areas, among others agricultural and environmental sciences.This thesis concerns data and applications where the classical Gaussian spatial model is not appropriate. A transformation could be used in an attempt to obtain data that are approximat...
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...
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 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
A geostatistical methodology to assess the accuracy of unsaturated flow models
International Nuclear Information System (INIS)
The Pacific Northwest National Laboratory spatiotemporal movement of water injected into (PNNL) has developed a Hydrologic unsaturated sediments at the Hanford Site in Evaluation Methodology (HEM) to assist the Washington State was used to develop a new U.S. Nuclear Regulatory Commission in method for evaluating mathematical model evaluating the potential that infiltrating meteoric predictions. Measured water content data were water will produce leachate at commercial low- interpolated geostatistically to a 16 x 16 x 36 level radioactive waste disposal sites. Two key grid at several time intervals. Then a issues are raised in the HEM: (1) evaluation of mathematical model was used to predict water mathematical models that predict facility content at the same grid locations at the selected performance, and (2) estimation of the times. Node-by-node comparison of the uncertainty associated with these mathematical mathematical model predictions with the model predictions. The technical objective of geostatistically interpolated values was this research is to adapt geostatistical tools conducted. The method facilitates a complete commonly used for model parameter estimation accounting and categorization of model error at to the problem of estimating the spatial every node. The comparison suggests that distribution of the dependent variable to be model results generally are within measurement calculated by the model. To fulfill this error. The worst model error occurs in silt objective, a database describing the lenses and is in excess of measurement error
A geostatistical methodology to assess the accuracy of unsaturated flow models
Energy Technology Data Exchange (ETDEWEB)
Smoot, J.L.; Williams, R.E.
1996-04-01
The Pacific Northwest National Laboratory spatiotemporal movement of water injected into (PNNL) has developed a Hydrologic unsaturated sediments at the Hanford Site in Evaluation Methodology (HEM) to assist the Washington State was used to develop a new U.S. Nuclear Regulatory Commission in method for evaluating mathematical model evaluating the potential that infiltrating meteoric predictions. Measured water content data were water will produce leachate at commercial low- interpolated geostatistically to a 16 x 16 x 36 level radioactive waste disposal sites. Two key grid at several time intervals. Then a issues are raised in the HEM: (1) evaluation of mathematical model was used to predict water mathematical models that predict facility content at the same grid locations at the selected performance, and (2) estimation of the times. Node-by-node comparison of the uncertainty associated with these mathematical mathematical model predictions with the model predictions. The technical objective of geostatistically interpolated values was this research is to adapt geostatistical tools conducted. The method facilitates a complete commonly used for model parameter estimation accounting and categorization of model error at to the problem of estimating the spatial every node. The comparison suggests that distribution of the dependent variable to be model results generally are within measurement calculated by the model. To fulfill this error. The worst model error occurs in silt objective, a database describing the lenses and is in excess of measurement error.
Assessment of effectiveness of geologic isolation systems: geostatistical modeling of pore velocity
International Nuclear Information System (INIS)
A significant part of evaluating a geologic formation as a nuclear waste repository involves the modeling of contaminant transport in the surrounding media in the event the repository is breached. The commonly used contaminant transport models are deterministic. However, the spatial variability of hydrologic field parameters introduces uncertainties into contaminant transport predictions. This paper discusses the application of geostatistical techniques to the modeling of spatially varying hydrologic field parameters required as input to contaminant transport analyses. Kriging estimation techniques were applied to Hanford Reservation field data to calculate hydraulic conductivity and the ground-water potential gradients. These quantities were statistically combined to estimate the groundwater pore velocity and to characterize the pore velocity estimation error. Combining geostatistical modeling techniques with product error propagation techniques results in an effective stochastic characterization of groundwater pore velocity, a hydrologic parameter required for contaminant transport analyses
International Nuclear Information System (INIS)
Two-dimensional, heterogeneous, spatially correlated models of thermal conductivity and bulk density have been created for a representative, east-west cross section of Yucca Mountain, Nevada, using geostatistical simulation. The thermal conductivity models are derived from spatially correlated, surrogate material-property models of porosity, through a multiple linear-regression equation, which expresses thermal conductivity as a function of porosity and initial temperature and saturation. Bulk-density values were obtained through a similar, linear-regression relationship with porosity. The use of a surrogate-property allows the use of spatially much-more-abundant porosity measurements to condition the simulations. Modeling was conducted in stratigraphic coordinates to represent original depositional continuity of material properties and the completed models were transformed to real-world coordinates to capture present-day tectonic tilting and faulting of the material-property units. Spatial correlation lengths required for geostatistical modeling were assumed, but are based on the results of previous transect-sampling and geostatistical-modeling work
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...
Bayesian Network Models for Adaptive Testing
Czech Academy of Sciences Publication Activity Database
Plajner, Martin; Vomlel, Jiří
Achen: Sun SITE Central Europe, 2016 - (Agosta, J.; Carvalho, R.), s. 24-33. (CEUR Workshop Proceedings. Vol 1565). ISSN 1613-0073. [The Twelfth UAI Bayesian Modeling Applications Workshop (BMAW 2015). Amsterdam (NL), 16.07.2015] R&D Projects: GA ČR GA13-20012S Institutional support: RVO:67985556 Keywords : Bayesian networks * Computerized adaptive testing Subject RIV: JD - Computer Applications, Robotics http://library.utia.cas.cz/separaty/2016/MTR/plajner-0458062.pdf
Schöniger, Anneli; Illman, Walter A.; Wöhling, Thomas; Nowak, Wolfgang
2015-12-01
Groundwater modelers face the challenge of how to assign representative parameter values to the studied aquifer. Several approaches are available to parameterize spatial heterogeneity in aquifer parameters. They differ in their conceptualization and complexity, ranging from homogeneous models to heterogeneous random fields. While it is common practice to invest more effort into data collection for models with a finer resolution of heterogeneities, there is a lack of advice which amount of data is required to justify a certain level of model complexity. In this study, we propose to use concepts related to Bayesian model selection to identify this balance. We demonstrate our approach on the characterization of a heterogeneous aquifer via hydraulic tomography in a sandbox experiment (Illman et al., 2010). We consider four increasingly complex parameterizations of hydraulic conductivity: (1) Effective homogeneous medium, (2) geology-based zonation, (3) interpolation by pilot points, and (4) geostatistical random fields. First, we investigate the shift in justified complexity with increasing amount of available data by constructing a model confusion matrix. This matrix indicates the maximum level of complexity that can be justified given a specific experimental setup. Second, we determine which parameterization is most adequate given the observed drawdown data. Third, we test how the different parameterizations perform in a validation setup. The results of our test case indicate that aquifer characterization via hydraulic tomography does not necessarily require (or justify) a geostatistical description. Instead, a zonation-based model might be a more robust choice, but only if the zonation is geologically adequate.
International Nuclear Information System (INIS)
Decommissioning of nuclear building structures usually leads to large amounts of low level radioactive waste. Using a reliable method to determine the contamination depth is indispensable prior to the start of decontamination works and also for minimizing the radioactive waste volume and the total workload. The method described in this paper is based on geostatistical modeling of in situ gamma-ray spectroscopy measurements using the multiple photo peak method. The method has been tested on the floor of the waste gas surge tank room within the BR3 (Belgian Reactor 3) decommissioning project and has delivered adequate results. - Highlights: • 137Cs depth contamination was determined using the multiple photo peak method. • Geostatistical modeling was used to determine treatment depth areas and perform risk analysis. • Results were evaluated using laser scanning and long term gamma-ray spectroscopy. • Waste volume reduction of about 1/3 compared to a more traditional approach
Assessing fit in Bayesian models for spatial processes
Jun, M.
2014-09-16
© 2014 John Wiley & Sons, Ltd. Gaussian random fields are frequently used to model spatial and spatial-temporal data, particularly in geostatistical settings. As much of the attention of the statistics community has been focused on defining and estimating the mean and covariance functions of these processes, little effort has been devoted to developing goodness-of-fit tests to allow users to assess the models\\' adequacy. We describe a general goodness-of-fit test and related graphical diagnostics for assessing the fit of Bayesian Gaussian process models using pivotal discrepancy measures. Our method is applicable for both regularly and irregularly spaced observation locations on planar and spherical domains. The essential idea behind our method is to evaluate pivotal quantities defined for a realization of a Gaussian random field at parameter values drawn from the posterior distribution. Because the nominal distribution of the resulting pivotal discrepancy measures is known, it is possible to quantitatively assess model fit directly from the output of Markov chain Monte Carlo algorithms used to sample from the posterior distribution on the parameter space. We illustrate our method in a simulation study and in two applications.
Karagiannis-Voules, Dimitrios-Alexios; Odermatt, Peter; Biedermann, Patricia; Khieu, Virak; Schär, Fabian; Muth, Sinuon; Utzinger, Jürg; Vounatsou, Penelope
2015-01-01
Soil-transmitted helminth infections are intimately connected with poverty. Yet, there is a paucity of using socioeconomic proxies in spatially explicit risk profiling. We compiled household-level socioeconomic data pertaining to sanitation, drinking-water, education and nutrition from readily available Demographic and Health Surveys, Multiple Indicator Cluster Surveys and World Health Surveys for Cambodia and aggregated the data at village level. We conducted a systematic review to identify parasitological surveys and made every effort possible to extract, georeference and upload the data in the open source Global Neglected Tropical Diseases database. Bayesian geostatistical models were employed to spatially align the village-aggregated socioeconomic predictors with the soil-transmitted helminth infection data. The risk of soil-transmitted helminth infection was predicted at a grid of 1×1km covering Cambodia. Additionally, two separate individual-level spatial analyses were carried out, for Takeo and Preah Vihear provinces, to assess and quantify the association between soil-transmitted helminth infection and socioeconomic indicators at an individual level. Overall, we obtained socioeconomic proxies from 1624 locations across the country. Surveys focussing on soil-transmitted helminth infections were extracted from 16 sources reporting data from 238 unique locations. We found that the risk of soil-transmitted helminth infection from 2000 onwards was considerably lower than in surveys conducted earlier. Population-adjusted prevalences for school-aged children from 2000 onwards were 28.7% for hookworm, 1.5% for Ascaris lumbricoides and 0.9% for Trichuris trichiura. Surprisingly, at the country-wide analyses, we did not find any significant association between soil-transmitted helminth infection and village-aggregated socioeconomic proxies. Based also on the individual-level analyses we conclude that socioeconomic proxies might not be good predictors at an
Linde, Niklas; Lochbühler, Tobias; Dogan, Mine; Van Dam, Remke L.
2015-12-01
We propose a new framework to compare alternative geostatistical descriptions of a given site. Multiple realizations of each of the considered geostatistical models and their corresponding tomograms (based on inversion of noise-contaminated simulated data) are used as a multivariate training image. The training image is scanned with a direct sampling algorithm to obtain conditional realizations of hydraulic conductivity that are not only in agreement with the geostatistical model, but also honor the spatially varying resolution of the site-specific tomogram. Model comparison is based on the quality of the simulated geophysical data from the ensemble of conditional realizations. The tomogram in this study is obtained by inversion of cross-hole ground-penetrating radar (GPR) first-arrival travel time data acquired at the MAcro-Dispersion Experiment (MADE) site in Mississippi (USA). Various heterogeneity descriptions ranging from multi-Gaussian fields to fields with complex multiple-point statistics inferred from outcrops are considered. Under the assumption that the relationship between porosity and hydraulic conductivity inferred from local measurements is valid, we find that conditioned multi-Gaussian realizations and derivatives thereof can explain the crosshole geophysical data. A training image based on an aquifer analog from Germany was found to be in better agreement with the geophysical data than the one based on the local outcrop, which appears to under-represent high hydraulic conductivity zones. These findings are only based on the information content in a single resolution-limited tomogram and extending the analysis to tracer or higher resolution surface GPR data might lead to different conclusions (e.g., that discrete facies boundaries are necessary). Our framework makes it possible to identify inadequate geostatistical models and petrophysical relationships, effectively narrowing the space of possible heterogeneity representations.
Waldir de Carvalho Junior; Cesar da Silva Chagas; Philippe Lagacherie; Braz Calderano Filho; Silvio Barge Bhering
2014-01-01
Soil properties have an enormous impact on economic and environmental aspects of agricultural production. Quantitative relationships between soil properties and the factors that influence their variability are the basis of digital soil mapping. The predictive models of soil properties evaluated in this work are statistical (multiple linear regression-MLR) and geostatistical (ordinary kriging and co-kriging). The study was conducted in the municipality of Bom Jardim, RJ, using a soil database ...
On Bayesian Nonparametric Continuous Time Series Models
Karabatsos, George; Walker, Stephen G.
2013-01-01
This paper is a note on the use of Bayesian nonparametric mixture models for continuous time series. We identify a key requirement for such models, and then establish that there is a single type of model which meets this requirement. As it turns out, the model is well known in multiple change-point problems.
A conceptual sedimentological-geostatistical model of aquifer heterogeneity based on outcrop studies
Energy Technology Data Exchange (ETDEWEB)
Davis, J.M.
1994-01-01
Three outcrop studies were conducted in deposits of different depositional environments. At each site, permeability measurements were obtained with an air-minipermeameter developed as part of this study. In addition, the geological units were mapped with either surveying, photographs, or both. Geostatistical analysis of the permeability data was performed to estimate the characteristics of the probability distribution function and the spatial correlation structure. The information obtained from the geological mapping was then compared with the results of the geostatistical analysis for any relationships that may exist. The main field site was located in the Albuquerque Basin of central New Mexico at an outcrop of the Pliocene-Pleistocene Sierra Ladrones Formation. The second study was conducted on the walls of waste pits in alluvial fan deposits at the Nevada Test Site. The third study was conducted on an outcrop of an eolian deposit (miocene) south of Socorro, New Mexico. The results of the three studies were then used to construct a conceptual model relating depositional environment to geostatistical models of heterogeneity. The model presented is largely qualitative but provides a basis for further hypothesis formulation and testing.
A conceptual sedimentological-geostatistical model of aquifer heterogeneity based on outcrop studies
International Nuclear Information System (INIS)
Three outcrop studies were conducted in deposits of different depositional environments. At each site, permeability measurements were obtained with an air-minipermeameter developed as part of this study. In addition, the geological units were mapped with either surveying, photographs, or both. Geostatistical analysis of the permeability data was performed to estimate the characteristics of the probability distribution function and the spatial correlation structure. The information obtained from the geological mapping was then compared with the results of the geostatistical analysis for any relationships that may exist. The main field site was located in the Albuquerque Basin of central New Mexico at an outcrop of the Pliocene-Pleistocene Sierra Ladrones Formation. The second study was conducted on the walls of waste pits in alluvial fan deposits at the Nevada Test Site. The third study was conducted on an outcrop of an eolian deposit (miocene) south of Socorro, New Mexico. The results of the three studies were then used to construct a conceptual model relating depositional environment to geostatistical models of heterogeneity. The model presented is largely qualitative but provides a basis for further hypothesis formulation and testing
Amiri, Arshia; Bakhshoodeh, Mohamad; Najafi, Bahaeddin
2011-01-01
This paper, we studied the ability of geostatistical models (ordinary kriging (OK) and Inverse distance weighting (IDW)), adaptive neuro-fuzzy inference system (ANFIS) and Winter method for prediction of seasonality in prices of potatoes and onions in Iran over the seasonal period 1986_2001. Results show that the best estimators in order are winter method, ANFIS and geostatistical methods. The results indicate that Winter and ANFIS had powerful results for prediction the prices while geostati...
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
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
Book review: Spatial statistics and geostatistics
Clift, Hamish
2013-01-01
"Spatial Statistics and Geostatistics." Yongwan Chun and Daniel A. Griffith. SAGE. January 2013. --- This book aims to explain and demonstrate techniques in spatial sampling, local statistics, and advanced topics including Bayesian methods, Monte Carlo simulation, error and uncertainty. Spatial Statistics and Geostatistics is highly recommended to researchers in geography, environmental science, health and epidemiology, population and demography, and planning, writes Hamish Clift.
Bayesian Semiparametric Modeling of Realized Covariance Matrices
Jin, Xin; John M Maheu
2014-01-01
This paper introduces several new Bayesian nonparametric models suitable for capturing the unknown conditional distribution of realized covariance (RCOV) matrices. Existing dynamic Wishart models are extended to countably infinite mixture models of Wishart and inverse-Wishart distributions. In addition to mixture models with constant weights we propose models with time-varying weights to capture time dependence in the unknown distribution. Each of our models can be combined with returns...
Complex Bayesian models: construction, and sampling strategies
Huston, Carolyn Marie
2011-01-01
Bayesian models are useful tools for realistically modeling processes occurring in the real world. In particular, we consider models for spatio-temporal data where the response vector is compositional, ie. has components that sum-to-one. A unique multivariate conditional hierarchical model (MVCAR) is proposed. Statistical methods for MVCAR models are well developed and we extend these tools for use with a discrete compositional response. We harness the advantages of an MVCAR model when the re...
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.
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.
Hodgetts, David; Burnham, Brian; Head, William; Jonathan, Atunima; Rarity, Franklin; Seers, Thomas; Spence, Guy
2013-04-01
In the hydrocarbon industry stochastic approaches are the main method by which reservoirs are modelled. These stochastic modelling approaches require geostatistical information on the geometry and distribution of the geological elements of the reservoir. As the reservoir itself cannot be viewed directly (only indirectly via seismic and/or well log data) this leads to a great deal of uncertainty in the geostatistics used, therefore outcrop analogues are characterised to help obtain the geostatistical information required to model the reservoir. Lidar derived Digital Outcrop Model's (DOM's) provide the ability to collect large quantities of statistical information on the geological architecture of the outcrop, far more than is possible by field work alone as the DOM allows accurate measurements to be made in normally inaccessible parts of the exposure. This increases the size of the measured statistical dataset, which in turn results in an increase in statistical significance. There are, however, many problems and biases in the data which cannot be overcome by sample size alone. These biases, for example, may relate to the orientation, size and quality of exposure, as well as the resolution of the DOM itself. Stochastic modelling used in the hydrocarbon industry fall mainly into 4 generic approaches: 1) Object Modelling where the geology is defined by a set of simplistic shapes (such as channels), where parameters such as width, height and orientation, among others, can be defined. 2) Sequential Indicator Simulations where geological shapes are less well defined and the size and distribution are defined using variograms. 3) Multipoint statistics where training images are used to define shapes and relationships between geological elements and 4) Discrete Fracture Networks for fractures reservoirs where information on fracture size and distribution are required. Examples of using DOM's to assist with each of these modelling approaches are presented, highlighting the
Modelling the presence of disease under spatial misalignment using Bayesian latent Gaussian models.
Barber, Xavier; Conesa, David; Lladosa, Silvia; López-Quílez, Antonio
2016-01-01
Modelling patterns of the spatial incidence of diseases using local environmental factors has been a growing problem in the last few years. Geostatistical models have become popular lately because they allow estimating and predicting the underlying disease risk and relating it with possible risk factors. Our approach to these models is based on the fact that the presence/absence of a disease can be expressed with a hierarchical Bayesian spatial model that incorporates the information provided by the geographical and environmental characteristics of the region of interest. Nevertheless, our main interest here is to tackle the misalignment problem arising when information about possible covariates are partially (or totally) different than those of the observed locations and those in which we want to predict. As a result, we present two different models depending on the fact that there is uncertainty on the covariates or not. In both cases, Bayesian inference on the parameters and prediction of presence/absence in new locations are made by considering the model as a latent Gaussian model, which allows the use of the integrated nested Laplace approximation. In particular, the spatial effect is implemented with the stochastic partial differential equation approach. The methodology is evaluated on the presence of the Fasciola hepatica in Galicia, a North-West region of Spain. PMID:27087038
International Nuclear Information System (INIS)
This report describes the comparison of stationary and non-stationary geostatistical models for the purpose of inferring block-scale hydraulic conductivity values from packer tests at Aespoe. The comparison between models is made through the evaluation of cross-validation statistics for three experimental designs. The first experiment consisted of a 'Delete-1' test previously used at Finnsjoen. The second test consisted of 'Delete-10%' and the third test was a 'Delete-50%' test. Preliminary data analysis showed that the 3 m and 30 m packer test data can be treated as a sample from a single population for the purposes of geostatistical analyses. Analysis of the 3 m data does not indicate that there are any systematic statistical changes with depth, rock type, fracture zone vs non-fracture zone or other mappable factor. Directional variograms are ambiguous to interpret due to the clustered nature of the data, but do not show any obvious anisotropy that should be accounted for in geostatistical analysis. Stationary analysis suggested that there exists a sizeable spatially uncorrelated component ('Nugget Effect') in the 3 m data, on the order of 60% of the observed variance for the various models fitted. Four different nested models were automatically fit to the data. Results for all models in terms of cross-validation statistics were very similar for the first set of validation tests. Non-stationary analysis established that both the order of drift and the order of the intrinsic random functions is low. This study also suggests that conventional cross-validation studies and automatic variogram fitting are not necessarily evaluating how well a model will infer block scale hydraulic conductivity values. 20 refs, 20 figs, 14 tabs
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...
The use of meshless method and geostatistical analysis in transport modelling
International Nuclear Information System (INIS)
The disposal of radioactive waste in geological formations is of great importance for nuclear safety. A number of key geosphere processes need to be considered when predicting the movement of radionuclides through the geosphere. The goal of this research is to investigate the influence of spatial variability of geo-hydrological data on the reliability and accuracy of computational modelling. We chose the Kansa meshless method that uses radial basis functions as the mathematical solution technique. The aim of this study is to determine the average and sample variance of radionuclide concentration with regard to spatial variability of hydraulic conductivity modelled by geostatistical approach.(author)
Geostatistical interpolation and aggregation of crop growth model outputs
Steinbuch, Luc; Brus, Dick J.; Bussel, van Lenny G.J.; Heuvelink, Gerard B.M.
2016-01-01
Many crop growth models require daily meteorological data. Consequently, model simulations can be obtained only at a limited number of locations, i.e. at weather stations with long-term records of daily data. To estimate the potential crop production at country level, we present in this study a g
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). ...
Directory of Open Access Journals (Sweden)
Waldir de Carvalho Junior
2014-06-01
Full Text Available Soil properties have an enormous impact on economic and environmental aspects of agricultural production. Quantitative relationships between soil properties and the factors that influence their variability are the basis of digital soil mapping. The predictive models of soil properties evaluated in this work are statistical (multiple linear regression-MLR and geostatistical (ordinary kriging and co-kriging. The study was conducted in the municipality of Bom Jardim, RJ, using a soil database with 208 sampling points. Predictive models were evaluated for sand, silt and clay fractions, pH in water and organic carbon at six depths according to the specifications of the consortium of digital soil mapping at the global level (GlobalSoilMap. Continuous covariates and categorical predictors were used and their contributions to the model assessed. Only the environmental covariates elevation, aspect, stream power index (SPI, soil wetness index (SWI, normalized difference vegetation index (NDVI, and b3/b2 band ratio were significantly correlated with soil properties. The predictive models had a mean coefficient of determination of 0.21. Best results were obtained with the geostatistical predictive models, where the highest coefficient of determination 0.43 was associated with sand properties between 60 to 100 cm deep. The use of a sparse data set of soil properties for digital mapping can explain only part of the spatial variation of these properties. The results may be related to the sampling density and the quantity and quality of the environmental covariates and predictive models used.
DEFF Research Database (Denmark)
Kessler, Timo Christian; Nilsson, Bertel; Klint, Knud Erik;
2010-01-01
of sand-lenses in clay till. Sand-lenses mainly account for horizontal transport and are prioritised in this study. Based on field observations, the distribution has been modeled using two different geostatistical approaches. One method uses a Markov chain model calculating the transition probabilities...... the geology of e.g. a contaminated site, it is not always possible to gather enough information to build a representative geological model. Mapping in analogue geological settings and applying geostatistical tools to simulate spatial variability of heterogeneities can improve ordinary geological models...
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...... mechanism efficiently combines distributed learner models without the need to exchange internal structure of local Bayesian networks, nor local evidence between the involved platforms....
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 ...
Jha, Sanjeev Kumar
2013-01-01
A downscaling approach based on multiple-point geostatistics (MPS) is presented. The key concept underlying MPS is to sample spatial patterns from within training images, which can then be used in characterizing the relationship between different variables across multiple scales. The approach is used here to downscale climate variables including skin surface temperature (TSK), soil moisture (SMOIS), and latent heat flux (LH). The performance of the approach is assessed by applying it to data derived from a regional climate model of the Murray-Darling basin in southeast Australia, using model outputs at two spatial resolutions of 50 and 10 km. The data used in this study cover the period from 1985 to 2006, with 1985 to 2005 used for generating the training images that define the relationships of the variables across the different spatial scales. Subsequently, the spatial distributions for the variables in the year 2006 are determined at 10 km resolution using the 50 km resolution data as input. The MPS geostatistical downscaling approach reproduces the spatial distribution of TSK, SMOIS, and LH at 10 km resolution with the correct spatial patterns over different seasons, while providing uncertainty estimates through the use of multiple realizations. The technique has the potential to not only bridge issues of spatial resolution in regional and global climate model simulations but also in feature sharpening in remote sensing applications through image fusion, filling gaps in spatial data, evaluating downscaled variables with available remote sensing images, and aggregating/disaggregating hydrological and groundwater variables for catchment studies.
Cay, Tayfun; Uyan, Mevlut
2009-12-01
Groundwater is one of the most important resources used for drinking and utility and irrigation purposes in the city of Konya, Turkey, as in many areas. The purpose of this study is to evaluate spatial and temporal changes in the level of groundwater by using geostatistical methods based on data from 91 groundwater wells during the period 1999 to 2003. Geostatistical methods have been used widely as a convenient tool to make decisions on the management of groundwater levels. To evaluate the spatial and temporal changes in the level of the groundwater, a vector-based geographic information system software package, ArcGIS 9.1 (Environmental Systems Research Institute, Redlands, California), was used for the application of an ordinary kriging method, with cross-validation leading to the estimation of groundwater levels. The average value of variogram (spherical model) for the spatial analysis was approximately 2150 m. Results of ordinary kriging for groundwater level drops were underestimated by 17%. Cross-validation errors were within an acceptable level. The kriging model also helps to detect risk-prone areas for groundwater abstraction. PMID:20099631
Atzberger, C.; Richter, K.
2009-09-01
The robust and accurate retrieval of vegetation biophysical variables using radiative transfer models (RTM) is seriously hampered by the ill-posedness of the inverse problem. With this research we further develop our previously published (object-based) inversion approach [Atzberger (2004)]. The object-based RTM inversion takes advantage of the geostatistical fact that the biophysical characteristics of nearby pixel are generally more similar than those at a larger distance. A two-step inversion based on PROSPECT+SAIL generated look-up-tables is presented that can be easily implemented and adapted to other radiative transfer models. The approach takes into account the spectral signatures of neighboring pixel and optimizes a common value of the average leaf angle (ALA) for all pixel of a given image object, such as an agricultural field. Using a large set of leaf area index (LAI) measurements (n = 58) acquired over six different crops of the Barrax test site, Spain), we demonstrate that the proposed geostatistical regularization yields in most cases more accurate and spatially consistent results compared to the traditional (pixel-based) inversion. Pros and cons of the approach are discussed and possible future extensions presented.
Bayesian Network Based XP Process Modelling
Directory of Open Access Journals (Sweden)
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.
A Bayesian Modelling of Wildfires in Portugal
Silva, Giovani L.; Soares, Paulo; Marques, Susete; Dias, Inês M.; Oliveira, Manuela M.; Borges, Guilherme J.
2015-01-01
In the last decade wildfires became a serious problem in Portugal due to different issues such as climatic characteristics and nature of Portuguese forest. In order to analyse wildfire data, we employ beta regression for modelling the proportion of burned forest area, under a Bayesian perspective. Our main goal is to find out fire risk factors that influence the proportion of area burned and what may make a forest type susceptible or resistant to fire. Then, we analyse wildfire...
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...
Centralized Bayesian reliability modelling with sensor networks
Czech Academy of Sciences Publication Activity Database
Dedecius, Kamil; Sečkárová, Vladimíra
2013-01-01
Roč. 19, č. 5 (2013), s. 471-482. ISSN 1387-3954 R&D Projects: GA MŠk 7D12004 Grant ostatní: GA MŠk(CZ) SVV-265315 Keywords : Bayesian modelling * Sensor network * Reliability Subject RIV: BD - Theory of Information Impact factor: 0.984, year: 2013 http://library.utia.cas.cz/separaty/2013/AS/dedecius-0392551.pdf
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...
Local Geostatistical Models and Big Data in Hydrological and Ecological Applications
Hristopulos, Dionissios
2015-04-01
The advent of the big data era creates new opportunities for environmental and ecological modelling but also presents significant challenges. The availability of remote sensing images and low-cost wireless sensor networks implies that spatiotemporal environmental data to cover larger spatial domains at higher spatial and temporal resolution for longer time windows. Handling such voluminous data presents several technical and scientific challenges. In particular, the geostatistical methods used to process spatiotemporal data need to overcome the dimensionality curse associated with the need to store and invert large covariance matrices. There are various mathematical approaches for addressing the dimensionality problem, including change of basis, dimensionality reduction, hierarchical schemes, and local approximations. We present a Stochastic Local Interaction (SLI) model that can be used to model local correlations in spatial data. SLI is a random field model suitable for data on discrete supports (i.e., regular lattices or irregular sampling grids). The degree of localization is determined by means of kernel functions and appropriate bandwidths. The strength of the correlations is determined by means of coefficients. In the "plain vanilla" version the parameter set involves scale and rigidity coefficients as well as a characteristic length. The latter determines in connection with the rigidity coefficient the correlation length of the random field. The SLI model is based on statistical field theory and extends previous research on Spartan spatial random fields [2,3] from continuum spaces to explicitly discrete supports. The SLI kernel functions employ adaptive bandwidths learned from the sampling spatial distribution [1]. The SLI precision matrix is expressed explicitly in terms of the model parameter and the kernel function. Hence, covariance matrix inversion is not necessary for parameter inference that is based on leave-one-out cross validation. This property
Energy Technology Data Exchange (ETDEWEB)
Costa Reis, L.
2001-01-01
We have developed in this thesis a methodology of integrated characterization of heterogeneous reservoirs, from geologic modeling to history matching. This methodology is applied to the reservoir PBR, situated in Campos Basin, offshore Brazil, which has been producing since June 1979. This work is an extension of two other thesis concerning geologic and geostatistical modeling of the reservoir PBR from well data and seismic information. We extended the geostatistical litho-type model to the whole reservoir by using a particular approach of the non-stationary truncated Gaussian simulation method. This approach facilitated the application of the gradual deformation method to history matching. The main stages of the methodology for dynamic data integration in a geostatistical reservoir model are presented. We constructed a reservoir model and the initial difficulties in the history matching led us to modify some choices in the geological, geostatistical and flow models. These difficulties show the importance of dynamic data integration in reservoir modeling. The petrophysical property assignment within the litho-types was done by using well test data. We used an inversion procedure to evaluate the petrophysical parameters of the litho-types. The up-scaling is a necessary stage to reduce the flow simulation time. We compared several up-scaling methods and we show that the passage from the fine geostatistical model to the coarse flow model should be done very carefully. The choice of the fitting parameter depends on the objective of the study. In the case of the reservoir PBR, where water is injected in order to improve the oil recovery, the water rate of the producing wells is directly related to the reservoir heterogeneity. Thus, the water rate was chosen as the fitting parameter. We obtained significant improvements in the history matching of the reservoir PBR. First, by using a method we have proposed, called patchwork. This method allows us to built a coherent
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.
Modelling ambient ozone in an urban area using an objective model and geostatistical algorithms
Moral, Francisco J.; Rebollo, Francisco J.; Valiente, Pablo; López, Fernando; Muñoz de la Peña, Arsenio
2012-12-01
Ground-level tropospheric ozone is one of the air pollutants of most concern. Ozone levels continue to exceed both target values and the long-term objectives established in EU legislation to protect human health and prevent damage to ecosystems, agricultural crops and materials. Researchers or decision-makers frequently need information about atmospheric pollution patterns in urbanized areas. The preparation of this type of information is a complex task, due to the influence of several factors and their variability over time. In this work, some results of urban ozone distribution patterns in the city of Badajoz, which is the largest (140,000 inhabitants) and most industrialized city in Extremadura region (southwest Spain) are shown. Twelve sampling campaigns, one per month, were carried out to measure ambient air ozone concentrations, during periods that were selected according to favourable conditions to ozone production, using an automatic portable analyzer. Later, to evaluate the overall ozone level at each sampling location during the time interval considered, the measured ozone data were analysed using a new methodology based on the formulation of the Rasch model. As a result, a measure of overall ozone level which consolidates the monthly ground-level ozone measurements was obtained, getting moreover information about the influence on the overall ozone level of each monthly ozone measure. Finally, overall ozone level at locations where no measurements were available was estimated with geostatistical techniques and hazard assessment maps based on the spatial distribution of ozone were also generated.
Geostatistical modelling of carbon monoxide levels in Khartoum State (Sudan) - GIS pilot based study
International Nuclear Information System (INIS)
The objective of this study is to develop a digital GIS model; that can evaluate, predict and visualize carbon monoxide (CO) levels in Khartoum state. To achieve this aim, sample data had been collected, processed and managed to generate a dynamic GIS model of carbon monoxide levels in the study area. Parametric data collected from the field and analysis carried throughout this study show that (CO) emissions were lower than the allowable ambient air quality standards released by National Environment Protection Council (NEPC-USA) for 1998. However, this pilot study has found emissions of (CO) in Omdurman city were the highest. This pilot study shows that GIS and geostatistical modeling can be used as a powerful tool to produce maps of exposure. (authors)
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.
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 mixture models for partially verified data
DEFF Research Database (Denmark)
Kostoulas, Polychronis; Browne, William J.; Nielsen, Søren Saxmose;
2013-01-01
, where a perfect reference test does not exist. However, their discriminatory ability diminishes with increasing overlap of the distributions and with increasing number of latent infection stages to be discriminated. We provide a method that uses partially verified data, with known infection status for......Bayesian mixture models can be used to discriminate between the distributions of continuous test responses for different infection stages. These models are particularly useful in case of chronic infections with a long latent period, like Mycobacterium avium subsp. paratuberculosis (MAP) infection...
Enhancing multiple-point geostatistical modeling: 1. Graph theory and pattern adjustment
Tahmasebi, Pejman; Sahimi, Muhammad
2016-03-01
In recent years, higher-order geostatistical methods have been used for modeling of a wide variety of large-scale porous media, such as groundwater aquifers and oil reservoirs. Their popularity stems from their ability to account for qualitative data and the great flexibility that they offer for conditioning the models to hard (quantitative) data, which endow them with the capability for generating realistic realizations of porous formations with very complex channels, as well as features that are mainly a barrier to fluid flow. One group of such models consists of pattern-based methods that use a set of data points for generating stochastic realizations by which the large-scale structure and highly-connected features are reproduced accurately. The cross correlation-based simulation (CCSIM) algorithm, proposed previously by the authors, is a member of this group that has been shown to be capable of simulating multimillion cell models in a matter of a few CPU seconds. The method is, however, sensitive to pattern's specifications, such as boundaries and the number of replicates. In this paper the original CCSIM algorithm is reconsidered and two significant improvements are proposed for accurately reproducing large-scale patterns of heterogeneities in porous media. First, an effective boundary-correction method based on the graph theory is presented by which one identifies the optimal cutting path/surface for removing the patchiness and discontinuities in the realization of a porous medium. Next, a new pattern adjustment method is proposed that automatically transfers the features in a pattern to one that seamlessly matches the surrounding patterns. The original CCSIM algorithm is then combined with the two methods and is tested using various complex two- and three-dimensional examples. It should, however, be emphasized that the methods that we propose in this paper are applicable to other pattern-based geostatistical simulation methods.
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
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...
4th International Geostatistics Congress
1993-01-01
The contributions in this book were presented at the Fourth International Geostatistics Congress held in Tróia, Portugal, in September 1992. They provide a comprehensive account of the current state of the art of geostatistics, including recent theoretical developments and new applications. In particular, readers will find descriptions and applications of the more recent methods of stochastic simulation together with data integration techniques applied to the modelling of hydrocabon reservoirs. In other fields there are stationary and non-stationary geostatistical applications to geology, climatology, pollution control, soil science, hydrology and human sciences. The papers also provide an insight into new trends in geostatistics particularly the increasing interaction with many other scientific disciplines. This book is a significant reference work for practitioners of geostatistics both in academia and industry.
7th International Geostatistics Congress
Deutsch, Clayton
2005-01-01
The conference proceedings consist of approximately 120 technical papers presented at the Seventh International Geostatistics Congress held in Banff, Alberta, Canada in 2004. All the papers were reviewed by an international panel of leading geostatisticians. The five major sections are: theory, mining, petroleum, environmental and other applications. The first section showcases new and innovative ideas in the theoretical development of geostatistics as a whole; these ideas will have large impact on (1) the directions of future geostatistical research, and (2) the conventional approaches to heterogeneity modelling in a wide range of natural resource industries. The next four sections are focused on applications and innovations relating to the use of geostatistics in specific industries. Historically, mining, petroleum and environmental industries have embraced the use of geostatistics for uncertainty characterization, so these three industries are identified as major application areas. The last section is open...
Adversarial life testing: A Bayesian negotiation model
International Nuclear Information System (INIS)
Life testing is a procedure intended for facilitating the process of making decisions in the context of industrial reliability. On the other hand, negotiation is a process of making joint decisions that has one of its main foundations in decision theory. A Bayesian sequential model of negotiation in the context of adversarial life testing is proposed. This model considers a general setting for which a manufacturer offers a product batch to a consumer. It is assumed that the reliability of the product is measured in terms of its lifetime. Furthermore, both the manufacturer and the consumer have to use their own information with respect to the quality of the product. Under these assumptions, two situations can be analyzed. For both of them, the main aim is to accept or reject the product batch based on the product reliability. This topic is related to a reliability demonstration problem. The procedure is applied to a class of distributions that belong to the exponential family. Thus, a unified framework addressing the main topics in the considered Bayesian model is presented. An illustrative example shows that the proposed technique can be easily applied in practice
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
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.
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...
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...
Merging Digital Surface Models Implementing Bayesian Approaches
Sadeq, H.; Drummond, J.; Li, Z.
2016-06-01
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.
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
Directory of Open Access Journals (Sweden)
Nadine Schur
2011-06-01
Full Text Available BACKGROUND: Schistosomiasis is a water-based disease that is believed to affect over 200 million people with an estimated 97% of the infections concentrated in Africa. However, these statistics are largely based on population re-adjusted data originally published by Utroska and colleagues more than 20 years ago. Hence, these estimates are outdated due to large-scale preventive chemotherapy programs, improved sanitation, water resources development and management, among other reasons. For planning, coordination, and evaluation of control activities, it is essential to possess reliable schistosomiasis prevalence maps. METHODOLOGY: We analyzed survey data compiled on a newly established open-access global neglected tropical diseases database (i to create smooth empirical prevalence maps for Schistosoma mansoni and S. haematobium for individuals aged ≤ 20 years in West Africa, including Cameroon, and (ii to derive country-specific prevalence estimates. We used Bayesian geostatistical models based on environmental predictors to take into account potential clustering due to common spatially structured exposures. Prediction at unobserved locations was facilitated by joint kriging. PRINCIPAL FINDINGS: Our models revealed that 50.8 million individuals aged ≤ 20 years in West Africa are infected with either S. mansoni, or S. haematobium, or both species concurrently. The country prevalence estimates ranged between 0.5% (The Gambia and 37.1% (Liberia for S. mansoni, and between 17.6% (The Gambia and 51.6% (Sierra Leone for S. haematobium. We observed that the combined prevalence for both schistosome species is two-fold lower in Gambia than previously reported, while we found an almost two-fold higher estimate for Liberia (58.3% than reported before (30.0%. Our predictions are likely to overestimate overall country prevalence, since modeling was based on children and adolescents up to the age of 20 years who are at highest risk of infection. CONCLUSION
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...
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 mixture models for Poisson astronomical images
Guglielmetti, Fabrizia; 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 well as the sources with their respective uncertainties. Background estimation and source detection is achieved in a single algorithm. A large variety of source morphologies is revealed. The technique is applied in the X-ray part of the electromagnetic spectrum on ROSAT and Chandra data sets and it is under a feasibility study for the forthcoming eROSITA mission.
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...
A new approach for Bayesian model averaging
Institute of Scientific and Technical Information of China (English)
TIAN XiangJun; XIE ZhengHui; WANG AiHui; YANG XiaoChun
2012-01-01
Bayesian model averaging (BMA) is a recently proposed statistical method for calibrating forecast ensembles from numerical weather models.However,successful implementation of BMA requires accurate estimates of the weights and variances of the individual competing models in the ensemble.Two methods,namely the Expectation-Maximization (EM) and the Markov Chain Monte Carlo (MCMC) algorithms,are widely used for BMA model training.Both methods have their own respective strengths and weaknesses.In this paper,we first modify the BMA log-likelihood function with the aim of removing the additional limitation that requires that the BMA weights add to one,and then use a limited memory quasi-Newtonian algorithm for solving the nonlinear optimization problem,thereby formulating a new approach for BMA (referred to as BMA-BFGS).Several groups of multi-model soil moisture simulation experiments from three land surface models show that the performance of BMA-BFGS is similar to the MCMC method in terms of simulation accuracy,and that both are superior to the EM algorithm.On the other hand,the computational cost of the BMA-BFGS algorithm is substantially less than for MCMC and is almost equivalent to that for EM.
International Nuclear Information System (INIS)
information, which is exhaustive throughout France, could help in estimating the telluric gamma dose rates. Such an approach is possible using multivariate geostatistics and cokriging. Multi-collocated cokriging has been performed on 1*1 km2 cells over the domain. This model used gamma dose rate measurement results and GUP classes. Our results provide useful information on the variability of the natural terrestrial gamma radiation in France (‘natural background’) and exposure data for epidemiological studies and risk assessment from low dose chronic exposures. - Highlights: • We estimate and map indoor terrestrial gamma rays in France. • Two geostatistical methods are compared to obtain the best estimation. • We use measurements results and a map of geological uranium potential. • The average gamma dose rate increases with classes of geological U potential. • The estimates are improved by using multi colocated co-kriging
Warnery, E; Ielsch, G; Lajaunie, C; Cale, E; Wackernagel, H; Debayle, C; Guillevic, J
2015-01-01
information, which is exhaustive throughout France, could help in estimating the telluric gamma dose rates. Such an approach is possible using multivariate geostatistics and cokriging. Multi-collocated cokriging has been performed on 1*1 km(2) cells over the domain. This model used gamma dose rate measurement results and GUP classes. Our results provide useful information on the variability of the natural terrestrial gamma radiation in France ('natural background') and exposure data for epidemiological studies and risk assessment from low dose chronic exposures. PMID:25464050
Energy Technology Data Exchange (ETDEWEB)
De Ascencao, Erika M.; Munckton, Toni; Digregorio, Ricardo [Petropiar (Venezuela)
2011-07-01
The Huyapari field, situated within the Faja Petrolifera del Orinoco (FPO) of Venezuela presents unique problems in terms of modeling. This field is spread over a wide area and is therefore subject to variable oil quality and complex fluvial facies architecture. Ameriven and PDVSA have been working on characterizing the ld's reservoirs in this field since 2000 and the aim of this paper is to present these efforts. Among others, a 3-D seismic survey completed in 1998 and a stratigraphic framework built from 149 vertical wells were used for reservoir characterization. Geostatistical techniques such as sequential Gaussian simulation with locally varying mean and cloud transform were also used. Results showed that these geostatistical methods accurately represented the architecture and properties of the reservoir and its fluid distribution. This paper showed that the application of numerous different techniques in the Hamasca area permitted reservoir complexity to be captured.
Bayesian Model Selection for LISA Pathfinder
Karnesis, Nikolaos; Sopuerta, Carlos F; Gibert, Ferran; Armano, Michele; Audley, Heather; Congedo, Giuseppe; Diepholz, Ingo; Ferraioli, Luigi; Hewitson, Martin; Hueller, Mauro; Korsakova, Natalia; Plagnol, Eric; Vitale, and Stefano
2013-01-01
The main goal of the LISA Pathfinder (LPF) mission is to fully characterize the acceleration noise models and to test key technologies for future space-based gravitational-wave observatories similar to the LISA/eLISA concept. The Data Analysis (DA) team has developed complex three-dimensional models of the LISA Technology Package (LTP) experiment on-board LPF. These models are used for simulations, but more importantly, they will be used for parameter estimation purposes during flight operations. One of the tasks of the DA team is to identify the physical effects that contribute significantly to the properties of the instrument noise. A way of approaching to this problem is to recover the essential parameters of the LTP which describe the data. Thus, we want to define the simplest model that efficiently explains the observations. To do so, adopting a Bayesian framework, one has to estimate the so-called Bayes Factor between two competing models. In our analysis, we use three main different methods to estimate...
Bayesian Model Averaging in the Instrumental Variable Regression Model
Gary Koop; Robert Leon Gonzalez; Rodney Strachan
2011-01-01
This paper considers the instrumental variable regression model when there is uncertainly about the set of instruments, exogeneity restrictions, the validity of identifying restrictions and the set of exogenous regressors. This uncertainly can result in a huge number of models. To avoid statistical problems associated with standard model selection procedures, we develop a reversible jump Markov chain Monte Carlo algorithm that allows us to do Bayesian model averaging. The algorithm is very fl...
EVENT MODEL: A ROBUST BAYESIAN TOOL FOR CHRONOLOGICAL MODELING
Lanos, Philippe; Philippe, Anne
2015-01-01
We propose a new modeling approach for combining dates through the Event model by using hierarchical Bayesian statistics. The Event model aims to estimate the date of a context (unit of stratification) from individual dates assumed to be contemporaneous and which are affected by errors of different types: laboratory and calibration curve errors and also irreducible errors related to contaminations, taphonomic disturbances, etc, hence the possible presence of outliers. The Event model has a hi...
Stochastic model updating utilizing Bayesian approach and Gaussian process model
Wan, Hua-Ping; Ren, Wei-Xin
2016-03-01
Stochastic model updating (SMU) has been increasingly applied in quantifying structural parameter uncertainty from responses variability. SMU for parameter uncertainty quantification refers to the problem of inverse uncertainty quantification (IUQ), which is a nontrivial task. Inverse problem solved with optimization usually brings about the issues of gradient computation, ill-conditionedness, and non-uniqueness. Moreover, the uncertainty present in response makes the inverse problem more complicated. In this study, Bayesian approach is adopted in SMU for parameter uncertainty quantification. The prominent strength of Bayesian approach for IUQ problem is that it solves IUQ problem in a straightforward manner, which enables it to avoid the previous issues. However, when applied to engineering structures that are modeled with a high-resolution finite element model (FEM), Bayesian approach is still computationally expensive since the commonly used Markov chain Monte Carlo (MCMC) method for Bayesian inference requires a large number of model runs to guarantee the convergence. Herein we reduce computational cost in two aspects. On the one hand, the fast-running Gaussian process model (GPM) is utilized to approximate the time-consuming high-resolution FEM. On the other hand, the advanced MCMC method using delayed rejection adaptive Metropolis (DRAM) algorithm that incorporates local adaptive strategy with global adaptive strategy is employed for Bayesian inference. In addition, we propose the use of the powerful variance-based global sensitivity analysis (GSA) in parameter selection to exclude non-influential parameters from calibration parameters, which yields a reduced-order model and thus further alleviates the computational burden. A simulated aluminum plate and a real-world complex cable-stayed pedestrian bridge are presented to illustrate the proposed framework and verify its feasibility.
Bayesian estimation of parameters in a regional hydrological model
Engeland, K.; Gottschalk, L.
2002-01-01
This study evaluates the applicability of the distributed, process-oriented Ecomag model for prediction of daily streamflow in ungauged basins. The Ecomag model is applied as a regional model to nine catchments in the NOPEX area, using Bayesian statistics to estimate the posterior distribution of the model parameters conditioned on the observed streamflow. The distribution is calculated by Markov Chain Monte Carlo (MCMC) analysis. The Bayesian method requires formulation of a likelihood funct...
Bayesian estimation of parameters in a regional hydrological model
Engeland, K.; Gottschalk, L.
2002-01-01
This study evaluates the applicability of the distributed, process-oriented Ecomag model for prediction of daily streamflow in ungauged basins. The Ecomag model is applied as a regional model to nine catchments in the NOPEX area, using Bayesian statistics to estimate the posterior distribution of the model parameters conditioned on the observed streamflow. The distribution is calculated by Markov Chain Monte Carlo (MCMC) analysis. The Bayesian method requires formulation of ...
Bayesian Analysis of Dynamic Multivariate Models with Multiple Structural Breaks
Sugita, Katsuhiro
2006-01-01
This paper considers a vector autoregressive model or a vector error correction model with multiple structural breaks in any subset of parameters, using a Bayesian approach with Markov chain Monte Carlo simulation technique. The number of structural breaks is determined as a sort of model selection by the posterior odds. For a cointegrated model, cointegrating rank is also allowed to change with breaks. Bayesian approach by Strachan (Journal of Business and Economic Statistics 21 (2003) 185) ...
GEOSTATISTICAL MODEL EVALUATION OF LIMING ON OSIJEK-BARANYA COUNTY EXAMPLE
Directory of Open Access Journals (Sweden)
Vladimir Vukadinović
2008-12-01
Full Text Available Unfavorable pH of soil is the main reason for several different problems in debalance of mineral nutrition which can cause many problems in plant growth; such as leaves and fruit chlorosis and necrosis; etc. Therefore; liming as a measure for improving amount of acids soils must be conducted very carefully; with detail chemical soil analyses. This paper presents a segment of computer model for liming recommendation at the example of Osijek-Baranya County. Results of liming recommendation were obtained by geostatistical interpolation method – kriging. Totals of 9023 soil samples were analyzed in the period 2003–2007. The substitution acidity average was 5.49 (minimum 3.41 to maximum 8.20. Kriging shown that 241 379 ha (58.3% area of Osijek-Baranya County were acids soil. Therefore 90 593 ha have substitution acidity lower than 4.5 and 150 786 ha have pH KCl between 4.5 and 5.5. Except carbocalk; other "slowly-effect" materials can be recommended for liming; especially for vineyards and orchards.
GEOSTATISTICAL MODEL EVALUATION OF LIMING ON OSIJEK-BARANYA COUNTY EXAMPLE
Directory of Open Access Journals (Sweden)
Vladimir Vukadinović
2008-12-01
Full Text Available Unfavorable pH of soil is the main reason for several different problems in debalance of mineral nutrition which can cause many problems in plant growth, such as leaves and fruit chlorosis and necrosis, etc. Therefore, liming as a measure for improving amount of acids soils must be conducted very carefully, with detail chemical soil analyses. This paper presents a segment of computer model for liming recommendation at the example of Osijek-Baranya County. Results of liming recommendation were obtained by geostatistical interpolation method – kriging. Totals of 9023 soil samples were analyzed in the period 2003–2007. The substitution acidity average was 5.49 (minimum 3.41 to maximum 8.20. Kriging shown that 241 379 ha (58.3% area of Osijek-Baranya County were acids soil. Therefore 90 593 ha have substitution acidity lower than 4.5 and 150 786 ha have pH International Symposium on Soil and Plant Analysis: Soil, Plant and Water Analysis: Quality Analytical Tools for an Era of Ecological Awareness. Soil and Plant Analysis Council, Cancun, Mexico, 36.KCl between 4.5 and 5.5. Except carbocalk, other "slowly-effect" materials can be recommended for liming, especially for vineyards and orchards.
You, Jiong; Pei, Zhiyuan
2015-01-01
With the development of remote sensing technology, its applications in agriculture monitoring systems, crop mapping accuracy, and spatial distribution are more and more being explored by administrators and users. Uncertainty in crop mapping is profoundly affected by the spatial pattern of spectral reflectance values obtained from the applied remote sensing data. Errors in remotely sensed crop cover information and the propagation in derivative products need to be quantified and handled correctly. Therefore, this study discusses the methods of error modeling for uncertainty characterization in crop mapping using GF-1 multispectral imagery. An error modeling framework based on geostatistics is proposed, which introduced the sequential Gaussian simulation algorithm to explore the relationship between classification errors and the spectral signature from remote sensing data source. On this basis, a misclassification probability model to produce a spatially explicit classification error probability surface for the map of a crop is developed, which realizes the uncertainty characterization for crop mapping. In this process, trend surface analysis was carried out to generate a spatially varying mean response and the corresponding residual response with spatial variation for the spectral bands of GF-1 multispectral imagery. Variogram models were employed to measure the spatial dependence in the spectral bands and the derived misclassification probability surfaces. Simulated spectral data and classification results were quantitatively analyzed. Through experiments using data sets from a region in the low rolling country located at the Yangtze River valley, it was found that GF-1 multispectral imagery can be used for crop mapping with a good overall performance, the proposal error modeling framework can be used to quantify the uncertainty in crop mapping, and the misclassification probability model can summarize the spatial variation in map accuracy and is helpful for
Bayesian Test of Significance for Conditional Independence: The Multinomial Model
de Morais Andrade, Pablo; Stern, Julio; de Bragança Pereira, Carlos
2014-03-01
Conditional independence tests (CI tests) have received special attention lately in Machine Learning and Computational Intelligence related literature as an important indicator of the relationship among the variables used by their models. In the field of Probabilistic Graphical Models (PGM)--which includes Bayesian Networks (BN) models--CI tests are especially important for the task of learning the PGM structure from data. In this paper, we propose the Full Bayesian Significance Test (FBST) for tests of conditional independence for discrete datasets. FBST is a powerful Bayesian test for precise hypothesis, as an alternative to frequentist's significance tests (characterized by the calculation of the \\emph{p-value}).
Bayesian Nonparametrics in Topic Modeling: A Brief Tutorial
Spangher, Alexander
2015-01-01
Using nonparametric methods has been increasingly explored in Bayesian hierarchical modeling as a way to increase model flexibility. Although the field shows a lot of promise, inference in many models, including Hierachical Dirichlet Processes (HDP), remain prohibitively slow. One promising path forward is to exploit the submodularity inherent in Indian Buffet Process (IBP) to derive near-optimal solutions in polynomial time. In this work, I will present a brief tutorial on Bayesian nonparame...
Two-Stage Bayesian Model Averaging in Endogenous Variable Models.
Lenkoski, Alex; Eicher, Theo S; Raftery, Adrian E
2014-01-01
Economic modeling in the presence of endogeneity is subject to model uncertainty at both the instrument and covariate level. We propose a Two-Stage Bayesian Model Averaging (2SBMA) methodology that extends the Two-Stage Least Squares (2SLS) estimator. By constructing a Two-Stage Unit Information Prior in the endogenous variable model, we are able to efficiently combine established methods for addressing model uncertainty in regression models with the classic technique of 2SLS. To assess the validity of instruments in the 2SBMA context, we develop Bayesian tests of the identification restriction that are based on model averaged posterior predictive p-values. A simulation study showed that 2SBMA has the ability to recover structure in both the instrument and covariate set, and substantially improves the sharpness of resulting coefficient estimates in comparison to 2SLS using the full specification in an automatic fashion. Due to the increased parsimony of the 2SBMA estimate, the Bayesian Sargan test had a power of 50 percent in detecting a violation of the exogeneity assumption, while the method based on 2SLS using the full specification had negligible power. We apply our approach to the problem of development accounting, and find support not only for institutions, but also for geography and integration as development determinants, once both model uncertainty and endogeneity have been jointly addressed. PMID:24223471
Bayesian model reduction and empirical Bayes for group (DCM) studies.
Friston, Karl J; Litvak, Vladimir; Oswal, Ashwini; Razi, Adeel; Stephan, Klaas E; van Wijk, Bernadette C M; Ziegler, Gabriel; Zeidman, Peter
2016-03-01
This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level - e.g., dynamic causal models - and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction. PMID:26569570
International Nuclear Information System (INIS)
UNCERT is a 2D and 3D geostatistics, uncertainty analysis and visualization software package applied to ground water flow and contaminant transport modeling. It is a collection of modules that provides tools for linear regression, univariate statistics, semivariogram analysis, inverse-distance gridding, trend-surface analysis, simple and ordinary kriging and discrete conditional indicator simulation. Graphical user interfaces for MODFLOW and MT3D, ground water flow and contaminant transport models, are provided for streamlined data input and result analysis. Visualization tools are included for displaying data input and output. These include, but are not limited to, 2D and 3D scatter plots, histograms, box and whisker plots, 2D contour maps, surface renderings of 2D gridded data and 3D views of gridded data. By design, UNCERT's graphical user interface and visualization tools facilitate model design and analysis. There are few built in restrictions on data set sizes and each module (with two exceptions) can be run in either graphical or batch mode. UNCERT is in the public domain and is available from the World Wide Web with complete on-line and printable (PDF) documentation. UNCERT is written in ANSI-C with a small amount of FORTRAN77, for UNIX workstations running X-Windows and Motif (or Lesstif). This article discusses the features of each module and demonstrates how they can be used individually and in combination. The tools are applicable to a wide range of fields and are currently used by researchers in the ground water, mining, mathematics, chemistry and geophysics, to name a few disciplines. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
Wingle, William L.; Poeter, Eileen P.; McKenna, Sean A.
1999-05-01
UNCERT is a 2D and 3D geostatistics, uncertainty analysis and visualization software package applied to ground water flow and contaminant transport modeling. It is a collection of modules that provides tools for linear regression, univariate statistics, semivariogram analysis, inverse-distance gridding, trend-surface analysis, simple and ordinary kriging and discrete conditional indicator simulation. Graphical user interfaces for MODFLOW and MT3D, ground water flow and contaminant transport models, are provided for streamlined data input and result analysis. Visualization tools are included for displaying data input and output. These include, but are not limited to, 2D and 3D scatter plots, histograms, box and whisker plots, 2D contour maps, surface renderings of 2D gridded data and 3D views of gridded data. By design, UNCERT's graphical user interface and visualization tools facilitate model design and analysis. There are few built in restrictions on data set sizes and each module (with two exceptions) can be run in either graphical or batch mode. UNCERT is in the public domain and is available from the World Wide Web with complete on-line and printable (PDF) documentation. UNCERT is written in ANSI-C with a small amount of FORTRAN77, for UNIX workstations running X-Windows and Motif (or Lesstif). This article discusses the features of each module and demonstrates how they can be used individually and in combination. The tools are applicable to a wide range of fields and are currently used by researchers in the ground water, mining, mathematics, chemistry and geophysics, to name a few disciplines.
Sampling Techniques in Bayesian Finite Element Model Updating
Boulkaibet, I; Mthembu, L; Friswell, M I; Adhikari, S
2011-01-01
Recent papers in the field of Finite Element Model (FEM) updating have highlighted the benefits of Bayesian techniques. The Bayesian approaches are designed to deal with the uncertainties associated with complex systems, which is the main problem in the development and updating of FEMs. This paper highlights the complexities and challenges of implementing any Bayesian method when the analysis involves a complicated structural dynamic model. In such systems an analytical Bayesian formulation might not be available in an analytic form; therefore this leads to the use of numerical methods, i.e. sampling methods. The main challenge then is to determine an efficient sampling of the model parameter space. In this paper, three sampling techniques, the Metropolis-Hastings (MH) algorithm, Slice Sampling and the Hybrid Monte Carlo (HMC) technique, are tested by updating a structural beam model. The efficiency and limitations of each technique is investigated when the FEM updating problem is implemented using the Bayesi...
Model-Based Geostatistical Mapping of the Prevalence of Onchocerca volvulus in West Africa
S.J. O’Hanlon (Simon J.); H.C. Slater (Hannah C.); R.A. Cheke (Robert A.); B.A. Boatin; L.E. Coffeng (Luc); S.D.S. Pion (Sébastien); M. Boussinesq (Michel); H.G.M. Zouré (Honorat G.); W.A. Stolk (Wilma); M-G. Basáñez (María-Gloria)
2016-01-01
textabstractBackground: The initial endemicity (pre-control prevalence) of onchocerciasis has been shown to be an important determinant of the feasibility of elimination by mass ivermectin distribution. We present the first geostatistical map of microfilarial prevalence in the former Onchocerciasis
Efficient Nonparametric Bayesian Modelling with Sparse Gaussian Process Approximations
Seeger, Matthias; Lawrence, Neil; Herbrich, Ralf
2006-01-01
Sparse approximations to Bayesian inference for nonparametric Gaussian Process models scale linearly in the number of training points, allowing for the application of powerful kernel-based models to large datasets. We present a general framework based on the informative vector machine (IVM) (Lawrence et.al., 2002) and show how the complete Bayesian task of inference and learning of free hyperparameters can be performed in a practically efficient manner. Our framework allows for arbitrary like...
Modelling biogeochemical cycles in forest ecosystems: a Bayesian approach
Bagnara, Maurizio
2015-01-01
Forest models are tools for explaining and predicting the dynamics of forest ecosystems. They simulate forest behavior by integrating information on the underlying processes in trees, soil and atmosphere. Bayesian calibration is the application of probability theory to parameter estimation. It is a method, applicable to all models, that quantifies output uncertainty and identifies key parameters and variables. This study aims at testing the Bayesian procedure for calibration to different t...
DEFF Research Database (Denmark)
Schur, Nadine; Hürlimann, Eveline; Stensgaard, Anna-Sofie;
2013-01-01
Schistosomiasis remains one of the most prevalent parasitic diseases in the tropics and subtropics, but current statistics are outdated due to demographic and ecological transformations and ongoing control efforts. Reliable risk estimates are important to plan and evaluate interventions...
Bayesian Inference and Optimal Design in the Sparse Linear Model
Seeger, Matthias; Steinke, Florian; Tsuda, Koji
2007-01-01
The sparse linear model has seen many successful applications in Statistics, Machine Learning, and Computational Biology, such as identification of gene regulatory networks from micro-array expression data. Prior work has either approximated Bayesian inference by expensive Markov chain Monte Carlo, or replaced it by point estimation. We show how to obtain a good approximation to Bayesian analysis efficiently, using the Expectation Propagation method. We also address the problems of optimal de...
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
Frystacky, H.; Osorio-Murillo, C. A.; Over, M. W.; Kalbacher, T.; Gunnell, D.; Kolditz, O.; Ames, D.; Rubin, Y.
2013-12-01
The Method of Anchored Distributions (MAD) is a Bayesian technique for characterizing the uncertainty in geostatistical model parameters. Open-source software has been developed in a modular framework such that this technique can be applied to any forward model software via a driver. This presentation is about the driver that has been developed for OpenGeoSys (OGS), open-source software that can simulate many hydrogeological processes, including couple processes. MAD allows the use of multiple data types for conditioning the spatially random fields and assessing model parameter likelihood. For example, if simulating flow and mass transport, the inversion target variable could be hydraulic conductivity and the inversion data types could be head, concentration, or both. The driver detects from the OGS files which processes and variables are being used in a given project and allows MAD to prompt the user to choose those that are to be modeled or to be treated deterministically. In this way, any combination of processes allowed by OGS can have MAD applied. As for the software, there are two versions, each with its own OGS driver. A Windows desktop version is available as a graphical user interface and is ideal for the learning and teaching environment. High-throughput computing can even be achieved with this version via HTCondor if large projects want to be pursued in a computer lab. In addition to this desktop application, a Linux version is available equipped with MPI such that it can be run in parallel on a computer cluster. All releases can be downloaded from the MAD Codeplex site given below.
Bayesian approach for three-dimensional aquifer characterization at the hanford 300 area
Directory of Open Access Journals (Sweden)
H. Murakami
2010-03-01
Full Text Available This study presents a stochastic, three-dimensional characterization of a heterogeneous hydraulic conductivity field within DOE's Hanford 300 Area site, Washington, by assimilating large-scale, constant-rate injection test data with small-scale, three-dimensional electromagnetic borehole flowmeter (EBF measurement data. We first inverted the injection test data to estimate the transmissivity field, using zeroth-order temporal moments of pressure buildup curves. We applied a newly developed Bayesian geostatistical inversion framework, the method of anchored distributions (MAD, to obtain a joint posterior distribution of geostatistical parameters and local log-transmissivities at multiple locations. The unique aspects of MAD that make it suitable for this purpose are its ability to integrate multi-scale, multi-type data within a Bayesian framework and to compute a nonparametric posterior distribution. After we combined the distribution of transmissivities with depth-discrete relative-conductivity profile from the EBF data, we inferred the three-dimensional geostatistical parameters of the log-conductivity field, using the Bayesian model-based geostatistics. Such consistent use of the Bayesian approach throughout the procedure enabled us to systematically incorporate data uncertainty into the final posterior distribution. The method was tested in a synthetic study and validated using the actual data that was not part of the estimation. Results showed broader and skewed posterior distributions of geostatistical parameters except for the mean, which suggests the importance of inferring the entire distribution to quantify the parameter uncertainty.
Modelling of JET diagnostics using Bayesian Graphical Models
Energy Technology Data Exchange (ETDEWEB)
Svensson, J. [IPP Greifswald, Greifswald (Germany); Ford, O. [Imperial College, London (United Kingdom); McDonald, D.; Hole, M.; Nessi, G. von; Meakins, A.; Brix, M.; Thomsen, H.; Werner, A.; Sirinelli, A.
2011-07-01
The mapping between physics parameters (such as densities, currents, flows, temperatures etc) defining the plasma 'state' under a given model and the raw observations of each plasma diagnostic will 1) depend on the particular physics model used, 2) is inherently probabilistic, from uncertainties on both observations and instrumental aspects of the mapping, such as calibrations, instrument functions etc. A flexible and principled way of modelling such interconnected probabilistic systems is through so called Bayesian graphical models. Being an amalgam between graph theory and probability theory, Bayesian graphical models can simulate the complex interconnections between physics models and diagnostic observations from multiple heterogeneous diagnostic systems, making it relatively easy to optimally combine the observations from multiple diagnostics for joint inference on parameters of the underlying physics model, which in itself can be represented as part of the graph. At JET about 10 diagnostic systems have to date been modelled in this way, and has lead to a number of new results, including: the reconstruction of the flux surface topology and q-profiles without any specific equilibrium assumption, using information from a number of different diagnostic systems; profile inversions taking into account the uncertainties in the flux surface positions and a substantial increase in accuracy of JET electron density and temperature profiles, including improved pedestal resolution, through the joint analysis of three diagnostic systems. It is believed that the Bayesian graph approach could potentially be utilised for very large sets of diagnostics, providing a generic data analysis framework for nuclear fusion experiments, that would be able to optimally utilize the information from multiple diagnostics simultaneously, and where the explicit graph representation of the connections to underlying physics models could be used for sophisticated model testing. This
Bayesian model discrimination for glucose-insulin homeostasis
DEFF Research Database (Denmark)
Andersen, Kim Emil; Brooks, Stephen P.; Højbjerre, Malene
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......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...
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.
International Nuclear Information System (INIS)
Numerical and geostatistical analyses show that the artificial smoothing effect of kriging removes high permeability flow paths from hydrogeologic data sets, reducing simulated contaminant transport rates in heterogeneous vadose zone systems. therefore, kriging alone is not recommended for estimating the spatial distribution of soil hydraulic properties for contaminant transport analysis at vadose zone sites. Vadose zone transport if modeled more effectively by combining kriging with stochastic simulation to better represent the high degree of spatial variability usually found in the hydraulic properties of field soils. However, kriging is a viable technique for estimating the initial mass distribution of contaminants in the subsurface
Geostatistical simulations for radon indoor with a nested model including the housing factor.
Cafaro, C; Giovani, C; Garavaglia, M
2016-01-01
The radon prone areas definition is matter of many researches in radioecology, since radon is considered a leading cause of lung tumours, therefore the authorities ask for support to develop an appropriate sanitary prevention strategy. In this paper, we use geostatistical tools to elaborate a definition accounting for some of the available information about the dwellings. Co-kriging is the proper interpolator used in geostatistics to refine the predictions by using external covariates. In advance, co-kriging is not guaranteed to improve significantly the results obtained by applying the common lognormal kriging. Here, instead, such multivariate approach leads to reduce the cross-validation residual variance to an extent which is deemed as satisfying. Furthermore, with the application of Monte Carlo simulations, the paradigm provides a more conservative radon prone areas definition than the one previously made by lognormal kriging. PMID:26547362
International Nuclear Information System (INIS)
The objective of this work is to combine several approaches to better understand nitrate fate in the Grand Morin aquifers (2700 km2), part of the Seine basin. CAWAQS results from the coupling of the hydrogeological model NEWSAM with the hydrodynamic and biogeochemical model of river PROSE. CAWAQS is coupled with the agronomic model STICS in order to simulate nitrate migration in basins. First, kriging provides a satisfactory representation of aquifer nitrate contamination from local observations, to set initial conditions for the physically based model. Then associated confidence intervals, derived from data using geostatistics, are used to validate CAWAQS results. Results and evaluation obtained from the combination of these approaches are given (period 1977-1988). Then CAWAQS is used to simulate nitrate fate for a 20-year period (1977-1996). The mean nitrate concentrations increase in aquifers is 0.09 mgN L-1 yr-1, resulting from an average infiltration flux of 3500 kgN.km-2 yr-1. - Combined use of geostatistics and physically based modeling allows assessment of nitrate concentrations in aquifer systems
Muthusamy, Manoranjan; Schellart, Alma; TAIT, Simon; B. M. Heuvelink, Gerard
2016-01-01
In this study we develop a method to estimate the spatially averaged rainfall intensity together with associated level of uncertainty using geostatistical upscaling. Rainfall data collected from a cluster of eight paired rain gauges in a 400 x 200 m2 urban catchment are used in combination with spatial stochastic simulation to obtain optimal predictions of the spatially averaged rainfall intensity at any point in time within the urban catchment. The uncertainty in the prediction of...
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...
Analysis of Gumbel Model for Software Reliability Using Bayesian Paradigm
Directory of Open Access Journals (Sweden)
Raj Kumar
2012-12-01
Full Text Available In this paper, we have illustrated the suitability of Gumbel Model for software reliability data. The model parameters are estimated using likelihood based inferential procedure: classical as well as Bayesian. The quasi Newton-Raphson algorithm is applied to obtain the maximum likelihood estimates and associated probability intervals. The Bayesian estimates of the parameters of Gumbel model are obtained using Markov Chain Monte Carlo(MCMC simulation method in OpenBUGS(established software for Bayesian analysis using Markov Chain Monte Carlo methods. The R functions are developed to study the statistical properties, model validation and comparison tools of the model and the output analysis of MCMC samples generated from OpenBUGS. Details of applying MCMC to parameter estimation for the Gumbel model are elaborated and a real software reliability data set is considered to illustrate the methods of inference discussed in this paper.
Moradkhani, Hamid; Yan, Hongxiang
2016-04-01
Soil moisture simulation and prediction are increasingly used to characterize agricultural droughts but the process suffers from data scarcity and quality. The satellite soil moisture observations could be used to improve model predictions with data assimilation. Remote sensing products, however, are typically discontinuous in spatial-temporal coverages; while simulated soil moisture products are potentially biased due to the errors in forcing data, parameters, and deficiencies of model physics. This study attempts to provide a detailed analysis of the joint and separate assimilation of streamflow and Advanced Scatterometer (ASCAT) surface soil moisture into a fully distributed hydrologic model, with the use of recently developed particle filter-Markov chain Monte Carlo (PF-MCMC) method. A geostatistical model is introduced to overcome the satellite soil moisture discontinuity issue where satellite data does not cover the whole study region or is significantly biased, and the dominant land cover is dense vegetation. The results indicate that joint assimilation of soil moisture and streamflow has minimal effect in improving the streamflow prediction, however, the surface soil moisture field is significantly improved. The combination of DA and geostatistical approach can further improve the surface soil moisture prediction.
Lack of Confidence in Approximate Bayesian Computation Model Choice
Robert, Christian P.; Cornuet, Jean-Marie; Marin, Jean-Michel; Pillai, Natesh S.
2011-01-01
Approximate Bayesian computation (ABC) have become an essential tool for the analysis of complex stochastic models. Grelaud et al. [(2009) Bayesian Anal 3:427–442] advocated the use of ABC for model choice in the specific case of Gibbs random fields, relying on an intermodel sufficiency property to show that the approximation was legitimate. We implemented ABC model choice in a wide range of phylogenetic models in the Do It Yourself-ABC (DIY-ABC) software [Cornuet et al. (2008) Bioinformatics...
Regional-scale geostatistical inverse modeling of North American CO2 fluxes: a synthetic data study
Directory of Open Access Journals (Sweden)
A. M. Michalak
2010-07-01
Full Text Available A series of synthetic data experiments is performed to investigate the ability of a regional atmospheric inversion to estimate grid-scale CO2 fluxes during the growing season over North America. The inversions are performed within a geostatistical framework without the use of any prior flux estimates or auxiliary variables, in order to focus on the atmospheric constraint provided by the nine towers collecting continuous, calibrated CO2 measurements in 2004. Using synthetic measurements and their associated concentration footprints, flux and model-data mismatch covariance parameters are first optimized, and then fluxes and their uncertainties are estimated at three different temporal resolutions. These temporal resolutions, which include a four-day average, a four-day-average diurnal cycle with 3-hourly increments, and 3-hourly fluxes, are chosen to help assess the impact of temporal aggregation errors on the estimated fluxes and covariance parameters. Estimating fluxes at a temporal resolution that can adjust the diurnal variability is found to be critical both for recovering covariance parameters directly from the atmospheric data, and for inferring accurate ecoregion-scale fluxes. Accounting for both spatial and temporal a priori covariance in the flux distribution is also found to be necessary for recovering accurate a posteriori uncertainty bounds on the estimated fluxes. Overall, the results suggest that even a fairly sparse network of 9 towers collecting continuous CO2 measurements across the continent, used with no auxiliary information or prior estimates of the flux distribution in time or space, can be used to infer relatively accurate monthly ecoregion scale CO2 surface fluxes over North America within estimated uncertainty bounds. Simulated random transport error is shown to decrease the quality of flux estimates in under-constrained areas at the ecoregion scale, although the uncertainty bounds remain realistic. While these synthetic
On the Bayesian Nonparametric Generalization of IRT-Type Models
San Martin, Ernesto; Jara, Alejandro; Rolin, Jean-Marie; Mouchart, Michel
2011-01-01
We study the identification and consistency of Bayesian semiparametric IRT-type models, where the uncertainty on the abilities' distribution is modeled using a prior distribution on the space of probability measures. We show that for the semiparametric Rasch Poisson counts model, simple restrictions ensure the identification of a general…
Bayesian inference model for fatigue life of laminated composites
DEFF Research Database (Denmark)
Dimitrov, Nikolay Krasimirov; Kiureghian, Armen Der; Berggreen, Christian
2016-01-01
A probabilistic model for estimating the fatigue life of laminated composite plates is developed. The model is based on lamina-level input data, making it possible to predict fatigue properties for a wide range of laminate configurations. Model parameters are estimated by Bayesian inference. The...
A Practical Primer on Geostatistics
Olea, Ricardo A.
2009-01-01
THE CHALLENGE Most geological phenomena are extraordinarily complex in their interrelationships and vast in their geographical extension. Ordinarily, engineers and geoscientists are faced with corporate or scientific requirements to properly prepare geological models with measurements involving a small fraction of the entire area or volume of interest. Exact description of a system such as an oil reservoir is neither feasible nor economically possible. The results are necessarily uncertain. Note that the uncertainty is not an intrinsic property of the systems; it is the result of incomplete knowledge by the observer. THE AIM OF GEOSTATISTICS The main objective of geostatistics is the characterization of spatial systems that are incompletely known, systems that are common in geology. A key difference from classical statistics is that geostatistics uses the sampling location of every measurement. Unless the measurements show spatial correlation, the application of geostatistics is pointless. Ordinarily the need for additional knowledge goes beyond a few points, which explains the display of results graphically as fishnet plots, block diagrams, and maps. GEOSTATISTICAL METHODS Geostatistics is a collection of numerical techniques for the characterization of spatial attributes using primarily two tools: probabilistic models, which are used for spatial data in a manner similar to the way in which time-series analysis characterizes temporal data, or pattern recognition techniques. The probabilistic models are used as a way to handle uncertainty in results away from sampling locations, making a radical departure from alternative approaches like inverse distance estimation methods. DIFFERENCES WITH TIME SERIES On dealing with time-series analysis, users frequently concentrate their attention on extrapolations for making forecasts. Although users of geostatistics may be interested in extrapolation, the methods work at their best interpolating. This simple difference has
Modelling LGD for unsecured retail loans using Bayesian methods
Katarzyna Bijak; Thomas, Lyn C
2015-01-01
Loss Given Default (LGD) is the loss borne by the bank when a customer defaults on a loan. LGD for unsecured retail loans is often found difficult to model. In the frequentist (non-Bayesian) two-step approach, two separate regression models are estimated independently, which can be considered potentially problematic when trying to combine them to make predictions about LGD. The result is a point estimate of LGD for each loan. Alternatively, LGD can be modelled using Bayesian methods. In the B...
A Bayesian Matrix Factorization Model for Relational Data
Singh, Ajit P
2012-01-01
Relational learning can be used to augment one data source with other correlated sources of information, to improve predictive accuracy. We frame a large class of relational learning problems as matrix factorization problems, and propose a hierarchical Bayesian model. Training our Bayesian model using random-walk Metropolis-Hastings is impractically slow, and so we develop a block Metropolis- Hastings sampler which uses the gradient and Hessian of the likelihood to dynamically tune the proposal. We demonstrate that a predictive model of brain response to stimuli can be improved by augmenting it with side information about the stimuli.
Bayesian inference of chemical kinetic models from proposed reactions
Galagali, Nikhil
2015-02-01
© 2014 Elsevier Ltd. Bayesian inference provides a natural framework for combining experimental data with prior knowledge to develop chemical kinetic models and quantify the associated uncertainties, not only in parameter values but also in model structure. Most existing applications of Bayesian model selection methods to chemical kinetics have been limited to comparisons among a small set of models, however. The significant computational cost of evaluating posterior model probabilities renders traditional Bayesian methods infeasible when the model space becomes large. We present a new framework for tractable Bayesian model inference and uncertainty quantification using a large number of systematically generated model hypotheses. The approach involves imposing point-mass mixture priors over rate constants and exploring the resulting posterior distribution using an adaptive Markov chain Monte Carlo method. The posterior samples are used to identify plausible models, to quantify rate constant uncertainties, and to extract key diagnostic information about model structure-such as the reactions and operating pathways most strongly supported by the data. We provide numerical demonstrations of the proposed framework by inferring kinetic models for catalytic steam and dry reforming of methane using available experimental data.
The Bayesian Modelling Of Inflation Rate In Romania
Directory of Open Access Journals (Sweden)
Mihaela Simionescu (Bratu
2014-06-01
Full Text Available 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 estimation was presented, realizing two empirical studies for data taken from the Romanian economy. Thus, an autoregressive model of order 2 and a multiple regression model were built for the index of consumer prices. The Gibbs sampling algorithm was used for estimation in R software, computing the posterior means and the standard deviations. The parameters’ stability proved to be greater than in the case of estimations based on the methods of classical Econometrics.
Bayesian Subset Modeling for High-Dimensional Generalized Linear Models
Liang, Faming
2013-06-01
This article presents a new prior setting for high-dimensional generalized linear models, which leads to a Bayesian subset regression (BSR) with the maximum a posteriori model approximately equivalent to the minimum extended Bayesian information criterion model. The consistency of the resulting posterior is established under mild conditions. Further, a variable screening procedure is proposed based on the marginal inclusion probability, which shares the same properties of sure screening and consistency with the existing sure independence screening (SIS) and iterative sure independence screening (ISIS) procedures. However, since the proposed procedure makes use of joint information from all predictors, it generally outperforms SIS and ISIS in real applications. This article also makes extensive comparisons of BSR with the popular penalized likelihood methods, including Lasso, elastic net, SIS, and ISIS. The numerical results indicate that BSR can generally outperform the penalized likelihood methods. The models selected by BSR tend to be sparser and, more importantly, of higher prediction ability. In addition, the performance of the penalized likelihood methods tends to deteriorate as the number of predictors increases, while this is not significant for BSR. Supplementary materials for this article are available online. © 2013 American Statistical Association.
Involving Stakeholders in Building Integrated Fisheries Models Using Bayesian Methods
Haapasaari, Päivi; Mäntyniemi, Samu; Kuikka, Sakari
2013-06-01
A participatory Bayesian approach was used to investigate how the views of stakeholders could be utilized to develop models to help understand the Central Baltic herring fishery. In task one, we applied the Bayesian belief network methodology to elicit the causal assumptions of six stakeholders on factors that influence natural mortality, growth, and egg survival of the herring stock in probabilistic terms. We also integrated the expressed views into a meta-model using the Bayesian model averaging (BMA) method. In task two, we used influence diagrams to study qualitatively how the stakeholders frame the management problem of the herring fishery and elucidate what kind of causalities the different views involve. The paper combines these two tasks to assess the suitability of the methodological choices to participatory modeling in terms of both a modeling tool and participation mode. The paper also assesses the potential of the study to contribute to the development of participatory modeling practices. It is concluded that the subjective perspective to knowledge, that is fundamental in Bayesian theory, suits participatory modeling better than a positivist paradigm that seeks the objective truth. The methodology provides a flexible tool that can be adapted to different kinds of needs and challenges of participatory modeling. The ability of the approach to deal with small data sets makes it cost-effective in participatory contexts. However, the BMA methodology used in modeling the biological uncertainties is so complex that it needs further development before it can be introduced to wider use in participatory contexts.
Energy Technology Data Exchange (ETDEWEB)
Gauthier, Y.
1997-10-20
Geostatistical tools are increasingly used to model permeability fields in subsurface reservoirs, which are considered as a particular random variable development depending of several geostatistical parameters such as variance and correlation length. The first part of the thesis is devoted to the study of relations existing between the transient well pressure (the well test) and the stochastic permeability field, using the apparent permeability concept.The well test performs a moving permeability average over larger and larger volume with increasing time. In the second part, the geostatistical parameters are evaluated using well test data; a Bayesian framework is used and parameters are estimated using the maximum likelihood principle by maximizing the well test data probability density function with respect to these parameters. This method, involving a well test fast evaluation, provides an estimation of the correlation length and the variance over different realizations of a two-dimensional permeability field
Bayesian modeling and prediction of solar particles flux
Czech Academy of Sciences Publication Activity Database
Dedecius, Kamil; Kalová, J.
Praha: FJFI ČVUT v Praze, 2009 - (Štěpán, V.), s. 77-77 ISBN 978-80-01-04430-8. [XXXI. Dny radiační ochrany. Kouty nad Desnou, Hrubý Jeseník (CZ), 02.11.2009-06.11.2009] R&D Projects: GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : Bayesian model * solar particle * solar wind Subject RIV: IN - Informatics, Computer Science http://library.utia.cas.cz/separaty/2009/AS/dedecius-bayesian modeling and prediction of solar particle s flux.pdf
Research & development and growth: A Bayesian model averaging analysis
Czech Academy of Sciences Publication Activity Database
Horváth, Roman
2011-01-01
Roč. 28, č. 6 (2011), s. 2669-2673. ISSN 0264-9993. [Society for Non-linear Dynamics and Econometrics Annual Conferencen. Washington DC, 16.03.2011-18.03.2011] R&D Projects: GA ČR GA402/09/0965 Institutional research plan: CEZ:AV0Z10750506 Keywords : Research and development * Growth * Bayesian model averaging Subject RIV: AH - Economics Impact factor: 0.701, year: 2011 http://library.utia.cas.cz/separaty/2011/E/horvath-research & development and growth a bayesian model averaging analysis.pdf
Approximate Bayesian Recursive Estimation of Linear Model with Uniform Noise
Czech Academy of Sciences Publication Activity Database
Pavelková, Lenka; Kárný, Miroslav
Brussels: IFAC, 2012, s. 1803-1807. ISBN 978-3-902823-06-9. [16th IFAC Symposium on System Identification The International Federation of Automatic Control. Brussels (BE), 11.07.2012-13.07.2012] R&D Projects: GA TA ČR TA01030123 Institutional support: RVO:67985556 Keywords : recursive parameter estimation * bounded noise * Bayesian learning * autoregressive models Subject RIV: BC - Control System s Theory http://library.utia.cas.cz/separaty/2012/AS/pavelkova-approximate bayesian recursive estimation of linear model with uniform noise.pdf
Comparing Bayesian models for multisensory cue combination without mandatory integration
Beierholm, Ulrik R.; Shams, Ladan; Kording, Konrad P; Ma, Wei Ji
2009-01-01
Bayesian models of multisensory perception traditionally address the problem of estimating an underlying variable that is assumed to be the cause of the two sensory signals. The brain, however, has to solve a more general problem: it also has to establish which signals come from the same source and should be integrated, and which ones do not and should be segregated. In the last couple of years, a few models have been proposed to solve this problem in a Bayesian fashion. One of these ha...
Bayesian model mixing for cold rolling mills: Test results
Czech Academy of Sciences Publication Activity Database
Ettler, P.; Puchr, I.; Dedecius, Kamil
Slovensko: Slovak University of Technology, 2013, s. 359-364. ISBN 978-1-4799-0926-1. [19th International Conference on Process Control . Štrbské Pleso (SK), 18.06.2013-21.06.2013] R&D Projects: GA MŠk(CZ) 7D09008; GA MŠk 7D12004 Keywords : Bayesian statistics * model mixing * process control Subject RIV: BC - Control Systems Theory http://library.utia.cas.cz/separaty/2013/AS/dedecius-bayesian model mixing for cold rolling mills test results.pdf
Bayesian Model Comparison With the g-Prior
DEFF Research Database (Denmark)
Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Cemgil, Ali Taylan;
2014-01-01
Model comparison and selection is an important problem in many model-based signal processing applications. Often, very simple information criteria such as the Akaike information criterion or the Bayesian information criterion are used despite their shortcomings. Compared to these methods, Djuric’...
Bayesian Estimation of the DINA Model with Gibbs Sampling
Culpepper, Steven Andrew
2015-01-01
A Bayesian model formulation of the deterministic inputs, noisy "and" gate (DINA) model is presented. Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. The procedure extends concepts in Béguin and Glas,…
Directory of Open Access Journals (Sweden)
Laura Grisotto
2016-04-01
Full Text Available In this paper the focus is on environmental statistics, with the aim of estimating the concentration surface and related uncertainty of an air pollutant. We used air quality data recorded by a network of monitoring stations within a Bayesian framework to overcome difficulties in accounting for prediction uncertainty and to integrate information provided by deterministic models based on emissions meteorology and chemico-physical characteristics of the atmosphere. Several authors have proposed such integration, but all the proposed approaches rely on representativeness and completeness of existing air pollution monitoring networks. We considered the situation in which the spatial process of interest and the sampling locations are not independent. This is known in the literature as the preferential sampling problem, which if ignored in the analysis, can bias geostatistical inferences. We developed a Bayesian geostatistical model to account for preferential sampling with the main interest in statistical integration and uncertainty. We used PM10 data arising from the air quality network of the Environmental Protection Agency of Lombardy Region (Italy and numerical outputs from the deterministic model. We specified an inhomogeneous Poisson process for the sampling locations intensities and a shared spatial random component model for the dependence between the spatial location of monitors and the pollution surface. We found greater predicted standard deviation differences in areas not properly covered by the air quality network. In conclusion, in this context inferences on prediction uncertainty may be misleading when geostatistical modelling does not take into account preferential sampling.
Grisotto, Laura; Consonni, Dario; Cecconi, Lorenzo; Catelan, Dolores; Lagazio, Corrado; Bertazzi, Pier Alberto; Baccini, Michela; Biggeri, Annibale
2016-01-01
In this paper the focus is on environmental statistics, with the aim of estimating the concentration surface and related uncertainty of an air pollutant. We used air quality data recorded by a network of monitoring stations within a Bayesian framework to overcome difficulties in accounting for prediction uncertainty and to integrate information provided by deterministic models based on emissions meteorology and chemico-physical characteristics of the atmosphere. Several authors have proposed such integration, but all the proposed approaches rely on representativeness and completeness of existing air pollution monitoring networks. We considered the situation in which the spatial process of interest and the sampling locations are not independent. This is known in the literature as the preferential sampling problem, which if ignored in the analysis, can bias geostatistical inferences. We developed a Bayesian geostatistical model to account for preferential sampling with the main interest in statistical integration and uncertainty. We used PM10 data arising from the air quality network of the Environmental Protection Agency of Lombardy Region (Italy) and numerical outputs from the deterministic model. We specified an inhomogeneous Poisson process for the sampling locations intensities and a shared spatial random component model for the dependence between the spatial location of monitors and the pollution surface. We found greater predicted standard deviation differences in areas not properly covered by the air quality network. In conclusion, in this context inferences on prediction uncertainty may be misleading when geostatistical modelling does not take into account preferential sampling. PMID:27087040
Computational system for geostatistical analysis
Directory of Open Access Journals (Sweden)
Vendrusculo Laurimar Gonçalves
2004-01-01
Full Text Available Geostatistics identifies the spatial structure of variables representing several phenomena and its use is becoming more intense in agricultural activities. This paper describes a computer program, based on Windows Interfaces (Borland Delphi, which performs spatial analyses of datasets through geostatistic tools: Classical statistical calculations, average, cross- and directional semivariograms, simple kriging estimates and jackknifing calculations. A published dataset of soil Carbon and Nitrogen was used to validate the system. The system was useful for the geostatistical analysis process, for the manipulation of the computational routines in a MS-DOS environment. The Windows development approach allowed the user to model the semivariogram graphically with a major degree of interaction, functionality rarely available in similar programs. Given its characteristic of quick prototypation and simplicity when incorporating correlated routines, the Delphi environment presents the main advantage of permitting the evolution of this system.
Bayesian Joint Modelling for Object Localisation in Weakly Labelled Images.
Shi, Zhiyuan; Hospedales, Timothy M; Xiang, Tao
2015-10-01
We address the problem of localisation of objects as bounding boxes in images and videos with weak labels. This weakly supervised object localisation problem has been tackled in the past using discriminative models where each object class is localised independently from other classes. In this paper, a novel framework based on Bayesian joint topic modelling is proposed, which differs significantly from the existing ones in that: (1) All foreground object classes are modelled jointly in a single generative model that encodes multiple object co-existence so that "explaining away" inference can resolve ambiguity and lead to better learning and localisation. (2) Image backgrounds are shared across classes to better learn varying surroundings and "push out" objects of interest. (3) Our model can be learned with a mixture of weakly labelled and unlabelled data, allowing the large volume of unlabelled images on the Internet to be exploited for learning. Moreover, the Bayesian formulation enables the exploitation of various types of prior knowledge to compensate for the limited supervision offered by weakly labelled data, as well as Bayesian domain adaptation for transfer learning. Extensive experiments on the PASCAL VOC, ImageNet and YouTube-Object videos datasets demonstrate the effectiveness of our Bayesian joint model for weakly supervised object localisation. PMID:26340253
Energy Technology Data Exchange (ETDEWEB)
Zargar, G.
2005-10-15
In this thesis, we present a new approach, which consists in directly up-scaling the geostatistical permeability distribution rather than the individual realizations. Practically, filtering techniques based on. the FFT (Fast Fourier Transform), allows us to generate geostatistical images, which sample the up-scaled distributions. In the log normal case, an equivalence hydraulic criterion is proposed, allowing to re-estimate the geometric mean of the permeabilities. In the anisotropic case, the effective geometric mean becomes a tensor which depends on the level of filtering used and it can be calculated by a method of renormalisation. Then, the method was generalized for the categorial model. Numerical tests of the method were set up for isotropic, anisotropic and categorial models, which shows good agreement with theory. (author)
Maximum Likelihood Bayesian Averaging of Spatial Variability Models in Unsaturated Fractured Tuff
International Nuclear Information System (INIS)
Hydrologic analyses typically rely on a single conceptual-mathematical model. Yet hydrologic environments are open and complex, rendering them prone to multiple interpretations and mathematical descriptions. Adopting only one of these may lead to statistical bias and underestimation of uncertainty. Bayesian Model Averaging (BMA) provides an optimal way to combine the predictions of several competing models and to assess their joint predictive uncertainty. However, it tends to be computationally demanding and relies heavily on prior information about model parameters. We apply a maximum likelihood (ML) version of BMA (MLBMA) to seven alternative variogram models of log air permeability data from single-hole pneumatic injection tests in six boreholes at the Apache Leap Research Site (ALRS) in central Arizona. Unbiased ML estimates of variogram and drift parameters are obtained using Adjoint State Maximum Likelihood Cross Validation in conjunction with Universal Kriging and Generalized L east Squares. Standard information criteria provide an ambiguous ranking of the models, which does not justify selecting one of them and discarding all others as is commonly done in practice. Instead, we eliminate some of the models based on their negligibly small posterior probabilities and use the rest to project the measured log permeabilities by kriging onto a rock volume containing the six boreholes. We then average these four projections, and associated kriging variances, using the posterior probability of each model as weight. Finally, we cross-validate the results by eliminating from consideration all data from one borehole at a time, repeating the above process, and comparing the predictive capability of MLBMA with that of each individual model. We find that MLBMA is superior to any individual geostatistical model of log permeability among those we consider at the ALRS
P Moraga; Cano, J; Baggaley, RF; Gyapong, JO; Njenga, SM; Nikolay, B.; Davies, E.; Rebollo, MP; Pullan, RL; Bockarie, MJ; Hollingsworth, TD; Gambhir, M; Brooker, SJ
2015-01-01
Background Lymphatic filariasis (LF) is one of the neglected tropical diseases targeted for global elimination. The ability to interrupt transmission is, partly, influenced by the underlying intensity of transmission and its geographical variation. This information can also help guide the design of targeted surveillance activities. The present study uses a combination of geostatistical and mathematical modelling to predict the prevalence and transmission intensity of LF prior to the implement...
Spatial and spatio-temporal bayesian models with R - INLA
Blangiardo, Marta
2015-01-01
Dedication iiiPreface ix1 Introduction 11.1 Why spatial and spatio-temporal statistics? 11.2 Why do we use Bayesian methods for modelling spatial and spatio-temporal structures? 21.3 Why INLA? 31.4 Datasets 32 Introduction to 212.1 The language 212.2 objects 222.3 Data and session management 342.4 Packages 352.5 Programming in 362.6 Basic statistical analysis with 393 Introduction to Bayesian Methods 533.1 Bayesian Philosophy 533.2 Basic Probability Elements 573.3 Bayes Theorem 623.4 Prior and Posterior Distributions 643.5 Working with the Posterior Distribution 663.6 Choosing the Prior Distr
Modeling error distributions of growth curve models through Bayesian methods.
Zhang, Zhiyong
2016-06-01
Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is proposed to flexibly model normal and non-normal data through the explicit specification of the error distributions. A simulation study shows when the distribution of the error is correctly specified, one can avoid the loss in the efficiency of standard error estimates. A real example on the analysis of mathematical ability growth data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 is used to show the application of the proposed methods. Instructions and code on how to conduct growth curve analysis with both normal and non-normal error distributions using the the MCMC procedure of SAS are provided. PMID:26019004
Asymptotically minimax Bayesian predictive densities for multinomial models
Komaki, Fumiyasu
2011-01-01
One-step ahead prediction for the multinomial model is considered. The performance of a predictive density is evaluated by the average Kullback-Leibler divergence from the true density to the predictive density. Asymptotic approximations of risk functions of Bayesian predictive densities based on Dirichlet priors are obtained. It is shown that a Bayesian predictive density based on a specific Dirichlet prior is asymptotically minimax. The asymptotically minimax prior is different from known objective priors such as the Jeffreys prior or the uniform prior.
Uncertainty Modeling Based on Bayesian Network in Ontology Mapping
Institute of Scientific and Technical Information of China (English)
LI Yuhua; LIU Tao; SUN Xiaolin
2006-01-01
How to deal with uncertainty is crucial in exact concept mapping between ontologies. This paper presents a new framework on modeling uncertainty in ontologies based on bayesian networks (BN). In our approach, ontology Web language (OWL) is extended to add probabilistic markups for attaching probability information, the source and target ontologies (expressed by patulous OWL) are translated into bayesian networks (BNs), the mapping between the two ontologies can be digged out by constructing the conditional probability tables (CPTs) of the BN using a improved algorithm named I-IPFP based on iterative proportional fitting procedure (IPFP). The basic idea of this framework and algorithm are validated by positive results from computer experiments.
Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring.
Carroll, Carlos; Johnson, Devin S; Dunk, Jeffrey R; Zielinski, William J
2010-12-01
Biologists who develop and apply habitat models are often familiar with the statistical challenges posed by their data's spatial structure but are unsure of whether the use of complex spatial models will increase the utility of model results in planning. We compared the relative performance of nonspatial and hierarchical Bayesian spatial models for three vertebrate and invertebrate taxa of conservation concern (Church's sideband snails [Monadenia churchi], red tree voles [Arborimus longicaudus], and Pacific fishers [Martes pennanti pacifica]) that provide examples of a range of distributional extents and dispersal abilities. We used presence-absence data derived from regional monitoring programs to develop models with both landscape and site-level environmental covariates. We used Markov chain Monte Carlo algorithms and a conditional autoregressive or intrinsic conditional autoregressive model framework to fit spatial models. The fit of Bayesian spatial models was between 35 and 55% better than the fit of nonspatial analogue models. Bayesian spatial models outperformed analogous models developed with maximum entropy (Maxent) methods. Although the best spatial and nonspatial models included similar environmental variables, spatial models provided estimates of residual spatial effects that suggested how ecological processes might structure distribution patterns. Spatial models built from presence-absence data improved fit most for localized endemic species with ranges constrained by poorly known biogeographic factors and for widely distributed species suspected to be strongly affected by unmeasured environmental variables or population processes. By treating spatial effects as a variable of interest rather than a nuisance, hierarchical Bayesian spatial models, especially when they are based on a common broad-scale spatial lattice (here the national Forest Inventory and Analysis grid of 24 km(2) hexagons), can increase the relevance of habitat models to multispecies
Bayesian Modelling of fMRI Time Series
DEFF Research Database (Denmark)
Højen-Sørensen, Pedro; Hansen, Lars Kai; Rasmussen, Carl Edward
2000-01-01
We present a Hidden Markov Model (HMM) for inferring the hidden psychological state (or neural activity) during single trial fMRI activation experiments with blocked task paradigms. Inference is based on Bayesian methodology, using a combination of analytical and a variety of Markov Chain Monte...
Bayesian Modelling of fMRI Time Series
DEFF Research Database (Denmark)
Højen-Sørensen, Pedro; Hansen, Lars Kai; Rasmussen, Carl Edward
We present a Hidden Markov Model (HMM) for inferring the hidden psychological state (or neural activity) during single trial fMRI activation experiments with blocked task paradigms. Inference is based on Bayesian methodology, using a combination of analytical and a variety of Markov Chain Monte...
Bayesian nonparametric estimation of hazard rate in monotone Aalen model
Czech Academy of Sciences Publication Activity Database
Timková, Jana
2014-01-01
Roč. 50, č. 6 (2014), s. 849-868. ISSN 0023-5954 Institutional support: RVO:67985556 Keywords : Aalen model * Bayesian estimation * MCMC Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.541, year: 2014 http://library.utia.cas.cz/separaty/2014/SI/timkova-0438210.pdf
An Inhomogeneous Bayesian Texture Model for Spatially Varying Parameter Estimation
Dharmagunawardhana, Chathurika; Mahmoodi, Sasan; Bennett, Michael; Niranjan, Mahesan
2014-01-01
In statistical model based texture feature extraction, features based on spatially varying parameters achieve higher discriminative performances compared to spatially constant parameters. In this paper we formulate a novel Bayesian framework which achieves texture characterization by spatially varying parameters based on Gaussian Markov random fields. The parameter estimation is carried out by Metropolis-Hastings algorithm. The distributions of estimated spatially varying paramete...
Andrade, A I A S S; Stigter, T Y
2013-04-01
In this study multivariate and geostatistical methods are jointly applied to model the spatial and temporal distribution of arsenic (As) concentrations in shallow groundwater as a function of physicochemical, hydrogeological and land use parameters, as well as to assess the related uncertainty. The study site is located in the Mondego River alluvial body in Central Portugal, where maize, rice and some vegetable crops dominate. In a first analysis scatter plots are used, followed by the application of principal component analysis to two different data matrices, of 112 and 200 samples, with the aim of detecting associations between As levels and other quantitative parameters. In the following phase explanatory models of As are created through factorial regression based on correspondence analysis, integrating both quantitative and qualitative parameters. Finally, these are combined with indicator-geostatistical techniques to create maps indicating the predicted probability of As concentrations in groundwater exceeding the current global drinking water guideline of 10 μg/l. These maps further allow assessing the uncertainty and representativeness of the monitoring network. A clear effect of the redox state on the presence of As is observed, and together with significant correlations with dissolved oxygen, nitrate, sulfate, iron, manganese and alkalinity, points towards the reductive dissolution of Fe (hydr)oxides as the essential mechanism of As release. The association of high As values with rice crop, known to promote reduced environments due to ponding, further corroborates this hypothesis. An additional source of As from fertilizers cannot be excluded, as the correlation with As is higher where rice is associated with vegetables, normally associated with higher fertilization rates. The best explanatory model of As occurrence integrates the parameters season, crop type, well and water depth, nitrate and Eh, though a model without the last two parameters also gives
Research on Bayesian Network Based User's Interest Model
Institute of Scientific and Technical Information of China (English)
ZHANG Weifeng; XU Baowen; CUI Zifeng; XU Lei
2007-01-01
It has very realistic significance for improving the quality of users' accessing information to filter and selectively retrieve the large number of information on the Internet. On the basis of analyzing the existing users' interest models and some basic questions of users' interest (representation, derivation and identification of users' interest), a Bayesian network based users' interest model is given. In this model, the users' interest reduction algorithm based on Markov Blanket model is used to reduce the interest noise, and then users' interested and not interested documents are used to train the Bayesian network. Compared to the simple model, this model has the following advantages like small space requirements, simple reasoning method and high recognition rate. The experiment result shows this model can more appropriately reflect the user's interest, and has higher performance and good usability.
Bayesian estimation of parameters in a regional hydrological model
Directory of Open Access Journals (Sweden)
K. Engeland
2002-01-01
Full Text Available This study evaluates the applicability of the distributed, process-oriented Ecomag model for prediction of daily streamflow in ungauged basins. The Ecomag model is applied as a regional model to nine catchments in the NOPEX area, using Bayesian statistics to estimate the posterior distribution of the model parameters conditioned on the observed streamflow. The distribution is calculated by Markov Chain Monte Carlo (MCMC analysis. The Bayesian method requires formulation of a likelihood function for the parameters and three alternative formulations are used. The first is a subjectively chosen objective function that describes the goodness of fit between the simulated and observed streamflow, as defined in the GLUE framework. The second and third formulations are more statistically correct likelihood models that describe the simulation errors. The full statistical likelihood model describes the simulation errors as an AR(1 process, whereas the simple model excludes the auto-regressive part. The statistical parameters depend on the catchments and the hydrological processes and the statistical and the hydrological parameters are estimated simultaneously. The results show that the simple likelihood model gives the most robust parameter estimates. The simulation error may be explained to a large extent by the catchment characteristics and climatic conditions, so it is possible to transfer knowledge about them to ungauged catchments. The statistical models for the simulation errors indicate that structural errors in the model are more important than parameter uncertainties. Keywords: regional hydrological model, model uncertainty, Bayesian analysis, Markov Chain Monte Carlo analysis
International Nuclear Information System (INIS)
Knowledge of the subject matter is obviously important to fill in the gaps between the information we have and information we want to have (or we wish at least). Assume a geological example where knowing that we are dealing with a sand bar or a meandering channel increase our ability to predict the location, geometry, and orientation of a petroleum reservoir. Such knowledge is largely qualitative rather than quantitative but notwithstanding they must be integrate in a geostatistical model. The paper deals with incorporation of the geological interpretation of a fault system into a three dimensional geostatistical model of geometry of the lignite seam b1 - Beladice. When the fault system is defined, the data must be considered with regard to all fault segments: data points located in the 'shadow' of a fault segment, when seen from the target pont, cannot be selected during interpolation procedure as well as during calculation of the experimental variogram. In this way, the fault system divides a studied area into some smaller sub-areas. In presented paper, the single steps of the geostatistical case study are compared to the case ignoring the influence of the fault system on the final results. (authors)
Implementation of the Iterative Proportion Fitting Algorithm for Geostatistical Facies Modeling
Energy Technology Data Exchange (ETDEWEB)
Li Yupeng, E-mail: yupeng@ualberta.ca; Deutsch, Clayton V. [University of Alberta (Canada)
2012-06-15
In geostatistics, most stochastic algorithm for simulation of categorical variables such as facies or rock types require a conditional probability distribution. The multivariate probability distribution of all the grouped locations including the unsampled location permits calculation of the conditional probability directly based on its definition. In this article, the iterative proportion fitting (IPF) algorithm is implemented to infer this multivariate probability. Using the IPF algorithm, the multivariate probability is obtained by iterative modification to an initial estimated multivariate probability using lower order bivariate probabilities as constraints. The imposed bivariate marginal probabilities are inferred from profiles along drill holes or wells. In the IPF process, a sparse matrix is used to calculate the marginal probabilities from the multivariate probability, which makes the iterative fitting more tractable and practical. This algorithm can be extended to higher order marginal probability constraints as used in multiple point statistics. The theoretical framework is developed and illustrated with estimation and simulation example.
Implementation of the Iterative Proportion Fitting Algorithm for Geostatistical Facies Modeling
International Nuclear Information System (INIS)
In geostatistics, most stochastic algorithm for simulation of categorical variables such as facies or rock types require a conditional probability distribution. The multivariate probability distribution of all the grouped locations including the unsampled location permits calculation of the conditional probability directly based on its definition. In this article, the iterative proportion fitting (IPF) algorithm is implemented to infer this multivariate probability. Using the IPF algorithm, the multivariate probability is obtained by iterative modification to an initial estimated multivariate probability using lower order bivariate probabilities as constraints. The imposed bivariate marginal probabilities are inferred from profiles along drill holes or wells. In the IPF process, a sparse matrix is used to calculate the marginal probabilities from the multivariate probability, which makes the iterative fitting more tractable and practical. This algorithm can be extended to higher order marginal probability constraints as used in multiple point statistics. The theoretical framework is developed and illustrated with estimation and simulation example.
Bayesian and maximin optimal designs for heteroscedastic regression models
Dette, Holger; Haines, Linda M.; Imhof, Lorens A.
2003-01-01
The problem of constructing standardized maximin D-optimal designs for weighted polynomial regression models is addressed. In particular it is shown that, by following the broad approach to the construction of maximin designs introduced recently by Dette, Haines and Imhof (2003), such designs can be obtained as weak limits of the corresponding Bayesian Φq-optimal designs. The approach is illustrated for two specific weighted polynomial models and also for a particular growth model.
Bayesian modeling growth curves for quail assuming skewness in errors
Directory of Open Access Journals (Sweden)
Robson Marcelo Rossi
2014-06-01
Full Text Available Bayesian modeling growth curves for quail assuming skewness in errors - To assume normal distributions in the data analysis is common in different areas of the knowledge. However we can make use of the other distributions that are capable to model the skewness parameter in the situations that is needed to model data with tails heavier than the normal. This article intend to present alternatives to the assumption of the normality in the errors, adding asymmetric distributions. A Bayesian approach is proposed to fit nonlinear models when the errors are not normal, thus, the distributions t, skew-normal and skew-t are adopted. The methodology is intended to apply to different growth curves to the quail body weights. It was found that the Gompertz model assuming skew-normal errors and skew-t errors, respectively for male and female, were the best fitted to the data.
Uncertainties in ozone concentrations predicted with a Lagrangian photochemical air quality model have been estimated using Bayesian Monte Carlo (BMC) analysis. Bayesian Monte Carlo analysis provides a means of combining subjective "prior" uncertainty estimates developed ...
A Bayesian nonlinear mixed-effects disease progression model
Kim, Seongho; Jang, Hyejeong; Wu, Dongfeng; Abrams, Judith
2016-01-01
A nonlinear mixed-effects approach is developed for disease progression models that incorporate variation in age in a Bayesian framework. We further generalize the probability model for sensitivity to depend on age at diagnosis, time spent in the preclinical state and sojourn time. The developed models are then applied to the Johns Hopkins Lung Project data and the Health Insurance Plan for Greater New York data using Bayesian Markov chain Monte Carlo and are compared with the estimation method that does not consider random-effects from age. Using the developed models, we obtain not only age-specific individual-level distributions, but also population-level distributions of sensitivity, sojourn time and transition probability. PMID:26798562
Non-stationarity in GARCH models: A Bayesian analysis
Kleibergen, Frank; Dijk, Herman
1993-01-01
textabstractFirst, the non-stationarity properties of the conditional variances in the GARCH(1,1) model are analysed using the concept of infinite persistence of shocks. Given a time sequence of probabilities for increasing/decreasing conditional variances, a theoretical formula for quasi-strict non-stationarity is defined. The resulting conditions for the GARCH(1,1) model are shown to differ from the weak stationarity conditions mainly used in the literature. Bayesian statistical analysis us...
A New Bayesian Unit Root Test in Stochastic Volatility Models
Yong Li; Jun Yu
2010-01-01
A new posterior odds analysis is proposed to test for a unit root in volatility dynamics in the context of stochastic volatility models. This analysis extends the Bayesian unit root test of So and Li (1999, Journal of Business Economic Statistics) in two important ways. First, a numerically more stable algorithm is introduced to compute the Bayes factor, taking into account the special structure of the competing models. Owing to its numerical stability, the algorithm overcomes the problem of ...
Bayesian Modelling in Machine Learning: A Tutorial Review
Seeger, Matthias
2006-01-01
Many facets of Bayesian Modelling are firmly established in Machine Learning and give rise to state-of-the-art solutions to application problems. The sheer number of techniques, ideas and models which have been proposed, and the terminology, can be bewildering. With this tutorial review, we aim to give a wide high-level overview over this important field, concentrating on central ideas and methods, and on their interconnections. The reader will gain a basic understanding of the topics and the...
Performance and prediction: Bayesian modelling of fallible choice in chess
Haworth, Guy McCrossan; Regan, Ken; Di Fatta, Giuseppe
2010-01-01
Evaluating agents in decision-making applications requires assessing their skill and predicting their behaviour. Both are well developed in Poker-like situations, but less so in more complex game and model domains. This paper addresses both tasks by using Bayesian inference in a benchmark space of reference agents. The concepts are explained and demonstrated using the game of chess but the model applies generically to any domain with quantifiable options and fallible choice. Demonstration ...
Bayesian modeling and prediction of solar particles flux
International Nuclear Information System (INIS)
An autoregression model was developed based on the Bayesian approach. Considering the solar wind non-homogeneity, the idea was applied of combining the pure autoregressive properties of the model with expert knowledge based on a similar behaviour of the various phenomena related to the flux properties. Examples of such situations include the hardening of the X-ray spectrum, which is often followed by coronal mass ejection and a significant increase in the particles flux intensity
Bayesian modeling and prediction of solar particles flux
Czech Academy of Sciences Publication Activity Database
Dedecius, Kamil; Kalová, J.
18/56/, 7/8 (2010), s. 228-230. ISSN 1210-7085 R&D Projects: GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : mathematical models * solar activity * solar flares * solar flux * solar particles Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2010/AS/dedecius-bayesian modeling and prediction of solar particles flux.pdf
Hierarchical Bayesian Modeling of Hitting Performance in Baseball
Jensen, Shane T.; McShane, Blake; Wyner, Abraham J.
2009-01-01
We have developed a sophisticated statistical model for predicting the hitting performance of Major League baseball players. The Bayesian paradigm provides a principled method for balancing past performance with crucial covariates, such as player age and position. We share information across time and across players by using mixture distributions to control shrinkage for improved accuracy. We compare the performance of our model to current sabermetric methods on a held-out seaso...
Bayesian estimation of a DSGE model with inventories
Foerster, Marcel
2011-01-01
This paper introduces inventories in an otherwise standard Dynamic Stochastic General Equilibrium Model (DSGE) of the business cycle. Firms accumulate inventories to facilitate sales, but face a cost of doing so in terms of costly storage of intermediate goods. The paper's main contribution is to present a DSGE model with inventories that is estimated using Bayesian methods. Based on US data we show that accounting for inventory dynamics has a significant impact on parameter estimates and imp...
Markov Model of Wind Power Time Series UsingBayesian Inference of Transition Matrix
Chen, Peiyuan; Berthelsen, Kasper Klitgaard; Bak-Jensen, Birgitte; Chen, Zhe
2009-01-01
This paper proposes to use Bayesian inference of transition matrix when developing a discrete Markov model of a wind speed/power time series and 95% credible interval for the model verification. The Dirichlet distribution is used as a conjugate prior for the transition matrix. Three discrete Markov models are compared, i.e. the basic Markov model, the Bayesian Markov model and the birth-and-death Markov model. The proposed Bayesian Markov model shows the best accuracy in modeling the autocorr...
Bayesian point event modeling in spatial and environmental epidemiology.
Lawson, Andrew B
2012-10-01
This paper reviews the current state of point event modeling in spatial epidemiology from a Bayesian perspective. Point event (or case event) data arise when geo-coded addresses of disease events are available. Often, this level of spatial resolution would not be accessible due to medical confidentiality constraints. However, for the examination of small spatial scales, it is important to be capable of examining point process data directly. Models for such data are usually formulated based on point process theory. In addition, special conditioning arguments can lead to simpler Bernoulli likelihoods and logistic spatial models. Goodness-of-fit diagnostics and Bayesian residuals are also considered. Applications within putative health hazard risk assessment, cluster detection, and linkage to environmental risk fields (misalignment) are considered. PMID:23035034
Geostatistics for fracture characterization
International Nuclear Information System (INIS)
As the critical role of fractures has become more apparent in fluid flow and contaminant transport studies, the characterization of fracture networks has received considerable attention in a wide variety of applications such as nuclear waste repository design. The application of geostatistics to fracture characterization has traditionally involved modelling fractures as thin disks; assumptions about the frequency, orientation, length and width of these disks allow the construction of a 3D model of the fracture network. This paper examines alternatives whose statistical parameters are more relevant for contaminant transport studies and are also easier to infer and validate. A new algorithm for conditional simulation is presented, one that is able to honor multipoint statistics through annealing. By honoring statistics that capture with two-point spatial convariances, this algorithm offers an important new tool not only for the specific problem of fracture characterization but also for the more general problem of spatial simulation
Geostatistics and Analysis of Spatial Data
Nielsen, Allan Aasbjerg
2007-01-01
This note deals with geostatistical measures for spatial correlation, namely the auto-covariance function and the semi-variogram, as well as deterministic and geostatistical methods for spatial interpolation, namely inverse distance weighting and kriging. Some semi-variogram models are mentioned, specifically the spherical, the exponential and the Gaussian models. Equations to carry out simple og ordinary kriging are deduced. Other types of kriging are mentioned, and references to internation...
Energy Technology Data Exchange (ETDEWEB)
Haghighi-Fashi, F.; Sharifi, F.; Kamali, K.
2014-06-01
Knowledge of infiltration characteristics is useful in hydrological studies of agricultural soils. Soil hydraulic parameters such as steady infiltration rate, sorptivity, and transmissivity can exhibit appreciable spatial variability. The main objectives of this study were to examine several mathematical models of infiltration and to analyze the spatial variability of observed final infiltration rate, estimated sorptivity and estimated transmissivity in flood spreading and control areas in Ilam province, Iran. The suitability of geostatistics to describe such spatial variability was assessed using data from 30 infiltration measurements sampled along three lines. The Horton model provided the most accurate simulation of infiltration considering all measurements and the Philips two-term model provided less accurate simulation. A comparison of the measured values and the estimated final infiltration rates showed that the Kostiakov- Lewis, Kostiakov, and SCS models could not estimate the final infiltration rate as well as Horton model. Estimated sorptivity and transmissivity parameters of the Philips two-term model and final infiltration rate had spatial structure, and were considered to be structural variables over the transect pattern. The Gaussian model provided the best-fit theoretical variogram for these three parameters. Variogram values ranged from 99 and 88 m for sorptivity and final infiltration rate to 686 (spherical) and 384 m (Gaussian) for transmissivity. Sorptivity, transmissivity and final infiltration attributes showed a high degree of spatial dependence, being 0.99, 0.81 and 1, respectively. Results showed that kriging could be used to predict the studied parameters in the study area. (Author)
Bayesian hierarchical modelling of weak lensing - the golden goal
Heavens, Alan; Jaffe, Andrew; Hoffmann, Till; Kiessling, Alina; Wandelt, Benjamin
2016-01-01
To accomplish correct Bayesian inference from weak lensing shear data requires a complete statistical description of the data. The natural framework to do this is a Bayesian Hierarchical Model, which divides the chain of reasoning into component steps. Starting with a catalogue of shear estimates in tomographic bins, we build a model that allows us to sample simultaneously from the the underlying tomographic shear fields and the relevant power spectra (E-mode, B-mode, and E-B, for auto- and cross-power spectra). The procedure deals easily with masked data and intrinsic alignments. Using Gibbs sampling and messenger fields, we show with simulated data that the large (over 67000-)dimensional parameter space can be efficiently sampled and the full joint posterior probability density function for the parameters can feasibly be obtained. The method correctly recovers the underlying shear fields and all of the power spectra, including at levels well below the shot noise.
A localization model to localize multiple sources using Bayesian inference
Dunham, Joshua Rolv
Accurate localization of a sound source in a room setting is important in both psychoacoustics and architectural acoustics. Binaural models have been proposed to explain how the brain processes and utilizes the interaural time differences (ITDs) and interaural level differences (ILDs) of sound waves arriving at the ears of a listener in determining source location. Recent work shows that applying Bayesian methods to this problem is proving fruitful. In this thesis, pink noise samples are convolved with head-related transfer functions (HRTFs) and compared to combinations of one and two anechoic speech signals convolved with different HRTFs or binaural room impulse responses (BRIRs) to simulate room positions. Through exhaustive calculation of Bayesian posterior probabilities and using a maximal likelihood approach, model selection will determine the number of sources present, and parameter estimation will result in azimuthal direction of the source(s).
Bayesian Inference and Forecasting in the Stationary Bilinear Model
Roberto Leon-Gonzalez; Fuyu Yang
2014-01-01
A stationary bilinear (SB) model can be used to describe processes with a time-varying degree of persistence that depends on past shocks. An example of such a process is inflation. This study develops methods for Bayesian inference, model comparison, and forecasting in the SB model. Using monthly U.K. inflation data, we find that the SB model outperforms the random walk and first order autoregressive AR(1) models in terms of root mean squared forecast errors for both the one-step-ahead and th...
Bayesian Age-Period-Cohort Modeling and Prediction - BAMP
Directory of Open Access Journals (Sweden)
Volker J. Schmid
2007-10-01
Full Text Available The software package BAMP provides a method of analyzing incidence or mortality data on the Lexis diagram, using a Bayesian version of an age-period-cohort model. A hierarchical model is assumed with a binomial model in the first-stage. As smoothing priors for the age, period and cohort parameters random walks of first and second order, with and without an additional unstructured component are available. Unstructured heterogeneity can also be included in the model. In order to evaluate the model fit, posterior deviance, DIC and predictive deviances are computed. By projecting the random walk prior into the future, future death rates can be predicted.
Introduction to Hierarchical Bayesian Modeling for Ecological Data
Parent, Eric
2012-01-01
Making statistical modeling and inference more accessible to ecologists and related scientists, Introduction to Hierarchical Bayesian Modeling for Ecological Data gives readers a flexible and effective framework to learn about complex ecological processes from various sources of data. It also helps readers get started on building their own statistical models. The text begins with simple models that progressively become more complex and realistic through explanatory covariates and intermediate hidden states variables. When fitting the models to data, the authors gradually present the concepts a
Simultaneous inversion of petrophysical parameters based on geostatistical a priori information
Institute of Scientific and Technical Information of China (English)
Yin Xing-Yao; Sun Rui-Ying; Wang Bao-Li; Zhang Guang-Zhi
2014-01-01
The high-resolution nonlinear simultaneous inversion of petrophysical parameters is based on Bayesian statistics and combines petrophysics with geostatistical a priori information. We used the fast Fourier transform-moving average (FFT-MA) and gradual deformation method (GDM) to obtain a reasonable variogram by using structural analysis and geostatistical a priori information of petrophysical parameters. Subsequently, we constructed the likelihood function according to the statistical petrophysical model. Finally, we used the Metropolis algorithm to sample the posteriori probability density and complete the inversion of the petrophysical parameters. We used the proposed method to process data from an oil fi eld in China and found good match between inversion and real data with high-resolution. In addition, the direct inversion of petrophysical parameters avoids the error accumulation and decreases the uncertainty, and increases the computational effi ciency.
Bayesian analysis of recursive SVAR models with overidentifying restrictions
Kociecki, Andrzej; Rubaszek, Michał; Ca' Zorzi, Michele
2012-01-01
The paper provides a novel Bayesian methodological framework to estimate structural VAR (SVAR) models with recursive identification schemes that allows for the inclusion of over-identifying restrictions. The proposed framework enables the researcher to (i) elicit the prior on the non-zero contemporaneous relations between economic variables and to (ii) derive an analytical expression for the posterior distribution and marginal data density. We illustrate our methodological framework by estima...
Differential gene co-expression networks via Bayesian biclustering models
Gao, Chuan; Zhao, Shiwen; McDowell, Ian C.; Brown, Christopher D.; Barbara E Engelhardt
2014-01-01
Identifying latent structure in large data matrices is essential for exploring biological processes. Here, we consider recovering gene co-expression networks from gene expression data, where each network encodes relationships between genes that are locally co-regulated by shared biological mechanisms. To do this, we develop a Bayesian statistical model for biclustering to infer subsets of co-regulated genes whose covariation may be observed in only a subset of the samples. Our biclustering me...
Bayesian parsimonious covariance estimation for hierarchical linear mixed models
Frühwirth-Schnatter, Sylvia; Tüchler, Regina
2004-01-01
We considered a non-centered parameterization of the standard random-effects model, which is based on the Cholesky decomposition of the variance-covariance matrix. The regression type structure of the non-centered parameterization allows to choose a simple, conditionally conjugate normal prior on the Cholesky factor. Based on the non-centered parameterization, we search for a parsimonious variance-covariance matrix by identifying the non-zero elements of the Cholesky factors using Bayesian va...
Diffusion Estimation Of State-Space Models: Bayesian Formulation
Czech Academy of Sciences Publication Activity Database
Dedecius, Kamil
Reims: IEEE, 2014. ISBN 978-1-4799-3693-9. [The 24th IEEE International Workshop on Machine Learning for Signal Processing (MLSP2014). Reims (FR), 21.09.2014-24.09.2014] R&D Projects: GA ČR(CZ) GP14-06678P Keywords : distributed estimation * state-space models * Bayesian estimation Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2014/AS/dedecius-0431804.pdf
Bayesian Methods for Neural Networks and Related Models
Titterington, D.M.
2004-01-01
Models such as feed-forward neural networks and certain other structures investigated in the computer science literature are not amenable to closed-form Bayesian analysis. The paper reviews the various approaches taken to overcome this difficulty, involving the use of Gaussian approximations, Markov chain Monte Carlo simulation routines and a class of non-Gaussian but “deterministic” approximations called variational approximations.
Bayesian network models in brain functional connectivity analysis
Ide, Jaime S.; Zhang, Sheng; Chiang-shan R. Li
2013-01-01
Much effort has been made to better understand the complex integration of distinct parts of the human brain using functional magnetic resonance imaging (fMRI). Altered functional connectivity between brain regions is associated with many neurological and mental illnesses, such as Alzheimer and Parkinson diseases, addiction, and depression. In computational science, Bayesian networks (BN) have been used in a broad range of studies to model complex data set in the presence of uncertainty and wh...
Bayesian Models of Learning and Reasoning with Relations
Chen, Dawn
2014-01-01
How do humans acquire relational concepts such as larger, which are essential for analogical inference and other forms of high-level reasoning? Are they necessarily innate, or can they be learned from non-relational inputs? Using comparative relations as a model domain, we show that structured relations can be learned from unstructured inputs of realistic complexity, applying bottom-up Bayesian learning mechanisms that make minimal assumptions about innate representations. First, we introduce...
Energy Technology Data Exchange (ETDEWEB)
Cardona, W.; Aranaga, R.; Siu, P.; Perez, L. [PDVSA Petroleos de Venezuela SA, Caracas (Venezuela, Bolivarian Republic of)
2009-07-01
The geological modelling of the Zuata Principal field in Venezuela, particularly the Junin Block 2 belonging to Orinoco oil belt, is a challenge because of the presence of thin sand bodies in an unexploited zone. This paper presented the results obtained from a horizontal well that contacted 96 per cent of pay count sand in the field. Geostatistical modelling and sensibility analysis were used for planning the well. The model was generated by processing and interpreting information from production and exploratory fishbones. Information provided by nearby wildcat wells suggested that the proposed area was not prospective. However, information provided by several exploratory fishbones offered some possibility of draining additional reserves. From available information, facies models and uncertainty analysis were made to statistically determine the best option, notably to drill additional stratwells to obtain a more accurate characterization or apply the already obtained model for drilling a production well in the investigated area. The study showed that geological uncertainty does not only depend on how much information is available, but also on how this information can be processed and interpreted. Decision analysis provides a rational basis for dealing with risk and uncertainties. 4 refs., 7 tabs., 7 figs., 1 appendix.
Bayesian regression model for seasonal forecast of precipitation over Korea
Jo, Seongil; Lim, Yaeji; Lee, Jaeyong; Kang, Hyun-Suk; Oh, Hee-Seok
2012-08-01
In this paper, we apply three different Bayesian methods to the seasonal forecasting of the precipitation in a region around Korea (32.5°N-42.5°N, 122.5°E-132.5°E). We focus on the precipitation of summer season (June-July-August; JJA) for the period of 1979-2007 using the precipitation produced by the Global Data Assimilation and Prediction System (GDAPS) as predictors. Through cross-validation, we demonstrate improvement for seasonal forecast of precipitation in terms of root mean squared error (RMSE) and linear error in probability space score (LEPS). The proposed methods yield RMSE of 1.09 and LEPS of 0.31 between the predicted and observed precipitations, while the prediction using GDAPS output only produces RMSE of 1.20 and LEPS of 0.33 for CPC Merged Analyzed Precipitation (CMAP) data. For station-measured precipitation data, the RMSE and LEPS of the proposed Bayesian methods are 0.53 and 0.29, while GDAPS output is 0.66 and 0.33, respectively. The methods seem to capture the spatial pattern of the observed precipitation. The Bayesian paradigm incorporates the model uncertainty as an integral part of modeling in a natural way. We provide a probabilistic forecast integrating model uncertainty.
Statistical modelling of railway track geometry degradation using hierarchical Bayesian models
Andrade, António Ramos; Teixeira, P. Fonseca
2015-01-01
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 c...
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.)
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
International Nuclear Information System (INIS)
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
Dissecting Magnetar Variability with Bayesian Hierarchical Models
Huppenkothen, Daniela; Brewer, Brendon J.; Hogg, David W.; Murray, Iain; Frean, Marcus; Elenbaas, Chris; Watts, Anna L.; Levin, Yuri; van der Horst, Alexander J.; Kouveliotou, Chryssa
2015-09-01
Neutron stars are a prime laboratory for testing physical processes under conditions of strong gravity, high density, and extreme magnetic fields. Among the zoo of neutron star phenomena, magnetars stand out for their bursting behavior, ranging from extremely bright, rare giant flares to numerous, less energetic recurrent bursts. The exact trigger and emission mechanisms for these bursts are not known; favored models involve either a crust fracture and subsequent energy release into the magnetosphere, or explosive reconnection of magnetic field lines. In the absence of a predictive model, understanding the physical processes responsible for magnetar burst variability is difficult. Here, we develop an empirical model that decomposes magnetar bursts into a superposition of small spike-like features with a simple functional form, where the number of model components is itself part of the inference problem. The cascades of spikes that we model might be formed by avalanches of reconnection, or crust rupture aftershocks. Using Markov Chain Monte Carlo sampling augmented with reversible jumps between models with different numbers of parameters, we characterize the posterior distributions of the model parameters and the number of components per burst. We relate these model parameters to physical quantities in the system, and show for the first time that the variability within a burst does not conform to predictions from ideas of self-organized criticality. We also examine how well the properties of the spikes fit the predictions of simplified cascade models for the different trigger mechanisms.
Parasyris, Antonios E.; Spanoudaki, Katerina; Kampanis, Nikolaos A.
2016-04-01
Groundwater level monitoring networks provide essential information for water resources management, especially in areas with significant groundwater exploitation for agricultural and domestic use. Given the high maintenance costs of these networks, development of tools, which can be used by regulators for efficient network design is essential. In this work, a monitoring network optimisation tool is presented. The network optimisation tool couples geostatistical modelling based on the Spartan family variogram with a genetic algorithm method and is applied to Mires basin in Crete, Greece, an area of high socioeconomic and agricultural interest, which suffers from groundwater overexploitation leading to a dramatic decrease of groundwater levels. The purpose of the optimisation tool is to determine which wells to exclude from the monitoring network because they add little or no beneficial information to groundwater level mapping of the area. Unlike previous relevant investigations, the network optimisation tool presented here uses Ordinary Kriging with the recently-established non-differentiable Spartan variogram for groundwater level mapping, which, based on a previous geostatistical study in the area leads to optimal groundwater level mapping. Seventy boreholes operate in the area for groundwater abstraction and water level monitoring. The Spartan variogram gives overall the most accurate groundwater level estimates followed closely by the power-law model. The geostatistical model is coupled to an integer genetic algorithm method programmed in MATLAB 2015a. The algorithm is used to find the set of wells whose removal leads to the minimum error between the original water level mapping using all the available wells in the network and the groundwater level mapping using the reduced well network (error is defined as the 2-norm of the difference between the original mapping matrix with 70 wells and the mapping matrix of the reduced well network). The solution to the
Dissecting magnetar variability with Bayesian hierarchical models
Huppenkothen, D; Hogg, D W; Murray, I; Frean, M; Elenbaas, C; Watts, A L; Levin, Y; van der Horst, A J; Kouveliotou, C
2015-01-01
Neutron stars are a prime laboratory for testing physical processes under conditions of strong gravity, high density, and extreme magnetic fields. Among the zoo of neutron star phenomena, magnetars stand out for their bursting behaviour, ranging from extremely bright, rare giant flares to numerous, less energetic recurrent bursts. The exact trigger and emission mechanisms for these bursts are not known; favoured models involve either a crust fracture and subsequent energy release into the magnetosphere, or explosive reconnection of magnetic field lines. In the absence of a predictive model, understanding the physical processes responsible for magnetar burst variability is difficult. Here, we develop an empirical model that decomposes magnetar bursts into a superposition of small spike-like features with a simple functional form, where the number of model components is itself part of the inference problem. The cascades of spikes that we model might be formed by avalanches of reconnection, or crust rupture afte...
Directory of Open Access Journals (Sweden)
X. He
2013-09-01
Full Text Available Multiple-point geostatistic simulation (MPS has recently become popular in stochastic hydrogeology, primarily because of its capability to derive multivariate distributions from the training image (TI. However, its application in three dimensional simulations has been constrained by the difficulty of constructing 3-D TI. The object-based TiGenerator may be a useful tool in this regard; yet the sensitivity of model predictions to the training image has not been documented. Another issue in MPS is the integration of multiple geophysical data. The best way to retrieve and incorporate information from high resolution geophysical data is still under discussion. This work shows that TI from TiGenerator delivers acceptable results when used for groundwater modeling, although the TI directly converted from high resolution geophysical data leads to better simulation. The model results also indicate that soft conditioning in MPS is a convenient and efficient way of integrating secondary data such as 3-D airborne electromagnetic data, but over conditioning has to be avoided.
Dynamic model based on Bayesian method for energy security assessment
International Nuclear Information System (INIS)
Highlights: • Methodology for dynamic indicator model construction and forecasting of indicators. • Application of dynamic indicator model for energy system development scenarios. • Expert judgement involvement using Bayesian method. - Abstract: The methodology for the dynamic indicator model construction and forecasting of indicators for the assessment of energy security level is presented in this article. An indicator is a special index, which provides numerical values to important factors for the investigated area. In real life, models of different processes take into account various factors that are time-dependent and dependent on each other. Thus, it is advisable to construct a dynamic model in order to describe these dependences. The energy security indicators are used as factors in the dynamic model. Usually, the values of indicators are obtained from statistical data. The developed dynamic model enables to forecast indicators’ variation taking into account changes in system configuration. The energy system development is usually based on a new object construction. Since the parameters of changes of the new system are not exactly known, information about their influences on indicators could not be involved in the model by deterministic methods. Thus, dynamic indicators’ model based on historical data is adjusted by probabilistic model with the influence of new factors on indicators using the Bayesian method
Directory of Open Access Journals (Sweden)
S. Ly
2011-07-01
Full Text Available Spatial interpolation of precipitation data is of great importance for hydrological modelling. Geostatistical methods (kriging are widely applied in spatial interpolation from point measurement to continuous surfaces. The first step in kriging computation is the semi-variogram modelling which usually used only one variogram model for all-moment data. The objective of this paper was to develop different algorithms of spatial interpolation for daily rainfall on 1 km^{2} regular grids in the catchment area and to compare the results of geostatistical and deterministic approaches. This study leaned on 30-yr daily rainfall data of 70 raingages in the hilly landscape of the Ourthe and Ambleve catchments in Belgium (2908 km^{2}. This area lies between 35 and 693 m in elevation and consists of river networks, which are tributaries of the Meuse River. For geostatistical algorithms, seven semi-variogram models (logarithmic, power, exponential, Gaussian, rational quadratic, spherical and penta-spherical were fitted to daily sample semi-variogram on a daily basis. These seven variogram models were also adopted to avoid negative interpolated rainfall. The elevation, extracted from a digital elevation model, was incorporated into multivariate geostatistics. Seven validation raingages and cross validation were used to compare the interpolation performance of these algorithms applied to different densities of raingages. We found that between the seven variogram models used, the Gaussian model was the most frequently best fit. Using seven variogram models can avoid negative daily rainfall in ordinary kriging. The negative estimates of kriging were observed for convective more than stratiform rain. The performance of the different methods varied slightly according to the density of raingages, particularly between 8 and 70 raingages but it was much different for interpolation using 4 raingages. Spatial interpolation with the geostatistical and
Energy Technology Data Exchange (ETDEWEB)
Sweet, M.L.; Carter, A.M.; Mills, C.A. [BP Exploration, Aberdeen (United Kingdom)] [and others
1996-11-01
Hyde field is a small (133 Gcf reserves) gas field in the United Kingdom southern North Sea. The reservoir, the Permian Rotliegende group, contains eolian, fluvial, and sabkha facies. The eolian facies constitute the dominant flow units. Illite cementation results in low reservoir quality. In the eolian facies permeability averages 2.5 md and rarely exceeds 10 md. To maximize recovery from this field, with its thin gas column and low reservoir quality, Hyde has been developed with three long-reach horizontal wells. A reservoir model that could accurately predict future production had to include a full range of heterogeneities from the effects of thin muddy laminations at the core-plug scale to the spatial distribution of eolian, fluvial, and sabkha facies over the entire field at the largest scale. By carefully defining the model`s layering scheme, we incorporated strongly deterministic elements where facies trends were influenced by laterally extensive stratigraphic surfaces. The distribution of facies within stratigraphic units was modeled using geostatistical techniques. Average permeability for the eolian and sandy sabkha facies were determined by upscaling models of their internal permeability structure. The resulting distribution of permeabilities across the field, present in a 2.2-million-cell model, was upscaled into a coarser grid suitable for simulating the full field. This new model produced a significantly better match to dynamic data than did an earlier simple layer model that was used to take the field to sanction. The results of our work suggest that stochastic modeling allowed us to represent a level of heterogeneity that was not captured by the earlier simple layer model. By capturing this level of heterogeneity, we were able to achieve a significantly better match of model predictions to production data.
A Bayesian Network View on Nested Effects Models
Directory of Open Access Journals (Sweden)
Fröhlich Holger
2009-01-01
Full Text Available Nested effects models (NEMs are a class of probabilistic models that were designed to reconstruct a hidden signalling structure from a large set of observable effects caused by active interventions into the signalling pathway. We give a more flexible formulation of NEMs in the language of Bayesian networks. Our framework constitutes a natural generalization of the original NEM model, since it explicitly states the assumptions that are tacitly underlying the original version. Our approach gives rise to new learning methods for NEMs, which have been implemented in the /Bioconductor package nem. We validate these methods in a simulation study and apply them to a synthetic lethality dataset in yeast.
Probe Error Modeling Research Based on Bayesian Network
Institute of Scientific and Technical Information of China (English)
Wu Huaiqiang; Xing Zilong; Zhang Jian; Yan Yan
2015-01-01
Probe calibration is carried out under specific conditions; most of the error caused by the change of speed parameter has not been corrected. In order to reduce the measuring error influence on measurement accuracy, this article analyzes the relationship between speed parameter and probe error, and use Bayesian network to establish the model of probe error. Model takes account of prior knowledge and sample data, with the updating of data, which can reflect the change of the errors of the probe and constantly revised modeling results.
Energy Technology Data Exchange (ETDEWEB)
Zhang Hua [Environmental Systems Engineering Program, Faculty of Engineering, University of Regina, Regina, Saskatchewan, S4S 0A2 (Canada); Huang Guohe, E-mail: huang@iseis.or [Environmental Systems Engineering Program, Faculty of Engineering, University of Regina, Regina, Saskatchewan, S4S 0A2 (Canada); Zeng Guangming [College of Environmental Science and Engineering, Hunan University, Changsha, Hunan 410082 (China)
2009-08-15
Elevated concentrations of arsenic were detected in surface soils adjacent to a smelting complex in northern Canada. We evaluated the cancer risks caused by exposure to arsenic in two communities through combining geostatistical simulation with demographic data and dose-response models in a framework. Distribution of arsenic was first estimated using geostatistical circulant-embedding simulation method. We then evaluated the exposures from inadvertent ingestion, inhalation and dermal contact. Risks of skin caner and three internal cancers were estimated at both grid scale and census-unit scale using parametric dose-response models. Results indicated that local residents could face non-negligible cancer risks (skin cancer and liver cancer mainly). Uncertainties of risk estimates were discussed from the aspects of arsenic concentrations, exposed population and dose-response model. Reducing uncertainties would require additional soil sampling, epidemic records as well as complementary studies on land use, demographic variation, outdoor activities and bioavailability of arsenic. - Cancer risks induced by arsenic in soil were evaluated using geostatistical simulation and dose-response model.