Quantifying natural delta variability using a multiple-point geostatistics prior uncertainty model

NASA Astrophysics Data System (ADS)

Scheidt, Céline; Fernandes, Anjali M.; Paola, Chris; Caers, Jef

2016-10-01

We address the question of quantifying uncertainty associated with autogenic pattern variability in a channelized transport system by means of a modern geostatistical method. This question has considerable relevance for practical subsurface applications as well, particularly those related to uncertainty quantification relying on Bayesian approaches. Specifically, we show how the autogenic variability in a laboratory experiment can be represented and reproduced by a multiple-point geostatistical prior uncertainty model. The latter geostatistical method requires selection of a limited set of training images from which a possibly infinite set of geostatistical model realizations, mimicking the training image patterns, can be generated. To that end, we investigate two methods to determine how many training images and what training images should be provided to reproduce natural autogenic variability. The first method relies on distance-based clustering of overhead snapshots of the experiment; the second method relies on a rate of change quantification by means of a computer vision algorithm termed the demon algorithm. We show quantitatively that with either training image selection method, we can statistically reproduce the natural variability of the delta formed in the experiment. In addition, we study the nature of the patterns represented in the set of training images as a representation of the "eigenpatterns" of the natural system. The eigenpattern in the training image sets display patterns consistent with previous physical interpretations of the fundamental modes of this type of delta system: a highly channelized, incisional mode; a poorly channelized, depositional mode; and an intermediate mode between the two.

APPLICATION OF BAYESIAN AND GEOSTATISTICAL MODELING TO THE ENVIRONMENTAL MONITORING OF CS-137 AT THE IDAHO NATIONAL LABORATORY

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 thatmore » 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.« less

Bayesian approach for three-dimensional aquifer characterization at the Hanford 300 Area

DOE Office of Scientific and Technical Information (OSTI.GOV)

Murakami, Haruko; Chen, X.; Hahn, Melanie S.

2010-10-21

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 itsmore » 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 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.« less

High-Dimensional Bayesian Geostatistics

PubMed Central

Banerjee, Sudipto

2017-01-01

With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and time points. Over the last decade, hierarchical spatiotemporal process models have become widely deployed statistical tools for researchers to better understand the complex nature of spatial and temporal variability. However, fitting hierarchical spatiotemporal models often involves expensive matrix computations with complexity increasing in cubic order for the number of spatial locations and temporal points. This renders such models unfeasible for large data sets. This article offers a focused review of two methods for constructing well-defined highly scalable spatiotemporal stochastic processes. Both these processes can be used as “priors” for spatiotemporal random fields. The first approach constructs a low-rank process operating on a lower-dimensional subspace. The second approach constructs a Nearest-Neighbor Gaussian Process (NNGP) that ensures sparse precision matrices for its finite realizations. Both processes can be exploited as a scalable prior embedded within a rich hierarchical modeling framework to deliver full Bayesian inference. These approaches can be described as model-based solutions for big spatiotemporal datasets. The models ensure that the algorithmic complexity has ~ n floating point operations (flops), where n the number of spatial locations (per iteration). We compare these methods and provide some insight into their methodological underpinnings. PMID:29391920

High-Dimensional Bayesian Geostatistics.

PubMed

Banerjee, Sudipto

2017-06-01

With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and time points. Over the last decade, hierarchical spatiotemporal process models have become widely deployed statistical tools for researchers to better understand the complex nature of spatial and temporal variability. However, fitting hierarchical spatiotemporal models often involves expensive matrix computations with complexity increasing in cubic order for the number of spatial locations and temporal points. This renders such models unfeasible for large data sets. This article offers a focused review of two methods for constructing well-defined highly scalable spatiotemporal stochastic processes. Both these processes can be used as "priors" for spatiotemporal random fields. The first approach constructs a low-rank process operating on a lower-dimensional subspace. The second approach constructs a Nearest-Neighbor Gaussian Process (NNGP) that ensures sparse precision matrices for its finite realizations. Both processes can be exploited as a scalable prior embedded within a rich hierarchical modeling framework to deliver full Bayesian inference. These approaches can be described as model-based solutions for big spatiotemporal datasets. The models ensure that the algorithmic complexity has ~ n floating point operations (flops), where n the number of spatial locations (per iteration). We compare these methods and provide some insight into their methodological underpinnings.

Bayesian Geostatistical Model-Based Estimates of Soil-Transmitted Helminth Infection in Nigeria, Including Annual Deworming Requirements

PubMed Central

Oluwole, Akinola S.; Ekpo, Uwem F.; Karagiannis-Voules, Dimitrios-Alexios; Abe, Eniola M.; Olamiju, Francisca O.; Isiyaku, Sunday; Okoronkwo, Chukwu; Saka, Yisa; Nebe, Obiageli J.; Braide, Eka I.; Mafiana, Chiedu F.; Utzinger, Jürg; Vounatsou, Penelope

2015-01-01

Background The acceleration of the control of soil-transmitted helminth (STH) infections in Nigeria, emphasizing preventive chemotherapy, has become imperative in light of the global fight against neglected tropical diseases. Predictive risk maps are an important tool to guide and support control activities. Methodology STH infection prevalence data were obtained from surveys carried out in 2011 using standard protocols. Data were geo-referenced and collated in a nationwide, geographic information system database. Bayesian geostatistical models with remotely sensed environmental covariates and variable selection procedures were utilized to predict the spatial distribution of STH infections in Nigeria. Principal Findings We found that hookworm, Ascaris lumbricoides, and Trichuris trichiura infections are endemic in 482 (86.8%), 305 (55.0%), and 55 (9.9%) locations, respectively. Hookworm and A. lumbricoides infection co-exist in 16 states, while the three species are co-endemic in 12 states. Overall, STHs are endemic in 20 of the 36 states of Nigeria, including the Federal Capital Territory of Abuja. The observed prevalence at endemic locations ranged from 1.7% to 51.7% for hookworm, from 1.6% to 77.8% for A. lumbricoides, and from 1.0% to 25.5% for T. trichiura. Model-based predictions ranged from 0.7% to 51.0% for hookworm, from 0.1% to 82.6% for A. lumbricoides, and from 0.0% to 18.5% for T. trichiura. Our models suggest that day land surface temperature and dense vegetation are important predictors of the spatial distribution of STH infection in Nigeria. In 2011, a total of 5.7 million (13.8%) school-aged children were predicted to be infected with STHs in Nigeria. Mass treatment at the local government area level for annual or bi-annual treatment of the school-aged population in Nigeria in 2011, based on World Health Organization prevalence thresholds, were estimated at 10.2 million tablets. Conclusions/Significance The predictive risk maps and estimated

Bayesian geostatistical model-based estimates of soil-transmitted helminth infection in Nigeria, including annual deworming requirements.

PubMed

Oluwole, Akinola S; Ekpo, Uwem F; Karagiannis-Voules, Dimitrios-Alexios; Abe, Eniola M; Olamiju, Francisca O; Isiyaku, Sunday; Okoronkwo, Chukwu; Saka, Yisa; Nebe, Obiageli J; Braide, Eka I; Mafiana, Chiedu F; Utzinger, Jürg; Vounatsou, Penelope

2015-04-01

The acceleration of the control of soil-transmitted helminth (STH) infections in Nigeria, emphasizing preventive chemotherapy, has become imperative in light of the global fight against neglected tropical diseases. Predictive risk maps are an important tool to guide and support control activities. STH infection prevalence data were obtained from surveys carried out in 2011 using standard protocols. Data were geo-referenced and collated in a nationwide, geographic information system database. Bayesian geostatistical models with remotely sensed environmental covariates and variable selection procedures were utilized to predict the spatial distribution of STH infections in Nigeria. We found that hookworm, Ascaris lumbricoides, and Trichuris trichiura infections are endemic in 482 (86.8%), 305 (55.0%), and 55 (9.9%) locations, respectively. Hookworm and A. lumbricoides infection co-exist in 16 states, while the three species are co-endemic in 12 states. Overall, STHs are endemic in 20 of the 36 states of Nigeria, including the Federal Capital Territory of Abuja. The observed prevalence at endemic locations ranged from 1.7% to 51.7% for hookworm, from 1.6% to 77.8% for A. lumbricoides, and from 1.0% to 25.5% for T. trichiura. Model-based predictions ranged from 0.7% to 51.0% for hookworm, from 0.1% to 82.6% for A. lumbricoides, and from 0.0% to 18.5% for T. trichiura. Our models suggest that day land surface temperature and dense vegetation are important predictors of the spatial distribution of STH infection in Nigeria. In 2011, a total of 5.7 million (13.8%) school-aged children were predicted to be infected with STHs in Nigeria. Mass treatment at the local government area level for annual or bi-annual treatment of the school-aged population in Nigeria in 2011, based on World Health Organization prevalence thresholds, were estimated at 10.2 million tablets. The predictive risk maps and estimated deworming needs presented here will be helpful for escalating the control

Gstat: a program for geostatistical modelling, prediction and simulation

NASA Astrophysics Data System (ADS)

Pebesma, Edzer J.; Wesseling, Cees G.

1998-01-01

Gstat is a computer program for variogram modelling, and geostatistical prediction and simulation. It provides a generic implementation of the multivariable linear model with trends modelled as a linear function of coordinate polynomials or of user-defined base functions, and independent or dependent, geostatistically modelled, residuals. Simulation in gstat comprises conditional or unconditional (multi-) Gaussian sequential simulation of point values or block averages, or (multi-) indicator sequential simulation. Besides many of the popular options found in other geostatistical software packages, gstat offers the unique combination of (i) an interactive user interface for modelling variograms and generalized covariances (residual variograms), that uses the device-independent plotting program gnuplot for graphical display, (ii) support for several ascii and binary data and map file formats for input and output, (iii) a concise, intuitive and flexible command language, (iv) user customization of program defaults, (v) no built-in limits, and (vi) free, portable ANSI-C source code. This paper describes the class of problems gstat can solve, and addresses aspects of efficiency and implementation, managing geostatistical projects, and relevant technical details.

Restricted spatial regression in practice: Geostatistical models, confounding, and robustness under model misspecification

USGS Publications Warehouse

Hanks, Ephraim M.; Schliep, Erin M.; Hooten, Mevin B.; Hoeting, Jennifer A.

2015-01-01

In spatial generalized linear mixed models (SGLMMs), covariates that are spatially smooth are often collinear with spatially smooth random effects. This phenomenon is known as spatial confounding and has been studied primarily in the case where the spatial support of the process being studied is discrete (e.g., areal spatial data). In this case, the most common approach suggested is restricted spatial regression (RSR) in which the spatial random effects are constrained to be orthogonal to the fixed effects. We consider spatial confounding and RSR in the geostatistical (continuous spatial support) setting. We show that RSR provides computational benefits relative to the confounded SGLMM, but that Bayesian credible intervals under RSR can be inappropriately narrow under model misspecification. We propose a posterior predictive approach to alleviating this potential problem and discuss the appropriateness of RSR in a variety of situations. We illustrate RSR and SGLMM approaches through simulation studies and an analysis of malaria frequencies in The Gambia, Africa.

Sequential Bayesian Geostatistical Inversion and Evaluation of Combined Data Worth for Aquifer Characterization at the Hanford 300 Area

NASA Astrophysics Data System (ADS)

Murakami, H.; Chen, X.; Hahn, M. S.; Over, M. W.; Rockhold, M. L.; Vermeul, V.; Hammond, G. E.; Zachara, J. M.; Rubin, Y.

2010-12-01

Subsurface characterization for predicting groundwater flow and contaminant transport requires us to integrate large and diverse datasets in a consistent manner, and quantify the associated uncertainty. In this study, we sequentially assimilated multiple types of datasets for characterizing a three-dimensional heterogeneous hydraulic conductivity field at the Hanford 300 Area. The datasets included constant-rate injection tests, electromagnetic borehole flowmeter tests, lithology profile and tracer tests. We used the method of anchored distributions (MAD), which is a modular-structured Bayesian geostatistical inversion method. MAD has two major advantages over the other inversion methods. First, it can directly infer a joint distribution of parameters, which can be used as an input in stochastic simulations for prediction. In MAD, in addition to typical geostatistical structural parameters, the parameter vector includes multiple point values of the heterogeneous field, called anchors, which capture local trends and reduce uncertainty in the prediction. Second, MAD allows us to integrate the datasets sequentially in a Bayesian framework such that it updates the posterior distribution, as a new dataset is included. The sequential assimilation can decrease computational burden significantly. We applied MAD to assimilate different combinations of the datasets, and then compared the inversion results. For the injection and tracer test assimilation, we calculated temporal moments of pressure build-up and breakthrough curves, respectively, to reduce the data dimension. A massive parallel flow and transport code PFLOTRAN is used for simulating the tracer test. For comparison, we used different metrics based on the breakthrough curves not used in the inversion, such as mean arrival time, peak concentration and early arrival time. This comparison intends to yield the combined data worth, i.e. which combination of the datasets is the most effective for a certain metric, which

Geostatistical applications in ground-water modeling in south-central Kansas

USGS Publications Warehouse

Ma, T.-S.; Sophocleous, M.; Yu, Y.-S.

1999-01-01

This paper emphasizes the supportive role of geostatistics in applying ground-water models. Field data of 1994 ground-water level, bedrock, and saltwater-freshwater interface elevations in south-central Kansas were collected and analyzed using the geostatistical approach. Ordinary kriging was adopted to estimate initial conditions for ground-water levels and topography of the Permian bedrock at the nodes of a finite difference grid used in a three-dimensional numerical model. Cokriging was used to estimate initial conditions for the saltwater-freshwater interface. An assessment of uncertainties in the estimated data is presented. The kriged and cokriged estimation variances were analyzed to evaluate the adequacy of data employed in the modeling. Although water levels and bedrock elevations are well described by spherical semivariogram models, additional data are required for better cokriging estimation of the interface data. The geostatistically analyzed data were employed in a numerical model of the Siefkes site in the project area. Results indicate that the computed chloride concentrations and ground-water drawdowns reproduced the observed data satisfactorily.This paper emphasizes the supportive role of geostatistics in applying ground-water models. Field data of 1994 ground-water level, bedrock, and saltwater-freshwater interface elevations in south-central Kansas were collected and analyzed using the geostatistical approach. Ordinary kriging was adopted to estimate initial conditions for ground-water levels and topography of the Permian bedrock at the nodes of a finite difference grid used in a three-dimensional numerical model. Cokriging was used to estimate initial conditions for the saltwater-freshwater interface. An assessment of uncertainties in the estimated data is presented. The kriged and cokriged estimation variances were analyzed to evaluate the adequacy of data employed in the modeling. Although water levels and bedrock elevations are well described

Integrated geostatistics for modeling fluid contacts and shales in Prudhoe Bay

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perez, G.; Chopra, A.K.; Severson, C.D.

1997-12-01

Geostatistics techniques are being used increasingly to model reservoir heterogeneity at a wide range of scales. A variety of techniques is now available with differing underlying assumptions, complexity, and applications. This paper introduces a novel method of geostatistics to model dynamic gas-oil contacts and shales in the Prudhoe Bay reservoir. The method integrates reservoir description and surveillance data within the same geostatistical framework. Surveillance logs and shale data are transformed to indicator variables. These variables are used to evaluate vertical and horizontal spatial correlation and cross-correlation of gas and shale at different times and to develop variogram models. Conditional simulationmore » techniques are used to generate multiple three-dimensional (3D) descriptions of gas and shales that provide a measure of uncertainty. These techniques capture the complex 3D distribution of gas-oil contacts through time. The authors compare results of the geostatistical method with conventional techniques as well as with infill wells drilled after the study. Predicted gas-oil contacts and shale distributions are in close agreement with gas-oil contacts observed at infill wells.« less

Applications of geostatistics and Markov models for logo recognition

NASA Astrophysics Data System (ADS)

Pham, Tuan

2003-01-01

Spatial covariances based on geostatistics are extracted as representative features of logo or trademark images. These spatial covariances are different from other statistical features for image analysis in that the structural information of an image is independent of the pixel locations and represented in terms of spatial series. We then design a classifier in the sense of hidden Markov models to make use of these geostatistical sequential data to recognize the logos. High recognition rates are obtained from testing the method against a public-domain logo database.

Application of geostatistics to risk assessment.

PubMed

Thayer, William C; Griffith, Daniel A; Goodrum, Philip E; Diamond, Gary L; Hassett, James M

2003-10-01

Geostatistics offers two fundamental contributions to environmental contaminant exposure assessment: (1) a group of methods to quantitatively describe the spatial distribution of a pollutant and (2) the ability to improve estimates of the exposure point concentration by exploiting the geospatial information present in the data. The second contribution is particularly valuable when exposure estimates must be derived from small data sets, which is often the case in environmental risk assessment. This article addresses two topics related to the use of geostatistics in human and ecological risk assessments performed at hazardous waste sites: (1) the importance of assessing model assumptions when using geostatistics and (2) the use of geostatistics to improve estimates of the exposure point concentration (EPC) in the limited data scenario. The latter topic is approached here by comparing design-based estimators that are familiar to environmental risk assessors (e.g., Land's method) with geostatistics, a model-based estimator. In this report, we summarize the basics of spatial weighting of sample data, kriging, and geostatistical simulation. We then explore the two topics identified above in a case study, using soil lead concentration data from a Superfund site (a skeet and trap range). We also describe several areas where research is needed to advance the use of geostatistics in environmental risk assessment.

Monte Carlo Analysis of Reservoir Models Using Seismic Data and Geostatistical Models

NASA Astrophysics Data System (ADS)

Zunino, A.; Mosegaard, K.; Lange, K.; Melnikova, Y.; Hansen, T. M.

2013-12-01

We present a study on the analysis of petroleum reservoir models consistent with seismic data and geostatistical constraints performed on a synthetic reservoir model. Our aim is to invert directly for structure and rock bulk properties of the target reservoir zone. To infer the rock facies, porosity and oil saturation seismology alone is not sufficient but a rock physics model must be taken into account, which links the unknown properties to the elastic parameters. We then combine a rock physics model with a simple convolutional approach for seismic waves to invert the "measured" seismograms. To solve this inverse problem, we employ a Markov chain Monte Carlo (MCMC) method, because it offers the possibility to handle non-linearity, complex and multi-step forward models and provides realistic estimates of uncertainties. However, for large data sets the MCMC method may be impractical because of a very high computational demand. To face this challenge one strategy is to feed the algorithm with realistic models, hence relying on proper prior information. To address this problem, we utilize an algorithm drawn from geostatistics to generate geologically plausible models which represent samples of the prior distribution. The geostatistical algorithm learns the multiple-point statistics from prototype models (in the form of training images), then generates thousands of different models which are accepted or rejected by a Metropolis sampler. To further reduce the computation time we parallelize the software and run it on multi-core machines. The solution of the inverse problem is then represented by a collection of reservoir models in terms of facies, porosity and oil saturation, which constitute samples of the posterior distribution. We are finally able to produce probability maps of the properties we are interested in by performing statistical analysis on the collection of solutions.

A practical primer on geostatistics

USGS Publications Warehouse

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

Model-Based Geostatistical Mapping of the Prevalence of Onchocerca volvulus in West Africa

PubMed Central

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

Risk mapping of clonorchiasis in the People’s Republic of China: A systematic review and Bayesian geostatistical analysis

PubMed Central

Lai, Ying-Si; Zhou, Xiao-Nong; Pan, Zhi-Heng; Utzinger, Jürg; Vounatsou, Penelope

2017-01-01

Background Clonorchiasis, one of the most important food-borne trematodiases, affects more than 12 million people in the People’s Republic of China (P.R. China). Spatially explicit risk estimates of Clonorchis sinensis infection are needed in order to target control interventions. Methodology Georeferenced survey data pertaining to infection prevalence of C. sinensis in P.R. China from 2000 onwards were obtained via a systematic review in PubMed, ISI Web of Science, Chinese National Knowledge Internet, and Wanfang Data from January 1, 2000 until January 10, 2016, with no restriction of language or study design. Additional disease data were provided by the National Institute of Parasitic Diseases, Chinese Center for Diseases Control and Prevention in Shanghai. Environmental and socioeconomic proxies were extracted from remote-sensing and other data sources. Bayesian variable selection was carried out to identify the most important predictors of C. sinensis risk. Geostatistical models were applied to quantify the association between infection risk and the predictors of the disease, and to predict the risk of infection across P.R. China at high spatial resolution (over a grid with grid cell size of 5×5 km). Principal findings We obtained clonorchiasis survey data at 633 unique locations in P.R. China. We observed that the risk of C. sinensis infection increased over time, particularly from 2005 onwards. We estimate that around 14.8 million (95% Bayesian credible interval 13.8–15.8 million) people in P.R. China were infected with C. sinensis in 2010. Highly endemic areas (≥ 20%) were concentrated in southern and northeastern parts of the country. The provinces with the highest risk of infection and the largest number of infected people were Guangdong, Guangxi, and Heilongjiang. Conclusions/Significance Our results provide spatially relevant information for guiding clonorchiasis control interventions in P.R. China. The trend toward higher risk of C. sinensis

Obtaining parsimonious hydraulic conductivity fields using head and transport observations: A Bayesian geostatistical parameter estimation approach

NASA Astrophysics Data System (ADS)

Fienen, M.; Hunt, R.; Krabbenhoft, D.; Clemo, T.

2009-08-01

Flow path delineation is a valuable tool for interpreting the subsurface hydrogeochemical environment. Different types of data, such as groundwater flow and transport, inform different aspects of hydrogeologic parameter values (hydraulic conductivity in this case) which, in turn, determine flow paths. This work combines flow and transport information to estimate a unified set of hydrogeologic parameters using the Bayesian geostatistical inverse approach. Parameter flexibility is allowed by using a highly parameterized approach with the level of complexity informed by the data. Despite the effort to adhere to the ideal of minimal a priori structure imposed on the problem, extreme contrasts in parameters can result in the need to censor correlation across hydrostratigraphic bounding surfaces. These partitions segregate parameters into facies associations. With an iterative approach in which partitions are based on inspection of initial estimates, flow path interpretation is progressively refined through the inclusion of more types of data. Head observations, stable oxygen isotopes (18O/16O ratios), and tritium are all used to progressively refine flow path delineation on an isthmus between two lakes in the Trout Lake watershed, northern Wisconsin, United States. Despite allowing significant parameter freedom by estimating many distributed parameter values, a smooth field is obtained.

Obtaining parsimonious hydraulic conductivity fields using head and transport observations: A Bayesian geostatistical parameter estimation approach

USGS Publications Warehouse

Fienen, M.; Hunt, R.; Krabbenhoft, D.; Clemo, T.

2009-01-01

Flow path delineation is a valuable tool for interpreting the subsurface hydrogeochemical environment. Different types of data, such as groundwater flow and transport, inform different aspects of hydrogeologic parameter values (hydraulic conductivity in this case) which, in turn, determine flow paths. This work combines flow and transport information to estimate a unified set of hydrogeologic parameters using the Bayesian geostatistical inverse approach. Parameter flexibility is allowed by using a highly parameterized approach with the level of complexity informed by the data. Despite the effort to adhere to the ideal of minimal a priori structure imposed on the problem, extreme contrasts in parameters can result in the need to censor correlation across hydrostratigraphic bounding surfaces. These partitions segregate parameters into facies associations. With an iterative approach in which partitions are based on inspection of initial estimates, flow path interpretation is progressively refined through the inclusion of more types of data. Head observations, stable oxygen isotopes (18O/16O ratios), and tritium are all used to progressively refine flow path delineation on an isthmus between two lakes in the Trout Lake watershed, northern Wisconsin, United States. Despite allowing significant parameter freedom by estimating many distributed parameter values, a smooth field is obtained.

Model Diagnostics for Bayesian Networks

ERIC Educational Resources Information Center

Sinharay, Sandip

2006-01-01

Bayesian networks are frequently used in educational assessments primarily for learning about students' knowledge and skills. There is a lack of works on assessing fit of Bayesian networks. This article employs the posterior predictive model checking method, a popular Bayesian model checking tool, to assess fit of simple Bayesian networks. A…

Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets.

PubMed

Datta, Abhirup; Banerjee, Sudipto; Finley, Andrew O; Gelfand, Alan E

2016-01-01

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This article develops a class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive U.S. Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods. Supplementary materials for this article are available online.

Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets

PubMed Central

Datta, Abhirup; Banerjee, Sudipto; Finley, Andrew O.; Gelfand, Alan E.

2018-01-01

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This article develops a class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive U.S. Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods. Supplementary materials for this article are available online. PMID:29720777

Bayesian Hierarchical Modeling for Big Data Fusion in Soil Hydrology

NASA Astrophysics Data System (ADS)

Mohanty, B.; Kathuria, D.; Katzfuss, M.

2016-12-01

Soil moisture datasets from remote sensing (RS) platforms (such as SMOS and SMAP) and reanalysis products from land surface models are typically available on a coarse spatial granularity of several square km. Ground based sensors on the other hand provide observations on a finer spatial scale (meter scale or less) but are sparsely available. Soil moisture is affected by high variability due to complex interactions between geologic, topographic, vegetation and atmospheric variables. Hydrologic processes usually occur at a scale of 1 km or less and therefore spatially ubiquitous and temporally periodic soil moisture products at this scale are required to aid local decision makers in agriculture, weather prediction and reservoir operations. Past literature has largely focused on downscaling RS soil moisture for a small extent of a field or a watershed and hence the applicability of such products has been limited. The present study employs a spatial Bayesian Hierarchical Model (BHM) to derive soil moisture products at a spatial scale of 1 km for the state of Oklahoma by fusing point scale Mesonet data and coarse scale RS data for soil moisture and its auxiliary covariates such as precipitation, topography, soil texture and vegetation. It is seen that the BHM model handles change of support problems easily while performing accurate uncertainty quantification arising from measurement errors and imperfect retrieval algorithms. The computational challenge arising due to the large number of measurements is tackled by utilizing basis function approaches and likelihood approximations. The BHM model can be considered as a complex Bayesian extension of traditional geostatistical prediction methods (such as Kriging) for large datasets in the presence of uncertainties.

Systematic evaluation of sequential geostatistical resampling within MCMC for posterior sampling of near-surface geophysical inverse problems

NASA Astrophysics Data System (ADS)

Ruggeri, Paolo; Irving, James; Holliger, Klaus

2015-08-01

We critically examine the performance of sequential geostatistical resampling (SGR) as a model proposal mechanism for Bayesian Markov-chain-Monte-Carlo (MCMC) solutions to near-surface geophysical inverse problems. Focusing on a series of simple yet realistic synthetic crosshole georadar tomographic examples characterized by different numbers of data, levels of data error and degrees of model parameter spatial correlation, we investigate the efficiency of three different resampling strategies with regard to their ability to generate statistically independent realizations from the Bayesian posterior distribution. Quite importantly, our results show that, no matter what resampling strategy is employed, many of the examined test cases require an unreasonably high number of forward model runs to produce independent posterior samples, meaning that the SGR approach as currently implemented will not be computationally feasible for a wide range of problems. Although use of a novel gradual-deformation-based proposal method can help to alleviate these issues, it does not offer a full solution. Further, we find that the nature of the SGR is found to strongly influence MCMC performance; however no clear rule exists as to what set of inversion parameters and/or overall proposal acceptance rate will allow for the most efficient implementation. We conclude that although the SGR methodology is highly attractive as it allows for the consideration of complex geostatistical priors as well as conditioning to hard and soft data, further developments are necessary in the context of novel or hybrid MCMC approaches for it to be considered generally suitable for near-surface geophysical inversions.

Intelligent Decisions Need Intelligent Choice of Models and Data - a Bayesian Justifiability Analysis for Models with Vastly Different Complexity

NASA Astrophysics Data System (ADS)

Nowak, W.; Schöniger, A.; Wöhling, T.; Illman, W. A.

2016-12-01

Model-based decision support requires justifiable models with good predictive capabilities. This, in turn, calls for a fine adjustment between predictive accuracy (small systematic model bias that can be achieved with rather complex models), and predictive precision (small predictive uncertainties that can be achieved with simpler models with fewer parameters). The implied complexity/simplicity trade-off depends on the availability of informative data for calibration. If not available, additional data collection can be planned through optimal experimental design. We present a model justifiability analysis that can compare models of vastly different complexity. It rests on Bayesian model averaging (BMA) to investigate the complexity/performance trade-off dependent on data availability. Then, we disentangle the complexity component from the performance component. We achieve this by replacing actually observed data by realizations of synthetic data predicted by the models. This results in a "model confusion matrix". Based on this matrix, the modeler can identify the maximum model complexity that can be justified by the available (or planned) amount and type of data. As a side product, the matrix quantifies model (dis-)similarity. We apply this analysis to aquifer characterization via hydraulic tomography, comparing four models with a vastly different number of parameters (from a homogeneous model to geostatistical random fields). As a testing scenario, we consider hydraulic tomography data. Using subsets of these data, we determine model justifiability as a function of data set size. The test case shows that geostatistical parameterization requires a substantial amount of hydraulic tomography data to be justified, while a zonation-based model can be justified with more limited data set sizes. The actual model performance (as opposed to model justifiability), however, depends strongly on the quality of prior geological information.

Reservoir studies with geostatistics to forecast performance

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tang, R.W.; Behrens, R.A.; Emanuel, A.S.

1991-05-01

In this paper example geostatistics and streamtube applications are presented for waterflood and CO{sub 2} flood in two low-permeability sandstone reservoirs. Thy hybrid approach of combining fine vertical resolution in cross-sectional models with streamtubes resulted in models that showed water channeling and provided realistic performance estimates. Results indicate that the combination of detailed geostatistical cross sections and fine-grid streamtube models offers a systematic approach for realistic performance forecasts.

Modelling Geomechanical Heterogeneity of Rock Masses Using Direct and Indirect Geostatistical Conditional Simulation Methods

NASA Astrophysics Data System (ADS)

Eivazy, Hesameddin; Esmaieli, Kamran; Jean, Raynald

2017-12-01

An accurate characterization and modelling of rock mass geomechanical heterogeneity can lead to more efficient mine planning and design. Using deterministic approaches and random field methods for modelling rock mass heterogeneity is known to be limited in simulating the spatial variation and spatial pattern of the geomechanical properties. Although the applications of geostatistical techniques have demonstrated improvements in modelling the heterogeneity of geomechanical properties, geostatistical estimation methods such as Kriging result in estimates of geomechanical variables that are not fully representative of field observations. This paper reports on the development of 3D models for spatial variability of rock mass geomechanical properties using geostatistical conditional simulation method based on sequential Gaussian simulation. A methodology to simulate the heterogeneity of rock mass quality based on the rock mass rating is proposed and applied to a large open-pit mine in Canada. Using geomechanical core logging data collected from the mine site, a direct and an indirect approach were used to model the spatial variability of rock mass quality. The results of the two modelling approaches were validated against collected field data. The study aims to quantify the risks of pit slope failure and provides a measure of uncertainties in spatial variability of rock mass properties in different areas of the pit.

Multiobjective design of aquifer monitoring networks for optimal spatial prediction and geostatistical parameter estimation

NASA Astrophysics Data System (ADS)

Alzraiee, Ayman H.; Bau, Domenico A.; Garcia, Luis A.

2013-06-01

Effective sampling of hydrogeological systems is essential in guiding groundwater management practices. Optimal sampling of groundwater systems has previously been formulated based on the assumption that heterogeneous subsurface properties can be modeled using a geostatistical approach. Therefore, the monitoring schemes have been developed to concurrently minimize the uncertainty in the spatial distribution of systems' states and parameters, such as the hydraulic conductivity K and the hydraulic head H, and the uncertainty in the geostatistical model of system parameters using a single objective function that aggregates all objectives. However, it has been shown that the aggregation of possibly conflicting objective functions is sensitive to the adopted aggregation scheme and may lead to distorted results. In addition, the uncertainties in geostatistical parameters affect the uncertainty in the spatial prediction of K and H according to a complex nonlinear relationship, which has often been ineffectively evaluated using a first-order approximation. In this study, we propose a multiobjective optimization framework to assist the design of monitoring networks of K and H with the goal of optimizing their spatial predictions and estimating the geostatistical parameters of the K field. The framework stems from the combination of a data assimilation (DA) algorithm and a multiobjective evolutionary algorithm (MOEA). The DA algorithm is based on the ensemble Kalman filter, a Monte-Carlo-based Bayesian update scheme for nonlinear systems, which is employed to approximate the posterior uncertainty in K, H, and the geostatistical parameters of K obtained by collecting new measurements. Multiple MOEA experiments are used to investigate the trade-off among design objectives and identify the corresponding monitoring schemes. The methodology is applied to design a sampling network for a shallow unconfined groundwater system located in Rocky Ford, Colorado. Results indicate that

Assessment and modeling of the groundwater hydrogeochemical quality parameters via geostatistical approaches

NASA Astrophysics Data System (ADS)

Karami, Shawgar; Madani, Hassan; Katibeh, Homayoon; Fatehi Marj, Ahmad

2018-03-01

Geostatistical methods are one of the advanced techniques used for interpolation of groundwater quality data. The results obtained from geostatistics will be useful for decision makers to adopt suitable remedial measures to protect the quality of groundwater sources. Data used in this study were collected from 78 wells in Varamin plain aquifer located in southeast of Tehran, Iran, in 2013. Ordinary kriging method was used in this study to evaluate groundwater quality parameters. According to what has been mentioned in this paper, seven main quality parameters (i.e. total dissolved solids (TDS), sodium adsorption ratio (SAR), electrical conductivity (EC), sodium (Na+), total hardness (TH), chloride (Cl-) and sulfate (SO4 2-)), have been analyzed and interpreted by statistical and geostatistical methods. After data normalization by Nscore method in WinGslib software, variography as a geostatistical tool to define spatial regression was compiled and experimental variograms were plotted by GS+ software. Then, the best theoretical model was fitted to each variogram based on the minimum RSS. Cross validation method was used to determine the accuracy of the estimated data. Eventually, estimation maps of groundwater quality were prepared in WinGslib software and estimation variance map and estimation error map were presented to evaluate the quality of estimation in each estimated point. Results showed that kriging method is more accurate than the traditional interpolation methods.

Introduction to Geostatistics

NASA Astrophysics Data System (ADS)

Kitanidis, P. K.

1997-05-01

Introduction to Geostatistics presents practical techniques for engineers and earth scientists who routinely encounter interpolation and estimation problems when analyzing data from field observations. Requiring no background in statistics, and with a unique approach that synthesizes classic and geostatistical methods, this book offers linear estimation methods for practitioners and advanced students. Well illustrated with exercises and worked examples, Introduction to Geostatistics is designed for graduate-level courses in earth sciences and environmental engineering.

Geostatistics and Bayesian updating for transmissivity estimation in a multiaquifer system in Manitoba, Canada.

PubMed

Kennedy, Paula L; Woodbury, Allan D

2002-01-01

In ground water flow and transport modeling, the heterogeneous nature of porous media has a considerable effect on the resulting flow and solute transport. Some method of generating the heterogeneous field from a limited dataset of uncertain measurements is required. Bayesian updating is one method that interpolates from an uncertain dataset using the statistics of the underlying probability distribution function. In this paper, Bayesian updating was used to determine the heterogeneous natural log transmissivity field for a carbonate and a sandstone aquifer in southern Manitoba. It was determined that the transmissivity in m2/sec followed a natural log normal distribution for both aquifers with a mean of -7.2 and - 8.0 for the carbonate and sandstone aquifers, respectively. The variograms were calculated using an estimator developed by Li and Lake (1994). Fractal nature was not evident in the variogram from either aquifer. The Bayesian updating heterogeneous field provided good results even in cases where little data was available. A large transmissivity zone in the sandstone aquifer was created by the Bayesian procedure, which is not a reflection of any deterministic consideration, but is a natural outcome of updating a prior probability distribution function with observations. The statistical model returns a result that is very reasonable; that is homogeneous in regions where little or no information is available to alter an initial state. No long range correlation trends or fractal behavior of the log-transmissivity field was observed in either aquifer over a distance of about 300 km.

Geostatistics and petroleum geology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hohn, M.E.

1988-01-01

This book examines purpose and use of geostatistics in exploration and development of oil and gas with an emphasis on appropriate and pertinent case studies. It present an overview of geostatistics. Topics covered include: The semivariogram; Linear estimation; Multivariate geostatistics; Nonlinear estimation; From indicator variables to nonparametric estimation; and More detail, less certainty; conditional simulation.

A geostatistics-informed hierarchical sensitivity analysis method for complex groundwater flow and transport modeling: GEOSTATISTICAL SENSITIVITY ANALYSIS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dai, Heng; Chen, Xingyuan; Ye, Ming

Sensitivity analysis is an important tool for quantifying uncertainty in the outputs of mathematical models, especially for complex systems with a high dimension of spatially correlated parameters. Variance-based global sensitivity analysis has gained popularity because it can quantify the relative contribution of uncertainty from different sources. However, its computational cost increases dramatically with the complexity of the considered model and the dimension of model parameters. In this study we developed a hierarchical sensitivity analysis method that (1) constructs an uncertainty hierarchy by analyzing the input uncertainty sources, and (2) accounts for the spatial correlation among parameters at each level ofmore » the hierarchy using geostatistical tools. The contribution of uncertainty source at each hierarchy level is measured by sensitivity indices calculated using the variance decomposition method. Using this methodology, we identified the most important uncertainty source for a dynamic groundwater flow and solute transport in model at the Department of Energy (DOE) Hanford site. The results indicate that boundary conditions and permeability field contribute the most uncertainty to the simulated head field and tracer plume, respectively. The relative contribution from each source varied spatially and temporally as driven by the dynamic interaction between groundwater and river water at the site. By using a geostatistical approach to reduce the number of realizations needed for the sensitivity analysis, the computational cost of implementing the developed method was reduced to a practically manageable level. The developed sensitivity analysis method is generally applicable to a wide range of hydrologic and environmental problems that deal with high-dimensional spatially-distributed parameters.« less

Random vectors and spatial analysis by geostatistics for geotechnical applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Young, D.S.

1987-08-01

Geostatistics is extended to the spatial analysis of vector variables by defining the estimation variance and vector variogram in terms of the magnitude of difference vectors. Many random variables in geotechnology are in vectorial terms rather than scalars, and its structural analysis requires those sample variable interpolations to construct and characterize structural models. A better local estimator will result in greater quality of input models; geostatistics can provide such estimators; kriging estimators. The efficiency of geostatistics for vector variables is demonstrated in a case study of rock joint orientations in geological formations. The positive cross-validation encourages application of geostatistics tomore » spatial analysis of random vectors in geoscience as well as various geotechnical fields including optimum site characterization, rock mechanics for mining and civil structures, cavability analysis of block cavings, petroleum engineering, and hydrologic and hydraulic modelings.« less

PCTO-SIM: Multiple-point geostatistical modeling using parallel conditional texture optimization

NASA Astrophysics Data System (ADS)

Pourfard, Mohammadreza; Abdollahifard, Mohammad J.; Faez, Karim; Motamedi, Sayed Ahmad; Hosseinian, Tahmineh

2017-05-01

Multiple-point Geostatistics is a well-known general statistical framework by which complex geological phenomena have been modeled efficiently. Pixel-based and patch-based are two major categories of these methods. In this paper, the optimization-based category is used which has a dual concept in texture synthesis as texture optimization. Our extended version of texture optimization uses the energy concept to model geological phenomena. While honoring the hard point, the minimization of our proposed cost function forces simulation grid pixels to be as similar as possible to training images. Our algorithm has a self-enrichment capability and creates a richer training database from a sparser one through mixing the information of all surrounding patches of the simulation nodes. Therefore, it preserves pattern continuity in both continuous and categorical variables very well. It also shows a fuzzy result in its every realization similar to the expected result of multi realizations of other statistical models. While the main core of most previous Multiple-point Geostatistics methods is sequential, the parallel main core of our algorithm enabled it to use GPU efficiently to reduce the CPU time. One new validation method for MPS has also been proposed in this paper.

Can Geostatistical Models Represent Nature's Variability? An Analysis Using Flume Experiments

NASA Astrophysics Data System (ADS)

Scheidt, C.; Fernandes, A. M.; Paola, C.; Caers, J.

2015-12-01

The lack of understanding in the Earth's geological and physical processes governing sediment deposition render subsurface modeling subject to large uncertainty. Geostatistics is often used to model uncertainty because of its capability to stochastically generate spatially varying realizations of the subsurface. These methods can generate a range of realizations of a given pattern - but how representative are these of the full natural variability? And how can we identify the minimum set of images that represent this natural variability? Here we use this minimum set to define the geostatistical prior model: a set of training images that represent the range of patterns generated by autogenic variability in the sedimentary environment under study. The proper definition of the prior model is essential in capturing the variability of the depositional patterns. This work starts with a set of overhead images from an experimental basin that showed ongoing autogenic variability. We use the images to analyze the essential characteristics of this suite of patterns. In particular, our goal is to define a prior model (a minimal set of selected training images) such that geostatistical algorithms, when applied to this set, can reproduce the full measured variability. A necessary prerequisite is to define a measure of variability. In this study, we measure variability using a dissimilarity distance between the images. The distance indicates whether two snapshots contain similar depositional patterns. To reproduce the variability in the images, we apply an MPS algorithm to the set of selected snapshots of the sedimentary basin that serve as training images. The training images are chosen from among the initial set by using the distance measure to ensure that only dissimilar images are chosen. Preliminary investigations show that MPS can reproduce fairly accurately the natural variability of the experimental depositional system. Furthermore, the selected training images provide

Bayesian Model Averaging for Propensity Score Analysis

ERIC Educational Resources Information Center

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…

Geostatistical applications in environmental remediation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stewart, R.N.; Purucker, S.T.; Lyon, B.F.

1995-02-01

Geostatistical analysis refers to a collection of statistical methods for addressing data that vary in space. By incorporating spatial information into the analysis, geostatistics has advantages over traditional statistical analysis for problems with a spatial context. Geostatistics has a history of success in earth science applications, and its popularity is increasing in other areas, including environmental remediation. Due to recent advances in computer technology, geostatistical algorithms can be executed at a speed comparable to many standard statistical software packages. When used responsibly, geostatistics is a systematic and defensible tool can be used in various decision frameworks, such as the Datamore » Quality Objectives (DQO) process. At every point in the site, geostatistics can estimate both the concentration level and the probability or risk of exceeding a given value. Using these probability maps can assist in identifying clean-up zones. Given any decision threshold and an acceptable level of risk, the probability maps identify those areas that are estimated to be above or below the acceptable risk. Those areas that are above the threshold are of the most concern with regard to remediation. In addition to estimating clean-up zones, geostatistics can assist in designing cost-effective secondary sampling schemes. Those areas of the probability map with high levels of estimated uncertainty are areas where more secondary sampling should occur. In addition, geostatistics has the ability to incorporate soft data directly into the analysis. These data include historical records, a highly correlated secondary contaminant, or expert judgment. The role of geostatistics in environmental remediation is a tool that in conjunction with other methods can provide a common forum for building consensus.« less

Carbon Tetrachloride Emissions from the US during 2008 - 2012 Derived from Atmospheric Data Using Bayesian and Geostatistical Inversions

NASA Astrophysics Data System (ADS)

Hu, L.; Montzka, S. A.; Miller, B.; Andrews, A. E.; Miller, J. B.; Lehman, S.; Sweeney, C.; Miller, S. M.; Thoning, K. W.; Siso, C.; Atlas, E. L.; Blake, D. R.; De Gouw, J. A.; Gilman, J.; Dutton, G. S.; Elkins, J. W.; Hall, B. D.; Chen, H.; Fischer, M. L.; Mountain, M. E.; Nehrkorn, T.; Biraud, S.; Tans, P. P.

2015-12-01

Global atmospheric observations suggest substantial ongoing emissions of carbon tetrachloride (CCl4) despite a 100% phase-out of production for dispersive uses since 1996 in developed countries and 2010 in other countries. Little progress has been made in understanding the causes of these ongoing emissions or identifying their contributing sources. In this study, we employed multiple inverse modeling techniques (i.e. Bayesian and geostatistical inversions) to assimilate CCl4 mole fractions observed from the National Oceanic and Atmospheric Administration (NOAA) flask-air sampling network over the US, and quantify its national and regional emissions during 2008 - 2012. Average national total emissions of CCl4 between 2008 and 2012 determined from these observations and an ensemble of inversions range between 2.1 and 6.1 Gg yr-1. This emission is substantially larger than the mean of 0.06 Gg/yr reported to the US EPA Toxics Release Inventory over these years, suggesting that under-reported emissions or non-reporting sources make up the bulk of CCl4 emissions from the US. But while the inventory does not account for the magnitude of observationally-derived CCl4 emissions, the regional distribution of derived and inventory emissions is similar. Furthermore, when considered relative to the distribution of uncapped landfills or population, the variability in measured mole fractions was most consistent with the distribution of industrial sources (i.e., those from the Toxics Release Inventory). Our results suggest that emissions from the US only account for a small fraction of the global on-going emissions of CCl4 (30 - 80 Gg yr-1 over this period). Finally, to ascertain the importance of the US emissions relative to the unaccounted global emission rate we considered multiple approaches to extrapolate our results to other countries and the globe.

Bayesian models: A statistical primer for ecologists

USGS Publications Warehouse

Hobbs, N. Thompson; Hooten, Mevin B.

2015-01-01

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

Bayesian Data-Model Fit Assessment for Structural Equation Modeling

ERIC Educational Resources Information Center

Levy, Roy

2011-01-01

Bayesian approaches to modeling are receiving an increasing amount of attention in the areas of model construction and estimation in factor analysis, structural equation modeling (SEM), and related latent variable models. However, model diagnostics and model criticism remain relatively understudied aspects of Bayesian SEM. This article describes…

Modeling Diagnostic Assessments with Bayesian Networks

ERIC Educational Resources Information Center

Almond, Russell G.; DiBello, Louis V.; Moulder, Brad; Zapata-Rivera, Juan-Diego

2007-01-01

This paper defines Bayesian network models and examines their applications to IRT-based cognitive diagnostic modeling. These models are especially suited to building inference engines designed to be synchronous with the finer grained student models that arise in skills diagnostic assessment. Aspects of the theory and use of Bayesian network models…

Applications of Geostatistics in Plant Nematology

PubMed Central

Wallace, M. K.; Hawkins, D. M.

1994-01-01

The application of geostatistics to plant nematology was made by evaluating soil and nematode data acquired from 200 soil samples collected from the Ap horizon of a reed canary-grass field in northern Minnesota. Geostatistical concepts relevant to nematology include semi-variogram modelling, kriging, and change of support calculations. Soil and nematode data generally followed a spherical semi-variogram model, with little random variability associated with soil data and large inherent variability for nematode data. Block kriging of soil and nematode data provided useful contour maps of the data. Change of snpport calculations indicated that most of the random variation in nematode data was due to short-range spatial variability in the nematode population densities. PMID:19279938

Applications of geostatistics in plant nematology.

PubMed

Wallace, M K; Hawkins, D M

1994-12-01

The application of geostatistics to plant nematology was made by evaluating soil and nematode data acquired from 200 soil samples collected from the A(p) horizon of a reed canary-grass field in northern Minnesota. Geostatistical concepts relevant to nematology include semi-variogram modelling, kriging, and change of support calculations. Soil and nematode data generally followed a spherical semi-variogram model, with little random variability associated with soil data and large inherent variability for nematode data. Block kriging of soil and nematode data provided useful contour maps of the data. Change of snpport calculations indicated that most of the random variation in nematode data was due to short-range spatial variability in the nematode population densities.

Moving beyond qualitative evaluations of Bayesian models of cognition.

PubMed

Hemmer, Pernille; Tauber, Sean; Steyvers, Mark

2015-06-01

Bayesian models of cognition provide a powerful way to understand the behavior and goals of individuals from a computational point of view. Much of the focus in the Bayesian cognitive modeling approach has been on qualitative model evaluations, where predictions from the models are compared to data that is often averaged over individuals. In many cognitive tasks, however, there are pervasive individual differences. We introduce an approach to directly infer individual differences related to subjective mental representations within the framework of Bayesian models of cognition. In this approach, Bayesian data analysis methods are used to estimate cognitive parameters and motivate the inference process within a Bayesian cognitive model. We illustrate this integrative Bayesian approach on a model of memory. We apply the model to behavioral data from a memory experiment involving the recall of heights of people. A cross-validation analysis shows that the Bayesian memory model with inferred subjective priors predicts withheld data better than a Bayesian model where the priors are based on environmental statistics. In addition, the model with inferred priors at the individual subject level led to the best overall generalization performance, suggesting that individual differences are important to consider in Bayesian models of cognition.

Bayesian modeling of flexible cognitive control

PubMed Central

Jiang, Jiefeng; Heller, Katherine; Egner, Tobias

2014-01-01

“Cognitive control” describes endogenous guidance of behavior in situations where routine stimulus-response associations are suboptimal for achieving a desired goal. The computational and neural mechanisms underlying this capacity remain poorly understood. We examine recent advances stemming from the application of a Bayesian learner perspective that provides optimal prediction for control processes. In reviewing the application of Bayesian models to cognitive control, we note that an important limitation in current models is a lack of a plausible mechanism for the flexible adjustment of control over conflict levels changing at varying temporal scales. We then show that flexible cognitive control can be achieved by a Bayesian model with a volatility-driven learning mechanism that modulates dynamically the relative dependence on recent and remote experiences in its prediction of future control demand. We conclude that the emergent Bayesian perspective on computational mechanisms of cognitive control holds considerable promise, especially if future studies can identify neural substrates of the variables encoded by these models, and determine the nature (Bayesian or otherwise) of their neural implementation. PMID:24929218

Latin hypercube sampling and geostatistical modeling of spatial uncertainty in a spatially explicit forest landscape model simulation

Treesearch

Chonggang Xu; Hong S. He; Yuanman Hu; Yu Chang; Xiuzhen Li; Rencang Bu

2005-01-01

Geostatistical stochastic simulation is always combined with Monte Carlo method to quantify the uncertainty in spatial model simulations. However, due to the relatively long running time of spatially explicit forest models as a result of their complexity, it is always infeasible to generate hundreds or thousands of Monte Carlo simulations. Thus, it is of great...

Bayesian analysis of CCDM models

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

A guide to Bayesian model selection for ecologists

USGS Publications Warehouse

Hooten, Mevin B.; Hobbs, N.T.

2015-01-01

The steady upward trend in the use of model selection and Bayesian methods in ecological research has made it clear that both approaches to inference are important for modern analysis of models and data. However, in teaching Bayesian methods and in working with our research colleagues, we have noticed a general dissatisfaction with the available literature on Bayesian model selection and multimodel inference. Students and researchers new to Bayesian methods quickly find that the published advice on model selection is often preferential in its treatment of options for analysis, frequently advocating one particular method above others. The recent appearance of many articles and textbooks on Bayesian modeling has provided welcome background on relevant approaches to model selection in the Bayesian framework, but most of these are either very narrowly focused in scope or inaccessible to ecologists. Moreover, the methodological details of Bayesian model selection approaches are spread thinly throughout the literature, appearing in journals from many different fields. Our aim with this guide is to condense the large body of literature on Bayesian approaches to model selection and multimodel inference and present it specifically for quantitative ecologists as neutrally as possible. We also bring to light a few important and fundamental concepts relating directly to model selection that seem to have gone unnoticed in the ecological literature. Throughout, we provide only a minimal discussion of philosophy, preferring instead to examine the breadth of approaches as well as their practical advantages and disadvantages. This guide serves as a reference for ecologists using Bayesian methods, so that they can better understand their options and can make an informed choice that is best aligned with their goals for inference.

Using geostatistics to evaluate cleanup goals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marcon, M.F.; Hopkins, L.P.

1995-12-01

Geostatistical analysis is a powerful predictive tool typically used to define spatial variability in environmental data. The information from a geostatistical analysis using kriging, a geostatistical. tool, can be taken a step further to optimize sampling location and frequency and help quantify sampling uncertainty in both the remedial investigation and remedial design at a hazardous waste site. Geostatistics were used to quantify sampling uncertainty in attainment of a risk-based cleanup goal and determine the optimal sampling frequency necessary to delineate the horizontal extent of impacted soils at a Gulf Coast waste site.

High Performance Geostatistical Modeling of Biospheric Resources

NASA Astrophysics Data System (ADS)

Pedelty, J. A.; Morisette, J. T.; Smith, J. A.; Schnase, J. L.; Crosier, C. S.; Stohlgren, T. J.

2004-12-01

We are using parallel geostatistical codes to study spatial relationships among biospheric resources in several study areas. For example, spatial statistical models based on large- and small-scale variability have been used to predict species richness of both native and exotic plants (hot spots of diversity) and patterns of exotic plant invasion. However, broader use of geostastics in natural resource modeling, especially at regional and national scales, has been limited due to the large computing requirements of these applications. To address this problem, we implemented parallel versions of the kriging spatial interpolation algorithm. The first uses the Message Passing Interface (MPI) in a master/slave paradigm on an open source Linux Beowulf cluster, while the second is implemented with the new proprietary Xgrid distributed processing system on an Xserve G5 cluster from Apple Computer, Inc. These techniques are proving effective and provide the basis for a national decision support capability for invasive species management that is being jointly developed by NASA and the US Geological Survey.

Hierarchical Bayesian Modeling of Fluid-Induced Seismicity

NASA Astrophysics Data System (ADS)

Broccardo, M.; Mignan, A.; Wiemer, S.; Stojadinovic, B.; Giardini, D.

2017-11-01

In this study, we present a Bayesian hierarchical framework to model fluid-induced seismicity. The framework is based on a nonhomogeneous Poisson process with a fluid-induced seismicity rate proportional to the rate of injected fluid. The fluid-induced seismicity rate model depends upon a set of physically meaningful parameters and has been validated for six fluid-induced case studies. In line with the vision of hierarchical Bayesian modeling, the rate parameters are considered as random variables. We develop both the Bayesian inference and updating rules, which are used to develop a probabilistic forecasting model. We tested the Basel 2006 fluid-induced seismic case study to prove that the hierarchical Bayesian model offers a suitable framework to coherently encode both epistemic uncertainty and aleatory variability. Moreover, it provides a robust and consistent short-term seismic forecasting model suitable for online risk quantification and mitigation.

Geostatistical regularization of inverse models for the retrieval of vegetation biophysical variables

NASA Astrophysics Data System (ADS)

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.

Local Geostatistical Models and Big Data in Hydrological and Ecological Applications

NASA Astrophysics Data System (ADS)

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

Bayesian assessment of the expected data impact on prediction confidence in optimal sampling design

NASA Astrophysics Data System (ADS)

Leube, P. C.; Geiges, A.; Nowak, W.

2012-02-01

Incorporating hydro(geo)logical data, such as head and tracer data, into stochastic models of (subsurface) flow and transport helps to reduce prediction uncertainty. Because of financial limitations for investigation campaigns, information needs toward modeling or prediction goals should be satisfied efficiently and rationally. Optimal design techniques find the best one among a set of investigation strategies. They optimize the expected impact of data on prediction confidence or related objectives prior to data collection. We introduce a new optimal design method, called PreDIA(gnosis) (Preposterior Data Impact Assessor). PreDIA derives the relevant probability distributions and measures of data utility within a fully Bayesian, generalized, flexible, and accurate framework. It extends the bootstrap filter (BF) and related frameworks to optimal design by marginalizing utility measures over the yet unknown data values. PreDIA is a strictly formal information-processing scheme free of linearizations. It works with arbitrary simulation tools, provides full flexibility concerning measurement types (linear, nonlinear, direct, indirect), allows for any desired task-driven formulations, and can account for various sources of uncertainty (e.g., heterogeneity, geostatistical assumptions, boundary conditions, measurement values, model structure uncertainty, a large class of model errors) via Bayesian geostatistics and model averaging. Existing methods fail to simultaneously provide these crucial advantages, which our method buys at relatively higher-computational costs. We demonstrate the applicability and advantages of PreDIA over conventional linearized methods in a synthetic example of subsurface transport. In the example, we show that informative data is often invisible for linearized methods that confuse zero correlation with statistical independence. Hence, PreDIA will often lead to substantially better sampling designs. Finally, we extend our example to specifically

Bayesian structural equation modeling in sport and exercise psychology.

PubMed

Stenling, Andreas; Ivarsson, Andreas; Johnson, Urban; Lindwall, Magnus

2015-08-01

Bayesian statistics is on the rise in mainstream psychology, but applications in sport and exercise psychology research are scarce. In this article, the foundations of Bayesian analysis are introduced, and we will illustrate how to apply Bayesian structural equation modeling in a sport and exercise psychology setting. More specifically, we contrasted a confirmatory factor analysis on the Sport Motivation Scale II estimated with the most commonly used estimator, maximum likelihood, and a Bayesian approach with weakly informative priors for cross-loadings and correlated residuals. The results indicated that the model with Bayesian estimation and weakly informative priors provided a good fit to the data, whereas the model estimated with a maximum likelihood estimator did not produce a well-fitting model. The reasons for this discrepancy between maximum likelihood and Bayesian estimation are discussed as well as potential advantages and caveats with the Bayesian approach.

Geostatistics and petroleum geology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hohn, M.E.

1988-01-01

The book reviewed is designed as a practical guide to geostatistics or kriging for the petroleum geologists. The author's aim in the book is to explain geostatistics as a working tool for petroleum geologists through extensive use of case-study material mostly drawn from his own research in gas potential evaluation in West Virginia. Theory and mathematics are pared down to immediate needs.

Reservoir property grids improve with geostatistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vogt, J.

1993-09-01

Visualization software, reservoir simulators and many other E and P software applications need reservoir property grids as input. Using geostatistics, as compared to other gridding methods, to produce these grids leads to the best output from the software programs. For the purpose stated herein, geostatistics is simply two types of gridding methods. Mathematically, these methods are based on minimizing or duplicating certain statistical properties of the input data. One geostatical method, called kriging, is used when the highest possible point-by-point accuracy is desired. The other method, called conditional simulation, is used when one wants statistics and texture of the resultingmore » grid to be the same as for the input data. In the following discussion, each method is explained, compared to other gridding methods, and illustrated through example applications. Proper use of geostatistical data in flow simulations, use of geostatistical data for history matching, and situations where geostatistics has no significant advantage over other methods, also will be covered.« less

Integrating Address Geocoding, Land Use Regression, and Spatiotemporal Geostatistical Estimation for Groundwater Tetrachloroethylene

PubMed Central

Messier, Kyle P.; Akita, Yasuyuki; Serre, Marc L.

2012-01-01

Geographic Information Systems (GIS) based techniques are cost-effective and efficient methods used by state agencies and epidemiology researchers for estimating concentration and exposure. However, budget limitations have made statewide assessments of contamination difficult, especially in groundwater media. Many studies have implemented address geocoding, land use regression, and geostatistics independently, but this is the first to examine the benefits of integrating these GIS techniques to address the need of statewide exposure assessments. A novel framework for concentration exposure is introduced that integrates address geocoding, land use regression (LUR), below detect data modeling, and Bayesian Maximum Entropy (BME). A LUR model was developed for Tetrachloroethylene that accounts for point sources and flow direction. We then integrate the LUR model into the BME method as a mean trend while also modeling below detects data as a truncated Gaussian probability distribution function. We increase available PCE data 4.7 times from previously available databases through multistage geocoding. The LUR model shows significant influence of dry cleaners at short ranges. The integration of the LUR model as mean trend in BME results in a 7.5% decrease in cross validation mean square error compared to BME with a constant mean trend. PMID:22264162

Integrating address geocoding, land use regression, and spatiotemporal geostatistical estimation for groundwater tetrachloroethylene.

PubMed

Messier, Kyle P; Akita, Yasuyuki; Serre, Marc L

2012-03-06

Geographic information systems (GIS) based techniques are cost-effective and efficient methods used by state agencies and epidemiology researchers for estimating concentration and exposure. However, budget limitations have made statewide assessments of contamination difficult, especially in groundwater media. Many studies have implemented address geocoding, land use regression, and geostatistics independently, but this is the first to examine the benefits of integrating these GIS techniques to address the need of statewide exposure assessments. A novel framework for concentration exposure is introduced that integrates address geocoding, land use regression (LUR), below detect data modeling, and Bayesian Maximum Entropy (BME). A LUR model was developed for tetrachloroethylene that accounts for point sources and flow direction. We then integrate the LUR model into the BME method as a mean trend while also modeling below detects data as a truncated Gaussian probability distribution function. We increase available PCE data 4.7 times from previously available databases through multistage geocoding. The LUR model shows significant influence of dry cleaners at short ranges. The integration of the LUR model as mean trend in BME results in a 7.5% decrease in cross validation mean square error compared to BME with a constant mean trend.

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

PubMed

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

A Novel Approach of Understanding and Incorporating Error of Chemical Transport Models into a Geostatistical Framework

NASA Astrophysics Data System (ADS)

Reyes, J.; Vizuete, W.; Serre, M. L.; Xu, Y.

2015-12-01

The EPA employs a vast monitoring network to measure ambient PM2.5 concentrations across the United States with one of its goals being to quantify exposure within the population. However, there are several areas of the country with sparse monitoring spatially and temporally. One means to fill in these monitoring gaps is to use PM2.5 modeled estimates from Chemical Transport Models (CTMs) specifically the Community Multi-scale Air Quality (CMAQ) model. CMAQ is able to provide complete spatial coverage but is subject to systematic and random error due to model uncertainty. Due to the deterministic nature of CMAQ, often these uncertainties are not quantified. Much effort is employed to quantify the efficacy of these models through different metrics of model performance. Currently evaluation is specific to only locations with observed data. Multiyear studies across the United States are challenging because the error and model performance of CMAQ are not uniform over such large space/time domains. Error changes regionally and temporally. Because of the complex mix of species that constitute PM2.5, CMAQ error is also a function of increasing PM2.5 concentration. To address this issue we introduce a model performance evaluation for PM2.5 CMAQ that is regionalized and non-linear. This model performance evaluation leads to error quantification for each CMAQ grid. Areas and time periods of error being better qualified. The regionalized error correction approach is non-linear and is therefore more flexible at characterizing model performance than approaches that rely on linearity assumptions and assume homoscedasticity of CMAQ predictions errors. Corrected CMAQ data are then incorporated into the modern geostatistical framework of Bayesian Maximum Entropy (BME). Through cross validation it is shown that incorporating error-corrected CMAQ data leads to more accurate estimates than just using observed data by themselves.

Multivariate Analysis and Modeling of Sediment Pollution Using Neural Network Models and Geostatistics

NASA Astrophysics Data System (ADS)

Golay, Jean; Kanevski, Mikhaïl

2013-04-01

The present research deals with the exploration and modeling of a complex dataset of 200 measurement points of sediment pollution by heavy metals in Lake Geneva. The fundamental idea was to use multivariate Artificial Neural Networks (ANN) along with geostatistical models and tools in order to improve the accuracy and the interpretability of data modeling. The results obtained with ANN were compared to those of traditional geostatistical algorithms like ordinary (co)kriging and (co)kriging with an external drift. Exploratory data analysis highlighted a great variety of relationships (i.e. linear, non-linear, independence) between the 11 variables of the dataset (i.e. Cadmium, Mercury, Zinc, Copper, Titanium, Chromium, Vanadium and Nickel as well as the spatial coordinates of the measurement points and their depth). Then, exploratory spatial data analysis (i.e. anisotropic variography, local spatial correlations and moving window statistics) was carried out. It was shown that the different phenomena to be modeled were characterized by high spatial anisotropies, complex spatial correlation structures and heteroscedasticity. A feature selection procedure based on General Regression Neural Networks (GRNN) was also applied to create subsets of variables enabling to improve the predictions during the modeling phase. The basic modeling was conducted using a Multilayer Perceptron (MLP) which is a workhorse of ANN. MLP models are robust and highly flexible tools which can incorporate in a nonlinear manner different kind of high-dimensional information. In the present research, the input layer was made of either two (spatial coordinates) or three neurons (when depth as auxiliary information could possibly capture an underlying trend) and the output layer was composed of one (univariate MLP) to eight neurons corresponding to the heavy metals of the dataset (multivariate MLP). MLP models with three input neurons can be referred to as Artificial Neural Networks with EXternal

Geostatistical regularization operators for geophysical inverse problems on irregular meshes

NASA Astrophysics Data System (ADS)

Jordi, C.; Doetsch, J.; Günther, T.; Schmelzbach, C.; Robertsson, J. OA

2018-05-01

Irregular meshes allow to include complicated subsurface structures into geophysical modelling and inverse problems. The non-uniqueness of these inverse problems requires appropriate regularization that can incorporate a priori information. However, defining regularization operators for irregular discretizations is not trivial. Different schemes for calculating smoothness operators on irregular meshes have been proposed. In contrast to classical regularization constraints that are only defined using the nearest neighbours of a cell, geostatistical operators include a larger neighbourhood around a particular cell. A correlation model defines the extent of the neighbourhood and allows to incorporate information about geological structures. We propose an approach to calculate geostatistical operators for inverse problems on irregular meshes by eigendecomposition of a covariance matrix that contains the a priori geological information. Using our approach, the calculation of the operator matrix becomes tractable for 3-D inverse problems on irregular meshes. We tested the performance of the geostatistical regularization operators and compared them against the results of anisotropic smoothing in inversions of 2-D surface synthetic electrical resistivity tomography (ERT) data as well as in the inversion of a realistic 3-D cross-well synthetic ERT scenario. The inversions of 2-D ERT and seismic traveltime field data with geostatistical regularization provide results that are in good accordance with the expected geology and thus facilitate their interpretation. In particular, for layered structures the geostatistical regularization provides geologically more plausible results compared to the anisotropic smoothness constraints.

Hydraulic Conductivity Estimation using Bayesian Model Averaging and Generalized Parameterization

NASA Astrophysics Data System (ADS)

Tsai, F. T.; Li, X.

2006-12-01

Non-uniqueness in parameterization scheme is an inherent problem in groundwater inverse modeling due to limited data. To cope with the non-uniqueness problem of parameterization, we introduce a Bayesian Model Averaging (BMA) method to integrate a set of selected parameterization methods. The estimation uncertainty in BMA includes the uncertainty in individual parameterization methods as the within-parameterization variance and the uncertainty from using different parameterization methods as the between-parameterization variance. Moreover, the generalized parameterization (GP) method is considered in the geostatistical framework in this study. The GP method aims at increasing the flexibility of parameterization through the combination of a zonation structure and an interpolation method. The use of BMP with GP avoids over-confidence in a single parameterization method. A normalized least-squares estimation (NLSE) is adopted to calculate the posterior probability for each GP. We employee the adjoint state method for the sensitivity analysis on the weighting coefficients in the GP method. The adjoint state method is also applied to the NLSE problem. The proposed methodology is implemented to the Alamitos Barrier Project (ABP) in California, where the spatially distributed hydraulic conductivity is estimated. The optimal weighting coefficients embedded in GP are identified through the maximum likelihood estimation (MLE) where the misfits between the observed and calculated groundwater heads are minimized. The conditional mean and conditional variance of the estimated hydraulic conductivity distribution using BMA are obtained to assess the estimation uncertainty.

GEOSTATISTICS FOR WASTE MANAGEMENT: A USER'S MANUAL FOR THE GEOPACK (VERSION 1.0) GEOSTATISTICAL SOFTWARE SYSTEM

EPA Science Inventory

GEOPACK, a comprehensive user-friendly geostatistical software system, was developed to help in the analysis of spatially correlated data. The software system was developed to be used by scientists, engineers, regulators, etc., with little experience in geostatistical techniques...

GEOSTATISTICS FOR WASTE MANAGEMENT: A USER'S MANUEL FOR THE GEOPACK (VERSION 1.0) GEOSTATISTICAL SOFTWARE SYSTEM

EPA Science Inventory

A comprehensive, user-friendly geostatistical software system called GEOPACk has been developed. The purpose of this software is to make available the programs necessary to undertake a geostatistical analysis of spatially correlated data. The programs were written so that they ...

Three-Dimensional Bayesian Geostatistical Aquifer Characterization at the Hanford 300 Area using Tracer Test Data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Xingyuan; Murakami, Haruko; Hahn, Melanie S.

2012-06-01

Tracer testing under natural or forced gradient flow holds the potential to provide useful information for characterizing subsurface properties, through monitoring, modeling and interpretation of the tracer plume migration in an aquifer. Non-reactive tracer experiments were conducted at the Hanford 300 Area, along with constant-rate injection tests and electromagnetic borehole flowmeter (EBF) profiling. 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 themore » Hanford formation. In this study, the Bayesian prior information on the underlying random hydraulic conductivity field was obtained from previous field characterization efforts using the constant-rate injection tests and the EBF 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 data shows that the hydrogeological model, when conditioned on the tracer test data, can reproduce the tracer transport behavior better than the field characterized without the tracer test data. This study successfully demonstrates that MAD can sequentially assimilate multi-scale multi-type field data through a consistent Bayesian framework.« less

A MS-lesion pattern discrimination plot based on geostatistics.

PubMed

Marschallinger, Robert; Schmidt, Paul; Hofmann, Peter; Zimmer, Claus; Atkinson, Peter M; Sellner, Johann; Trinka, Eugen; Mühlau, Mark

2016-03-01

A geostatistical approach to characterize MS-lesion patterns based on their geometrical properties is presented. A dataset of 259 binary MS-lesion masks in MNI space was subjected to directional variography. A model function was fit to express the observed spatial variability in x, y, z directions by the geostatistical parameters Range and Sill. Parameters Range and Sill correlate with MS-lesion pattern surface complexity and total lesion volume. A scatter plot of ln(Range) versus ln(Sill), classified by pattern anisotropy, enables a consistent and clearly arranged presentation of MS-lesion patterns based on geometry: the so-called MS-Lesion Pattern Discrimination Plot. The geostatistical approach and the graphical representation of results are considered efficient exploratory data analysis tools for cross-sectional, follow-up, and medication impact analysis.

Geostatistical estimation of forest biomass in interior Alaska combining Landsat-derived tree cover, sampled airborne lidar and field observations

NASA Astrophysics Data System (ADS)

Babcock, Chad; Finley, Andrew O.; Andersen, Hans-Erik; Pattison, Robert; Cook, Bruce D.; Morton, Douglas C.; Alonzo, Michael; Nelson, Ross; Gregoire, Timothy; Ene, Liviu; Gobakken, Terje; Næsset, Erik

2018-06-01

The goal of this research was to develop and examine the performance of a geostatistical coregionalization modeling approach for combining field inventory measurements, strip samples of airborne lidar and Landsat-based remote sensing data products to predict aboveground biomass (AGB) in interior Alaska's Tanana Valley. The proposed modeling strategy facilitates pixel-level mapping of AGB density predictions across the entire spatial domain. Additionally, the coregionalization framework allows for statistically sound estimation of total AGB for arbitrary areal units within the study area---a key advance to support diverse management objectives in interior Alaska. This research focuses on appropriate characterization of prediction uncertainty in the form of posterior predictive coverage intervals and standard deviations. Using the framework detailed here, it is possible to quantify estimation uncertainty for any spatial extent, ranging from pixel-level predictions of AGB density to estimates of AGB stocks for the full domain. The lidar-informed coregionalization models consistently outperformed their counterpart lidar-free models in terms of point-level predictive performance and total AGB precision. Additionally, the inclusion of Landsat-derived forest cover as a covariate further improved estimation precision in regions with lower lidar sampling intensity. Our findings also demonstrate that model-based approaches that do not explicitly account for residual spatial dependence can grossly underestimate uncertainty, resulting in falsely precise estimates of AGB. On the other hand, in a geostatistical setting, residual spatial structure can be modeled within a Bayesian hierarchical framework to obtain statistically defensible assessments of uncertainty for AGB estimates.

Imprecise (fuzzy) information in geostatistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bardossy, A.; Bogardi, I.; Kelly, W.E.

1988-05-01

A methodology based on fuzzy set theory for the utilization of imprecise data in geostatistics is presented. A common problem preventing a broader use of geostatistics has been the insufficient amount of accurate measurement data. In certain cases, additional but uncertain (soft) information is available and can be encoded as subjective probabilities, and then the soft kriging method can be applied (Journal, 1986). In other cases, a fuzzy encoding of soft information may be more realistic and simplify the numerical calculations. Imprecise (fuzzy) spatial information on the possible variogram is integrated into a single variogram which is used in amore » fuzzy kriging procedure. The overall uncertainty of prediction is represented by the estimation variance and the calculated membership function for each kriged point. The methodology is applied to the permeability prediction of a soil liner for hazardous waste containment. The available number of hard measurement data (20) was not enough for a classical geostatistical analysis. An additional 20 soft data made it possible to prepare kriged contour maps using the fuzzy geostatistical procedure.« less

Properties of the Bayesian Knowledge Tracing Model

ERIC Educational Resources Information Center

van de Sande, Brett

2013-01-01

Bayesian Knowledge Tracing is used very widely to model student learning. It comes in two different forms: The first form is the Bayesian Knowledge Tracing "hidden Markov model" which predicts the probability of correct application of a skill as a function of the number of previous opportunities to apply that skill and the model…

Improved Assimilation of Streamflow and Satellite Soil Moisture with the Evolutionary Particle Filter and Geostatistical Modeling

NASA Astrophysics Data System (ADS)

Yan, Hongxiang; Moradkhani, Hamid; Abbaszadeh, Peyman

2017-04-01

Assimilation of satellite soil moisture and streamflow data into hydrologic models using has received increasing attention over the past few years. Currently, these observations are increasingly used to improve the model streamflow and soil moisture predictions. However, the performance of this land data assimilation (DA) system still suffers from two limitations: 1) satellite data scarcity and quality; and 2) particle weight degeneration. In order to overcome these two limitations, we propose two possible solutions in this study. First, the general Gaussian geostatistical approach is proposed to overcome the limitation in the space/time resolution of satellite soil moisture products thus improving their accuracy at uncovered/biased grid cells. Secondly, an evolutionary PF approach based on Genetic Algorithm (GA) and Markov Chain Monte Carlo (MCMC), the so-called EPF-MCMC, is developed to further reduce weight degeneration and improve the robustness of the land DA system. This study provides a detailed analysis of the joint and separate assimilation of streamflow and satellite soil moisture into a distributed Sacramento Soil Moisture Accounting (SAC-SMA) model, with the use of recently developed EPF-MCMC and the general Gaussian geostatistical approach. Performance is assessed over several basins in the USA selected from Model Parameter Estimation Experiment (MOPEX) and located in different climate regions. The results indicate that: 1) the general Gaussian approach can predict the soil moisture at uncovered grid cells within the expected satellite data quality threshold; 2) assimilation of satellite soil moisture inferred from the general Gaussian model can significantly improve the soil moisture predictions; and 3) in terms of both deterministic and probabilistic measures, the EPF-MCMC can achieve better streamflow predictions. These results recommend that the geostatistical model is a helpful tool to aid the remote sensing technique and the EPF-MCMC is a

Perceptual decision making: drift-diffusion model is equivalent to a Bayesian model

PubMed Central

Bitzer, Sebastian; Park, Hame; Blankenburg, Felix; Kiebel, Stefan J.

2014-01-01

Behavioral data obtained with perceptual decision making experiments are typically analyzed with the drift-diffusion model. This parsimonious model accumulates noisy pieces of evidence toward a decision bound to explain the accuracy and reaction times of subjects. Recently, Bayesian models have been proposed to explain how the brain extracts information from noisy input as typically presented in perceptual decision making tasks. It has long been known that the drift-diffusion model is tightly linked with such functional Bayesian models but the precise relationship of the two mechanisms was never made explicit. Using a Bayesian model, we derived the equations which relate parameter values between these models. In practice we show that this equivalence is useful when fitting multi-subject data. We further show that the Bayesian model suggests different decision variables which all predict equal responses and discuss how these may be discriminated based on neural correlates of accumulated evidence. In addition, we discuss extensions to the Bayesian model which would be difficult to derive for the drift-diffusion model. We suggest that these and other extensions may be highly useful for deriving new experiments which test novel hypotheses. PMID:24616689

Posterior Predictive Bayesian Phylogenetic Model Selection

PubMed Central

Lewis, Paul O.; Xie, Wangang; Chen, Ming-Hui; Fan, Yu; Kuo, Lynn

2014-01-01

We present two distinctly different posterior predictive approaches to Bayesian phylogenetic model selection and illustrate these methods using examples from green algal protein-coding cpDNA sequences and flowering plant rDNA sequences. The Gelfand–Ghosh (GG) approach allows dissection of an overall measure of model fit into components due to posterior predictive variance (GGp) and goodness-of-fit (GGg), which distinguishes this method from the posterior predictive P-value approach. The conditional predictive ordinate (CPO) method provides a site-specific measure of model fit useful for exploratory analyses and can be combined over sites yielding the log pseudomarginal likelihood (LPML) which is useful as an overall measure of model fit. CPO provides a useful cross-validation approach that is computationally efficient, requiring only a sample from the posterior distribution (no additional simulation is required). Both GG and CPO add new perspectives to Bayesian phylogenetic model selection based on the predictive abilities of models and complement the perspective provided by the marginal likelihood (including Bayes Factor comparisons) based solely on the fit of competing models to observed data. [Bayesian; conditional predictive ordinate; CPO; L-measure; LPML; model selection; phylogenetics; posterior predictive.] PMID:24193892

Bayesian model reduction and empirical Bayes for group (DCM) studies

PubMed Central

Friston, Karl J.; Litvak, Vladimir; Oswal, Ashwini; Razi, Adeel; Stephan, Klaas E.; van Wijk, Bernadette C.M.; Ziegler, Gabriel; Zeidman, Peter

2016-01-01

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

Bayesian model reduction and empirical Bayes for group (DCM) studies.

PubMed

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. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Hydrogeologic unit flow characterization using transition probability geostatistics.

PubMed

Jones, Norman L; Walker, Justin R; Carle, Steven F

2005-01-01

This paper describes a technique for applying the transition probability geostatistics method for stochastic simulation to a MODFLOW model. Transition probability geostatistics has some advantages over traditional indicator kriging methods including a simpler and more intuitive framework for interpreting geologic relationships and the ability to simulate juxtapositional tendencies such as fining upward sequences. The indicator arrays generated by the transition probability simulation are converted to layer elevation and thickness arrays for use with the new Hydrogeologic Unit Flow package in MODFLOW 2000. This makes it possible to preserve complex heterogeneity while using reasonably sized grids and/or grids with nonuniform cell thicknesses.

Bayesian model evidence as a model evaluation metric

NASA Astrophysics Data System (ADS)

Guthke, Anneli; Höge, Marvin; Nowak, Wolfgang

2017-04-01

When building environmental systems models, we are typically confronted with the questions of how to choose an appropriate model (i.e., which processes to include or neglect) and how to measure its quality. Various metrics have been proposed that shall guide the modeller towards a most robust and realistic representation of the system under study. Criteria for evaluation often address aspects of accuracy (absence of bias) or of precision (absence of unnecessary variance) and need to be combined in a meaningful way in order to address the inherent bias-variance dilemma. We suggest using Bayesian model evidence (BME) as a model evaluation metric that implicitly performs a tradeoff between bias and variance. BME is typically associated with model weights in the context of Bayesian model averaging (BMA). However, it can also be seen as a model evaluation metric in a single-model context or in model comparison. It combines a measure for goodness of fit with a penalty for unjustifiable complexity. Unjustifiable refers to the fact that the appropriate level of model complexity is limited by the amount of information available for calibration. Derived in a Bayesian context, BME naturally accounts for measurement errors in the calibration data as well as for input and parameter uncertainty. BME is therefore perfectly suitable to assess model quality under uncertainty. We will explain in detail and with schematic illustrations what BME measures, i.e. how complexity is defined in the Bayesian setting and how this complexity is balanced with goodness of fit. We will further discuss how BME compares to other model evaluation metrics that address accuracy and precision such as the predictive logscore or other model selection criteria such as the AIC, BIC or KIC. Although computationally more expensive than other metrics or criteria, BME represents an appealing alternative because it provides a global measure of model quality. Even if not applicable to each and every case, we aim

Geostatistical three-dimensional modeling of oolite shoals, St. Louis Limestone, southwest Kansas

USGS Publications Warehouse

Qi, L.; Carr, T.R.; Goldstein, R.H.

2007-01-01

In the Hugoton embayment of southwestern Kansas, reservoirs composed of relatively thin (<4 m; <13.1 ft) oolitic deposits within the St. Louis Limestone have produced more than 300 million bbl of oil. The geometry and distribution of oolitic deposits control the heterogeneity of the reservoirs, resulting in exploration challenges and relatively low recovery. Geostatistical three-dimensional (3-D) models were constructed to quantify the geometry and spatial distribution of oolitic reservoirs, and the continuity of flow units within Big Bow and Sand Arroyo Creek fields. Lithofacies in uncored wells were predicted from digital logs using a neural network. The tilting effect from the Laramide orogeny was removed to construct restored structural surfaces at the time of deposition. Well data and structural maps were integrated to build 3-D models of oolitic reservoirs using stochastic simulations with geometry data. Three-dimensional models provide insights into the distribution, the external and internal geometry of oolitic deposits, and the sedimentologic processes that generated reservoir intervals. The structural highs and general structural trend had a significant impact on the distribution and orientation of the oolitic complexes. The depositional pattern and connectivity analysis suggest an overall aggradation of shallow-marine deposits during pulses of relative sea level rise followed by deepening near the top of the St. Louis Limestone. Cemented oolitic deposits were modeled as barriers and baffles and tend to concentrate at the edge of oolitic complexes. Spatial distribution of porous oolitic deposits controls the internal geometry of rock properties. Integrated geostatistical modeling methods can be applicable to other complex carbonate or siliciclastic reservoirs in shallow-marine settings. Copyright ?? 2007. The American Association of Petroleum Geologists. All rights reserved.

Enhancing multiple-point geostatistical modeling: 1. Graph theory and pattern adjustment

NASA Astrophysics Data System (ADS)

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 Bayesian Model of the Memory Colour Effect.

PubMed

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

2018-01-01

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

A Bayesian Model of the Memory Colour Effect

PubMed Central

Olkkonen, Maria; Gegenfurtner, Karl R.

2018-01-01

According to the memory colour effect, the colour of a colour-diagnostic object is not perceived independently of the object itself. Instead, it has been shown through an achromatic adjustment method that colour-diagnostic objects still appear slightly in their typical colour, even when they are colourimetrically grey. Bayesian models provide a promising approach to capture the effect of prior knowledge on colour perception and to link these effects to more general effects of cue integration. Here, we model memory colour effects using prior knowledge about typical colours as priors for the grey adjustments in a Bayesian model. This simple model does not involve any fitting of free parameters. The Bayesian model roughly captured the magnitude of the measured memory colour effect for photographs of objects. To some extent, the model predicted observed differences in memory colour effects across objects. The model could not account for the differences in memory colour effects across different levels of realism in the object images. The Bayesian model provides a particularly simple account of memory colour effects, capturing some of the multiple sources of variation of these effects. PMID:29760874

A Bayesian alternative for multi-objective ecohydrological model specification

NASA Astrophysics Data System (ADS)

Tang, Yating; Marshall, Lucy; Sharma, Ashish; Ajami, Hoori

2018-01-01

Recent studies have identified the importance of vegetation processes in terrestrial hydrologic systems. Process-based ecohydrological models combine hydrological, physical, biochemical and ecological processes of the catchments, and as such are generally more complex and parametric than conceptual hydrological models. Thus, appropriate calibration objectives and model uncertainty analysis are essential for ecohydrological modeling. In recent years, Bayesian inference has become one of the most popular tools for quantifying the uncertainties in hydrological modeling with the development of Markov chain Monte Carlo (MCMC) techniques. The Bayesian approach offers an appealing alternative to traditional multi-objective hydrologic model calibrations by defining proper prior distributions that can be considered analogous to the ad-hoc weighting often prescribed in multi-objective calibration. Our study aims to develop appropriate prior distributions and likelihood functions that minimize the model uncertainties and bias within a Bayesian ecohydrological modeling framework based on a traditional Pareto-based model calibration technique. In our study, a Pareto-based multi-objective optimization and a formal Bayesian framework are implemented in a conceptual ecohydrological model that combines a hydrological model (HYMOD) and a modified Bucket Grassland Model (BGM). Simulations focused on one objective (streamflow/LAI) and multiple objectives (streamflow and LAI) with different emphasis defined via the prior distribution of the model error parameters. Results show more reliable outputs for both predicted streamflow and LAI using Bayesian multi-objective calibration with specified prior distributions for error parameters based on results from the Pareto front in the ecohydrological modeling. The methodology implemented here provides insight into the usefulness of multiobjective Bayesian calibration for ecohydrologic systems and the importance of appropriate prior

Estimating Tree Height-Diameter Models with the Bayesian Method

PubMed Central

Duan, Aiguo; Zhang, Jianguo; Xiang, Congwei

2014-01-01

Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist) approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS) and the maximum likelihood method (ML). The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the “best” model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2. PMID:24711733

Estimating tree height-diameter models with the Bayesian method.

PubMed

Zhang, Xiongqing; Duan, Aiguo; Zhang, Jianguo; Xiang, Congwei

2014-01-01

Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist) approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS) and the maximum likelihood method (ML). The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the "best" model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2.

Dynamic Bayesian network modeling for longitudinal brain morphometry

PubMed Central

Chen, Rong; Resnick, Susan M; Davatzikos, Christos; Herskovits, Edward H

2011-01-01

Identifying interactions among brain regions from structural magnetic-resonance images presents one of the major challenges in computational neuroanatomy. We propose a Bayesian data-mining approach to the detection of longitudinal morphological changes in the human brain. Our method uses a dynamic Bayesian network to represent evolving inter-regional dependencies. The major advantage of dynamic Bayesian network modeling is that it can represent complicated interactions among temporal processes. We validated our approach by analyzing a simulated atrophy study, and found that this approach requires only a small number of samples to detect the ground-truth temporal model. We further applied dynamic Bayesian network modeling to a longitudinal study of normal aging and mild cognitive impairment — the Baltimore Longitudinal Study of Aging. We found that interactions among regional volume-change rates for the mild cognitive impairment group are different from those for the normal-aging group. PMID:21963916

A comment on priors for Bayesian occupancy models

PubMed Central

Gerber, Brian D.

2018-01-01

Understanding patterns of species occurrence and the processes underlying these patterns is fundamental to the study of ecology. One of the more commonly used approaches to investigate species occurrence patterns is occupancy modeling, which can account for imperfect detection of a species during surveys. In recent years, there has been a proliferation of Bayesian modeling in ecology, which includes fitting Bayesian occupancy models. The Bayesian framework is appealing to ecologists for many reasons, including the ability to incorporate prior information through the specification of prior distributions on parameters. While ecologists almost exclusively intend to choose priors so that they are “uninformative” or “vague”, such priors can easily be unintentionally highly informative. Here we report on how the specification of a “vague” normally distributed (i.e., Gaussian) prior on coefficients in Bayesian occupancy models can unintentionally influence parameter estimation. Using both simulated data and empirical examples, we illustrate how this issue likely compromises inference about species-habitat relationships. While the extent to which these informative priors influence inference depends on the data set, researchers fitting Bayesian occupancy models should conduct sensitivity analyses to ensure intended inference, or employ less commonly used priors that are less informative (e.g., logistic or t prior distributions). We provide suggestions for addressing this issue in occupancy studies, and an online tool for exploring this issue under different contexts. PMID:29481554

A comment on priors for Bayesian occupancy models.

PubMed

Northrup, Joseph M; Gerber, Brian D

2018-01-01

Understanding patterns of species occurrence and the processes underlying these patterns is fundamental to the study of ecology. One of the more commonly used approaches to investigate species occurrence patterns is occupancy modeling, which can account for imperfect detection of a species during surveys. In recent years, there has been a proliferation of Bayesian modeling in ecology, which includes fitting Bayesian occupancy models. The Bayesian framework is appealing to ecologists for many reasons, including the ability to incorporate prior information through the specification of prior distributions on parameters. While ecologists almost exclusively intend to choose priors so that they are "uninformative" or "vague", such priors can easily be unintentionally highly informative. Here we report on how the specification of a "vague" normally distributed (i.e., Gaussian) prior on coefficients in Bayesian occupancy models can unintentionally influence parameter estimation. Using both simulated data and empirical examples, we illustrate how this issue likely compromises inference about species-habitat relationships. While the extent to which these informative priors influence inference depends on the data set, researchers fitting Bayesian occupancy models should conduct sensitivity analyses to ensure intended inference, or employ less commonly used priors that are less informative (e.g., logistic or t prior distributions). We provide suggestions for addressing this issue in occupancy studies, and an online tool for exploring this issue under different contexts.

Bayesian modeling to assess populated areas impacted by radiation from Fukushima

NASA Astrophysics Data System (ADS)

Hultquist, C.; Cervone, G.

2017-12-01

Citizen-led movements producing spatio-temporal big data are increasingly important sources of information about populations that are impacted by natural disasters. Citizen science can be used to fill gaps in disaster monitoring data, in addition to inferring human exposure and vulnerability to extreme environmental impacts. As a response to the 2011 release of radiation from Fukushima, Japan, the Safecast project began collecting open radiation data which grew to be a global dataset of over 70 million measurements to date. This dataset is spatially distributed primarily where humans are located and demonstrates abnormal patterns of population movements as a result of the disaster. Previous work has demonstrated that Safecast is highly correlated in comparison to government radiation observations. However, there is still a scientific need to understand the geostatistical variability of Safecast data and to assess how reliable the data are over space and time. The Bayesian hierarchical approach can be used to model the spatial distribution of datasets and flexibly integrate new flows of data without losing previous information. This enables an understanding of uncertainty in the spatio-temporal data to inform decision makers on areas of high levels of radiation where populations are located. Citizen science data can be scientifically evaluated and used as a critical source of information about populations that are impacted by a disaster.

Sparse Event Modeling with Hierarchical Bayesian Kernel Methods

DTIC Science & Technology

2016-01-05

SECURITY CLASSIFICATION OF: The research objective of this proposal was to develop a predictive Bayesian kernel approach to model count data based on...several predictive variables. Such an approach, which we refer to as the Poisson Bayesian kernel model , is able to model the rate of occurrence of...which adds specificity to the model and can make nonlinear data more manageable. Early results show that the 1. REPORT DATE (DD-MM-YYYY) 4. TITLE

Model-based Bayesian inference for ROC data analysis

NASA Astrophysics Data System (ADS)

Lei, Tianhu; Bae, K. Ty

2013-03-01

This paper presents a study of model-based Bayesian inference to Receiver Operating Characteristics (ROC) data. The model is a simple version of general non-linear regression model. Different from Dorfman model, it uses a probit link function with a covariate variable having zero-one two values to express binormal distributions in a single formula. Model also includes a scale parameter. Bayesian inference is implemented by Markov Chain Monte Carlo (MCMC) method carried out by Bayesian analysis Using Gibbs Sampling (BUGS). Contrast to the classical statistical theory, Bayesian approach considers model parameters as random variables characterized by prior distributions. With substantial amount of simulated samples generated by sampling algorithm, posterior distributions of parameters as well as parameters themselves can be accurately estimated. MCMC-based BUGS adopts Adaptive Rejection Sampling (ARS) protocol which requires the probability density function (pdf) which samples are drawing from be log concave with respect to the targeted parameters. Our study corrects a common misconception and proves that pdf of this regression model is log concave with respect to its scale parameter. Therefore, ARS's requirement is satisfied and a Gaussian prior which is conjugate and possesses many analytic and computational advantages is assigned to the scale parameter. A cohort of 20 simulated data sets and 20 simulations from each data set are used in our study. Output analysis and convergence diagnostics for MCMC method are assessed by CODA package. Models and methods by using continuous Gaussian prior and discrete categorical prior are compared. Intensive simulations and performance measures are given to illustrate our practice in the framework of model-based Bayesian inference using MCMC method.

Geostatistical modelling of household malaria in Malawi

NASA Astrophysics Data System (ADS)

Chirombo, J.; Lowe, R.; Kazembe, L.

2012-04-01

Malaria is one of the most important diseases in the world today, common in tropical and subtropical areas with sub-Saharan Africa being the region most burdened, including Malawi. This region has the right combination of biotic and abiotic components, including socioeconomic, climatic and environmental factors that sustain transmission of the disease. Differences in these conditions across the country consequently lead to spatial variation in risk of the disease. Analysis of nationwide survey data that takes into account this spatial variation is crucial in a resource constrained country like Malawi for targeted allocation of scare resources in the fight against malaria. Previous efforts to map malaria risk in Malawi have been based on limited data collected from small surveys. The Malaria Indicator Survey conducted in 2010 is the most comprehensive malaria survey carried out in Malawi and provides point referenced data for the study. The data has been shown to be spatially correlated. We use Bayesian logistic regression models with spatial correlation to model the relationship between malaria presence in children and covariates such as socioeconomic status of households and meteorological conditions. This spatial model is then used to assess how malaria varies spatially and a malaria risk map for Malawi is produced. By taking intervention measures into account, the developed model is used to assess whether they have an effect on the spatial distribution of the disease and Bayesian kriging is used to predict areas where malaria risk is more likely to increase. It is hoped that this study can help reveal areas that require more attention from the authorities in the continuing fight against malaria, particularly in children under the age of five.

Bayesian Modeling of a Human MMORPG Player

NASA Astrophysics Data System (ADS)

Synnaeve, Gabriel; Bessière, Pierre

2011-03-01

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

Comparing the performance of geostatistical models with additional information from covariates for sewage plume characterization.

PubMed

Del Monego, Maurici; Ribeiro, Paulo Justiniano; Ramos, Patrícia

2015-04-01

In this work, kriging with covariates is used to model and map the spatial distribution of salinity measurements gathered by an autonomous underwater vehicle in a sea outfall monitoring campaign aiming to distinguish the effluent plume from the receiving waters and characterize its spatial variability in the vicinity of the discharge. Four different geostatistical linear models for salinity were assumed, where the distance to diffuser, the west-east positioning, and the south-north positioning were used as covariates. Sample variograms were fitted by the Matèrn models using weighted least squares and maximum likelihood estimation methods as a way to detect eventual discrepancies. Typically, the maximum likelihood method estimated very low ranges which have limited the kriging process. So, at least for these data sets, weighted least squares showed to be the most appropriate estimation method for variogram fitting. The kriged maps show clearly the spatial variation of salinity, and it is possible to identify the effluent plume in the area studied. The results obtained show some guidelines for sewage monitoring if a geostatistical analysis of the data is in mind. It is important to treat properly the existence of anomalous values and to adopt a sampling strategy that includes transects parallel and perpendicular to the effluent dispersion.

Development and comparison of Bayesian modularization method in uncertainty assessment of hydrological models

NASA Astrophysics Data System (ADS)

Li, L.; Xu, C.-Y.; Engeland, K.

2012-04-01

With respect to model calibration, parameter estimation and analysis of uncertainty sources, different approaches have been used in hydrological models. Bayesian method is one of the most widely used methods for uncertainty assessment of hydrological models, which incorporates different sources of information into a single analysis through Bayesian theorem. However, none of these applications can well treat the uncertainty in extreme flows of hydrological models' simulations. This study proposes a Bayesian modularization method approach in uncertainty assessment of conceptual hydrological models by considering the extreme flows. It includes a comprehensive comparison and evaluation of uncertainty assessments by a new Bayesian modularization method approach and traditional Bayesian models using the Metropolis Hasting (MH) algorithm with the daily hydrological model WASMOD. Three likelihood functions are used in combination with traditional Bayesian: the AR (1) plus Normal and time period independent model (Model 1), the AR (1) plus Normal and time period dependent model (Model 2) and the AR (1) plus multi-normal model (Model 3). The results reveal that (1) the simulations derived from Bayesian modularization method are more accurate with the highest Nash-Sutcliffe efficiency value, and (2) the Bayesian modularization method performs best in uncertainty estimates of entire flows and in terms of the application and computational efficiency. The study thus introduces a new approach for reducing the extreme flow's effect on the discharge uncertainty assessment of hydrological models via Bayesian. Keywords: extreme flow, uncertainty assessment, Bayesian modularization, hydrological model, WASMOD

TiConverter: A training image converting tool for multiple-point geostatistics

NASA Astrophysics Data System (ADS)

Fadlelmula F., Mohamed M.; Killough, John; Fraim, Michael

2016-11-01

TiConverter is a tool developed to ease the application of multiple-point geostatistics whether by the open source Stanford Geostatistical Modeling Software (SGeMS) or other available commercial software. TiConverter has a user-friendly interface and it allows the conversion of 2D training images into numerical representations in four different file formats without the need for additional code writing. These are the ASCII (.txt), the geostatistical software library (GSLIB) (.txt), the Isatis (.dat), and the VTK formats. It performs the conversion based on the RGB color system. In addition, TiConverter offers several useful tools including image resizing, smoothing, and segmenting tools. The purpose of this study is to introduce the TiConverter, and to demonstrate its application and advantages with several examples from the literature.

A flexible Bayesian assessment for the expected impact of data on prediction confidence for optimal sampling designs

NASA Astrophysics Data System (ADS)

Leube, Philipp; Geiges, Andreas; Nowak, Wolfgang

2010-05-01

Incorporating hydrogeological data, such as head and tracer data, into stochastic models of subsurface flow and transport helps to reduce prediction uncertainty. Considering limited financial resources available for the data acquisition campaign, information needs towards the prediction goal should be satisfied in a efficient and task-specific manner. For finding the best one among a set of design candidates, an objective function is commonly evaluated, which measures the expected impact of data on prediction confidence, prior to their collection. An appropriate approach to this task should be stochastically rigorous, master non-linear dependencies between data, parameters and model predictions, and allow for a wide variety of different data types. Existing methods fail to fulfill all these requirements simultaneously. For this reason, we introduce a new method, denoted as CLUE (Cross-bred Likelihood Uncertainty Estimator), that derives the essential distributions and measures of data utility within a generalized, flexible and accurate framework. The method makes use of Bayesian GLUE (Generalized Likelihood Uncertainty Estimator) and extends it to an optimal design method by marginalizing over the yet unknown data values. Operating in a purely Bayesian Monte-Carlo framework, CLUE is a strictly formal information processing scheme free of linearizations. It provides full flexibility associated with the type of measurements (linear, non-linear, direct, indirect) and accounts for almost arbitrary sources of uncertainty (e.g. heterogeneity, geostatistical assumptions, boundary conditions, model concepts) via stochastic simulation and Bayesian model averaging. This helps to minimize the strength and impact of possible subjective prior assumptions, that would be hard to defend prior to data collection. Our study focuses on evaluating two different uncertainty measures: (i) expected conditional variance and (ii) expected relative entropy of a given prediction goal. The

Bayesian population receptive field modelling.

PubMed

Zeidman, Peter; Silson, Edward Harry; Schwarzkopf, Dietrich Samuel; Baker, Chris Ian; Penny, Will

2017-09-08

We introduce a probabilistic (Bayesian) framework and associated software toolbox for mapping population receptive fields (pRFs) based on fMRI data. This generic approach is intended to work with stimuli of any dimension and is demonstrated and validated in the context of 2D retinotopic mapping. The framework enables the experimenter to specify generative (encoding) models of fMRI timeseries, in which experimental stimuli enter a pRF model of neural activity, which in turns drives a nonlinear model of neurovascular coupling and Blood Oxygenation Level Dependent (BOLD) response. The neuronal and haemodynamic parameters are estimated together on a voxel-by-voxel or region-of-interest basis using a Bayesian estimation algorithm (variational Laplace). This offers several novel contributions to receptive field modelling. The variance/covariance of parameters are estimated, enabling receptive fields to be plotted while properly representing uncertainty about pRF size and location. Variability in the haemodynamic response across the brain is accounted for. Furthermore, the framework introduces formal hypothesis testing to pRF analysis, enabling competing models to be evaluated based on their log model evidence (approximated by the variational free energy), which represents the optimal tradeoff between accuracy and complexity. Using simulations and empirical data, we found that parameters typically used to represent pRF size and neuronal scaling are strongly correlated, which is taken into account by the Bayesian methods we describe when making inferences. We used the framework to compare the evidence for six variants of pRF model using 7 T functional MRI data and we found a circular Difference of Gaussians (DoG) model to be the best explanation for our data overall. We hope this framework will prove useful for mapping stimulus spaces with any number of dimensions onto the anatomy of the brain. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

Two-Stage Bayesian Model Averaging in Endogenous Variable Models*

PubMed Central

Lenkoski, Alex; Eicher, Theo S.; Raftery, Adrian E.

2013-01-01

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

Estimation of Fine Particulate Matter in Taipei Using Landuse Regression and Bayesian Maximum Entropy Methods

PubMed Central

Yu, Hwa-Lung; Wang, Chih-Hsih; Liu, Ming-Che; Kuo, Yi-Ming

2011-01-01

Fine airborne particulate matter (PM2.5) has adverse effects on human health. Assessing the long-term effects of PM2.5 exposure on human health and ecology is often limited by a lack of reliable PM2.5 measurements. In Taipei, PM2.5 levels were not systematically measured until August, 2005. Due to the popularity of geographic information systems (GIS), the landuse regression method has been widely used in the spatial estimation of PM concentrations. This method accounts for the potential contributing factors of the local environment, such as traffic volume. Geostatistical methods, on other hand, account for the spatiotemporal dependence among the observations of ambient pollutants. This study assesses the performance of the landuse regression model for the spatiotemporal estimation of PM2.5 in the Taipei area. Specifically, this study integrates the landuse regression model with the geostatistical approach within the framework of the Bayesian maximum entropy (BME) method. The resulting epistemic framework can assimilate knowledge bases including: (a) empirical-based spatial trends of PM concentration based on landuse regression, (b) the spatio-temporal dependence among PM observation information, and (c) site-specific PM observations. The proposed approach performs the spatiotemporal estimation of PM2.5 levels in the Taipei area (Taiwan) from 2005–2007. PMID:21776223

Estimation of fine particulate matter in Taipei using landuse regression and bayesian maximum entropy methods.

PubMed

Yu, Hwa-Lung; Wang, Chih-Hsih; Liu, Ming-Che; Kuo, Yi-Ming

2011-06-01

Fine airborne particulate matter (PM2.5) has adverse effects on human health. Assessing the long-term effects of PM2.5 exposure on human health and ecology is often limited by a lack of reliable PM2.5 measurements. In Taipei, PM2.5 levels were not systematically measured until August, 2005. Due to the popularity of geographic information systems (GIS), the landuse regression method has been widely used in the spatial estimation of PM concentrations. This method accounts for the potential contributing factors of the local environment, such as traffic volume. Geostatistical methods, on other hand, account for the spatiotemporal dependence among the observations of ambient pollutants. This study assesses the performance of the landuse regression model for the spatiotemporal estimation of PM2.5 in the Taipei area. Specifically, this study integrates the landuse regression model with the geostatistical approach within the framework of the Bayesian maximum entropy (BME) method. The resulting epistemic framework can assimilate knowledge bases including: (a) empirical-based spatial trends of PM concentration based on landuse regression, (b) the spatio-temporal dependence among PM observation information, and (c) site-specific PM observations. The proposed approach performs the spatiotemporal estimation of PM2.5 levels in the Taipei area (Taiwan) from 2005-2007.

A SEMIPARAMETRIC BAYESIAN MODEL FOR CIRCULAR-LINEAR REGRESSION

EPA Science Inventory

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...

Estimation of geotechnical parameters on the basis of geophysical methods and geostatistics

NASA Astrophysics Data System (ADS)

Brom, Aleksander; Natonik, Adrianna

2017-12-01

The paper presents possible implementation of ordinary cokriging and geophysical investigation on humidity data acquired in geotechnical studies. The Author describes concept of geostatistics, terminology of geostatistical modelling, spatial correlation functions, principles of solving cokriging systems, advantages of (co-)kriging in comparison with other interpolation methods, obstacles in this type of attempt. Cross validation and discussion of results was performed with an indication of prospect of applying similar procedures in various researches..

Assessing the resolution-dependent utility of tomograms for geostatistics

USGS Publications Warehouse

Day-Lewis, F. D.; Lane, J.W.

2004-01-01

Geophysical tomograms are used increasingly as auxiliary data for geostatistical modeling of aquifer and reservoir properties. The correlation between tomographic estimates and hydrogeologic properties is commonly based on laboratory measurements, co-located measurements at boreholes, or petrophysical models. The inferred correlation is assumed uniform throughout the interwell region; however, tomographic resolution varies spatially due to acquisition geometry, regularization, data error, and the physics underlying the geophysical measurements. Blurring and inversion artifacts are expected in regions traversed by few or only low-angle raypaths. In the context of radar traveltime tomography, we derive analytical models for (1) the variance of tomographic estimates, (2) the spatially variable correlation with a hydrologic parameter of interest, and (3) the spatial covariance of tomographic estimates. Synthetic examples demonstrate that tomograms of qualitative value may have limited utility for geostatistics; moreover, the imprint of regularization may preclude inference of meaningful spatial statistics from tomograms.

Constructive Epistemic Modeling: A Hierarchical Bayesian Model Averaging Method

NASA Astrophysics Data System (ADS)

Tsai, F. T. C.; Elshall, A. S.

2014-12-01

Constructive epistemic modeling is the idea that our understanding of a natural system through a scientific model is a mental construct that continually develops through learning about and from the model. Using the hierarchical Bayesian model averaging (HBMA) method [1], this study shows that segregating different uncertain model components through a BMA tree of posterior model probabilities, model prediction, within-model variance, between-model variance and total model variance serves as a learning tool [2]. First, the BMA tree of posterior model probabilities permits the comparative evaluation of the candidate propositions of each uncertain model component. Second, systemic model dissection is imperative for understanding the individual contribution of each uncertain model component to the model prediction and variance. Third, the hierarchical representation of the between-model variance facilitates the prioritization of the contribution of each uncertain model component to the overall model uncertainty. We illustrate these concepts using the groundwater modeling of a siliciclastic aquifer-fault system. The sources of uncertainty considered are from geological architecture, formation dip, boundary conditions and model parameters. The study shows that the HBMA analysis helps in advancing knowledge about the model rather than forcing the model to fit a particularly understanding or merely averaging several candidate models. [1] Tsai, F. T.-C., and A. S. Elshall (2013), Hierarchical Bayesian model averaging for hydrostratigraphic modeling: Uncertainty segregation and comparative evaluation. Water Resources Research, 49, 5520-5536, doi:10.1002/wrcr.20428. [2] Elshall, A.S., and F. T.-C. Tsai (2014). Constructive epistemic modeling of groundwater flow with geological architecture and boundary condition uncertainty under Bayesian paradigm, Journal of Hydrology, 517, 105-119, doi: 10.1016/j.jhydrol.2014.05.027.

Hydrogeologic Unit Flow Characterization Using Transition Probability Geostatistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jones, N L; Walker, J R; Carle, S F

2003-11-21

This paper describes a technique for applying the transition probability geostatistics method for stochastic simulation to a MODFLOW model. Transition probability geostatistics has several advantages over traditional indicator kriging methods including a simpler and more intuitive framework for interpreting geologic relationships and the ability to simulate juxtapositional tendencies such as fining upwards sequences. The indicator arrays generated by the transition probability simulation are converted to layer elevation and thickness arrays for use with the new Hydrogeologic Unit Flow (HUF) package in MODFLOW 2000. This makes it possible to preserve complex heterogeneity while using reasonably sized grids. An application of themore » technique involving probabilistic capture zone delineation for the Aberjona Aquifer in Woburn, Ma. is included.« less

Three-Dimensional Bayesian Geostatistical Aquifer Characterization at the Hanford 300 Area using Tracer Test Data

NASA Astrophysics Data System (ADS)

Chen, X.; Murakami, H.; Hahn, M. S.; Hammond, G. E.; Rockhold, M. L.; Rubin, Y.

2010-12-01

Tracer testing under natural or forced gradient flow provides useful information for characterizing subsurface properties, by monitoring and modeling the tracer plume migration in a heterogeneous aquifer. At the Hanford 300 Area, non-reactive tracer experiments, in addition to constant-rate injection tests and electromagnetic borehole flowmeter (EBF) profiling, were conducted to characterize the heterogeneous hydraulic conductivity field. A Bayesian data assimilation technique, method of anchored distributions (MAD), is applied to assimilate the experimental tracer test 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 prior information of the underlying random hydraulic conductivity field was obtained from previous field characterization efforts using the constant-rate injection tests and the EBF data. The posterior distribution of the random field is obtained by further conditioning the field on the temporal moments of tracer breakthrough curves at various observation wells. The parallel three-dimensional flow and transport code PFLOTRAN is implemented to cope with the highly transient flow boundary conditions at the site and to meet the computational demand of the proposed method. The validation results show that the field conditioned on the tracer test data better reproduces the tracer transport behavior compared to the field characterized previously without the tracer test data. A synthetic study proves that the proposed method can effectively assimilate tracer test data to capture the essential spatial heterogeneity of the three-dimensional hydraulic conductivity field. These characterization results will improve conceptual models developed for the site, including reactive transport models. The study successfully demonstrates the capability of MAD to assimilate multi-scale multi-type field data within a consistent Bayesian framework. The MAD

Calibrating Bayesian Network Representations of Social-Behavioral Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Whitney, Paul D.; Walsh, Stephen J.

2010-04-08

While human behavior has long been studied, recent and ongoing advances in computational modeling present opportunities for recasting research outcomes in human behavior. In this paper we describe how Bayesian networks can represent outcomes of human behavior research. We demonstrate a Bayesian network that represents political radicalization research – and show a corresponding visual representation of aspects of this research outcome. Since Bayesian networks can be quantitatively compared with external observations, the representation can also be used for empirical assessments of the research which the network summarizes. For a political radicalization model based on published research, we show this empiricalmore » comparison with data taken from the Minorities at Risk Organizational Behaviors database.« less

Nonparametric Bayesian Modeling for Automated Database Schema Matching

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ferragut, Erik M; Laska, Jason A

2015-01-01

The problem of merging databases arises in many government and commercial applications. Schema matching, a common first step, identifies equivalent fields between databases. We introduce a schema matching framework that builds nonparametric Bayesian models for each field and compares them by computing the probability that a single model could have generated both fields. Our experiments show that our method is more accurate and faster than the existing instance-based matching algorithms in part because of the use of nonparametric Bayesian models.

Bayesian generalized linear mixed modeling of Tuberculosis using informative priors.

PubMed

Ojo, Oluwatobi Blessing; Lougue, Siaka; Woldegerima, Woldegebriel Assefa

2017-01-01

TB is rated as one of the world's deadliest diseases and South Africa ranks 9th out of the 22 countries with hardest hit of TB. Although many pieces of research have been carried out on this subject, this paper steps further by inculcating past knowledge into the model, using Bayesian approach with informative prior. Bayesian statistics approach is getting popular in data analyses. But, most applications of Bayesian inference technique are limited to situations of non-informative prior, where there is no solid external information about the distribution of the parameter of interest. The main aim of this study is to profile people living with TB in South Africa. In this paper, identical regression models are fitted for classical and Bayesian approach both with non-informative and informative prior, using South Africa General Household Survey (GHS) data for the year 2014. For the Bayesian model with informative prior, South Africa General Household Survey dataset for the year 2011 to 2013 are used to set up priors for the model 2014.

Bayesian generalized linear mixed modeling of Tuberculosis using informative priors

PubMed Central

Woldegerima, Woldegebriel Assefa

2017-01-01

TB is rated as one of the world’s deadliest diseases and South Africa ranks 9th out of the 22 countries with hardest hit of TB. Although many pieces of research have been carried out on this subject, this paper steps further by inculcating past knowledge into the model, using Bayesian approach with informative prior. Bayesian statistics approach is getting popular in data analyses. But, most applications of Bayesian inference technique are limited to situations of non-informative prior, where there is no solid external information about the distribution of the parameter of interest. The main aim of this study is to profile people living with TB in South Africa. In this paper, identical regression models are fitted for classical and Bayesian approach both with non-informative and informative prior, using South Africa General Household Survey (GHS) data for the year 2014. For the Bayesian model with informative prior, South Africa General Household Survey dataset for the year 2011 to 2013 are used to set up priors for the model 2014. PMID:28257437

Bayesian Analysis of Longitudinal Data Using Growth Curve Models

ERIC Educational Resources Information Center

Zhang, Zhiyong; Hamagami, Fumiaki; Wang, Lijuan Lijuan; Nesselroade, John R.; Grimm, Kevin J.

2007-01-01

Bayesian methods for analyzing longitudinal data in social and behavioral research are recommended for their ability to incorporate prior information in estimating simple and complex models. We first summarize the basics of Bayesian methods before presenting an empirical example in which we fit a latent basis growth curve model to achievement data…

When mechanism matters: Bayesian forecasting using models of ecological diffusion

USGS Publications Warehouse

Hefley, Trevor J.; Hooten, Mevin B.; Russell, Robin E.; Walsh, Daniel P.; Powell, James A.

2017-01-01

Ecological diffusion is a theory that can be used to understand and forecast spatio-temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white-tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression-based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.

Testing adaptive toolbox models: a Bayesian hierarchical approach.

PubMed

Scheibehenne, Benjamin; Rieskamp, Jörg; Wagenmakers, Eric-Jan

2013-01-01

Many theories of human cognition postulate that people are equipped with a repertoire of strategies to solve the tasks they face. This theoretical framework of a cognitive toolbox provides a plausible account of intra- and interindividual differences in human behavior. Unfortunately, it is often unclear how to rigorously test the toolbox framework. How can a toolbox model be quantitatively specified? How can the number of toolbox strategies be limited to prevent uncontrolled strategy sprawl? How can a toolbox model be formally tested against alternative theories? The authors show how these challenges can be met by using Bayesian inference techniques. By means of parameter recovery simulations and the analysis of empirical data across a variety of domains (i.e., judgment and decision making, children's cognitive development, function learning, and perceptual categorization), the authors illustrate how Bayesian inference techniques allow toolbox models to be quantitatively specified, strategy sprawl to be contained, and toolbox models to be rigorously tested against competing theories. The authors demonstrate that their approach applies at the individual level but can also be generalized to the group level with hierarchical Bayesian procedures. The suggested Bayesian inference techniques represent a theoretical and methodological advancement for toolbox theories of cognition and behavior.

Bayesian stable isotope mixing models

EPA Science Inventory

In this paper we review recent advances in Stable Isotope Mixing Models (SIMMs) and place them into an over-arching Bayesian statistical framework which allows for several useful extensions. SIMMs are used to quantify the proportional contributions of various sources to a mixtur...

BCM: toolkit for Bayesian analysis of Computational Models using samplers.

PubMed

Thijssen, Bram; Dijkstra, Tjeerd M H; Heskes, Tom; Wessels, Lodewyk F A

2016-10-21

Computational models in biology are characterized by a large degree of uncertainty. This uncertainty can be analyzed with Bayesian statistics, however, the sampling algorithms that are frequently used for calculating Bayesian statistical estimates are computationally demanding, and each algorithm has unique advantages and disadvantages. It is typically unclear, before starting an analysis, which algorithm will perform well on a given computational model. We present BCM, a toolkit for the Bayesian analysis of Computational Models using samplers. It provides efficient, multithreaded implementations of eleven algorithms for sampling from posterior probability distributions and for calculating marginal likelihoods. BCM includes tools to simplify the process of model specification and scripts for visualizing the results. The flexible architecture allows it to be used on diverse types of biological computational models. In an example inference task using a model of the cell cycle based on ordinary differential equations, BCM is significantly more efficient than existing software packages, allowing more challenging inference problems to be solved. BCM represents an efficient one-stop-shop for computational modelers wishing to use sampler-based Bayesian statistics.

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

NASA Astrophysics Data System (ADS)

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

2013-04-01

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

Mine planning and emission control strategies using geostatistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martino, F.; Kim, Y.C.

1983-03-01

This paper reviews the past four years' research efforts performed jointly by the University of Arizona and the Homer City Owners in which geostatistics were applied to solve various problems associated with coal characterization, mine planning, and development of emission control strategies. Because geostatistics is the only technique which can quantify the degree of confidence associated with a given estimate (or prediction), it played an important role throughout the research efforts. Through geostatistics, it was learned that there is an urgent need for closely spaced sample information, if short-term coal quality predictions are to be made for mine planning purposes.

Bayesian Models for Astrophysical Data Using R, JAGS, Python, and Stan

NASA Astrophysics Data System (ADS)

Hilbe, Joseph M.; de Souza, Rafael S.; Ishida, Emille E. O.

2017-05-01

This comprehensive guide to Bayesian methods in astronomy enables hands-on work by supplying complete R, JAGS, Python, and Stan code, to use directly or to adapt. It begins by examining the normal model from both frequentist and Bayesian perspectives and then progresses to a full range of Bayesian generalized linear and mixed or hierarchical models, as well as additional types of models such as ABC and INLA. The book provides code that is largely unavailable elsewhere and includes details on interpreting and evaluating Bayesian models. Initial discussions offer models in synthetic form so that readers can easily adapt them to their own data; later the models are applied to real astronomical data. The consistent focus is on hands-on modeling, analysis of data, and interpretations that address scientific questions. A must-have for astronomers, its concrete approach will also be attractive to researchers in the sciences more generally.

Integration of geology, geostatistics, well logs and pressure data to model a heterogeneous supergiant field in Iran

DOE Office of Scientific and Technical Information (OSTI.GOV)

Samimi, B.; Bagherpour, H.; Nioc, A.

1995-08-01

The geological reservoir study of the supergiant Ahwaz field significantly improved the history matching process in many aspects, particularly the development of a geostatistical model which allowed a sound basis for changes and by delivering much needed accurate estimates of grid block vertical permeabilities. The geostatistical reservoir evaluation was facilitated by using the Heresim package and litho-stratigraphic zonations for the entire field. For each of the geological zones, 3-dimensional electrolithofacies and petrophysical property distributions (realizations) were treated which captured the heterogeneities which significantly affected fluid flow. However, as this level of heterogeneity was at a significantly smaller scale than themore » flow simulation grid blocks, a scaling up effort was needed to derive the effective flow properties of the blocks (porosity, horizontal and vertical permeability, and water saturation). The properties relating to the static reservoir description were accurately derived by using stream tube techniques developed in-house whereas, the relative permeabilities of the grid block were derived by dynamic pseudo relative permeability techniques. The prediction of vertical and lateral communication and water encroachment was facilitated by a close integration of pressure, saturation data, geostatistical modelling and sedimentological studies of the depositional environments and paleocurrents. The nature of reservoir barriers and baffles varied both vertically and laterally in this heterogeneous reservoir. Maps showing differences in pressure between zones after years of production served as a guide to integrating the static geological studies to the dynamic behaviour of each of the 16 reservoir zones. The use of deep wells being drilled to a deeper reservoir provided data to better understand the sweep efficiency and the continuity of barriers and baffles.« less

Geostatistics: a new tool for describing spatially-varied surface conditions from timber harvested and burned hillslopes

Treesearch

Peter R. Robichaud

1997-01-01

Geostatistics provides a method to describe the spatial continuity of many natural phenomena. Spatial models are based upon the concept of scaling, kriging and conditional simulation. These techniques were used to describe the spatially-varied surface conditions on timber harvest and burned hillslopes. Geostatistical techniques provided estimates of the ground cover (...

Testing students' e-learning via Facebook through Bayesian structural equation modeling.

PubMed

Salarzadeh Jenatabadi, Hashem; Moghavvemi, Sedigheh; Wan Mohamed Radzi, Che Wan Jasimah Bt; Babashamsi, Parastoo; Arashi, Mohammad

2017-01-01

Learning is an intentional activity, with several factors affecting students' intention to use new learning technology. Researchers have investigated technology acceptance in different contexts by developing various theories/models and testing them by a number of means. Although most theories/models developed have been examined through regression or structural equation modeling, Bayesian analysis offers more accurate data analysis results. To address this gap, the unified theory of acceptance and technology use in the context of e-learning via Facebook are re-examined in this study using Bayesian analysis. The data (S1 Data) were collected from 170 students enrolled in a business statistics course at University of Malaya, Malaysia, and tested with the maximum likelihood and Bayesian approaches. The difference between the two methods' results indicates that performance expectancy and hedonic motivation are the strongest factors influencing the intention to use e-learning via Facebook. The Bayesian estimation model exhibited better data fit than the maximum likelihood estimator model. The results of the Bayesian and maximum likelihood estimator approaches are compared and the reasons for the result discrepancy are deliberated.

Testing students’ e-learning via Facebook through Bayesian structural equation modeling

PubMed Central

Moghavvemi, Sedigheh; Wan Mohamed Radzi, Che Wan Jasimah Bt; Babashamsi, Parastoo; Arashi, Mohammad

2017-01-01

Learning is an intentional activity, with several factors affecting students’ intention to use new learning technology. Researchers have investigated technology acceptance in different contexts by developing various theories/models and testing them by a number of means. Although most theories/models developed have been examined through regression or structural equation modeling, Bayesian analysis offers more accurate data analysis results. To address this gap, the unified theory of acceptance and technology use in the context of e-learning via Facebook are re-examined in this study using Bayesian analysis. The data (S1 Data) were collected from 170 students enrolled in a business statistics course at University of Malaya, Malaysia, and tested with the maximum likelihood and Bayesian approaches. The difference between the two methods’ results indicates that performance expectancy and hedonic motivation are the strongest factors influencing the intention to use e-learning via Facebook. The Bayesian estimation model exhibited better data fit than the maximum likelihood estimator model. The results of the Bayesian and maximum likelihood estimator approaches are compared and the reasons for the result discrepancy are deliberated. PMID:28886019

Development of uncertainty-based work injury model using Bayesian structural equation modelling.

PubMed

Chatterjee, Snehamoy

2014-01-01

This paper proposed a Bayesian method-based structural equation model (SEM) of miners' work injury for an underground coal mine in India. The environmental and behavioural variables for work injury were identified and causal relationships were developed. For Bayesian modelling, prior distributions of SEM parameters are necessary to develop the model. In this paper, two approaches were adopted to obtain prior distribution for factor loading parameters and structural parameters of SEM. In the first approach, the prior distributions were considered as a fixed distribution function with specific parameter values, whereas, in the second approach, prior distributions of the parameters were generated from experts' opinions. The posterior distributions of these parameters were obtained by applying Bayesian rule. The Markov Chain Monte Carlo sampling in the form Gibbs sampling was applied for sampling from the posterior distribution. The results revealed that all coefficients of structural and measurement model parameters are statistically significant in experts' opinion-based priors, whereas, two coefficients are not statistically significant when fixed prior-based distributions are applied. The error statistics reveals that Bayesian structural model provides reasonably good fit of work injury with high coefficient of determination (0.91) and less mean squared error as compared to traditional SEM.

Combining geostatistics with Moran's I analysis for mapping soil heavy metals in Beijing, China.

PubMed

Huo, Xiao-Ni; Li, Hong; Sun, Dan-Feng; Zhou, Lian-Di; Li, Bao-Guo

2012-03-01

Production of high quality interpolation maps of heavy metals is important for risk assessment of environmental pollution. In this paper, the spatial correlation characteristics information obtained from Moran's I analysis was used to supplement the traditional geostatistics. According to Moran's I analysis, four characteristics distances were obtained and used as the active lag distance to calculate the semivariance. Validation of the optimality of semivariance demonstrated that using the two distances where the Moran's I and the standardized Moran's I, Z(I) reached a maximum as the active lag distance can improve the fitting accuracy of semivariance. Then, spatial interpolation was produced based on the two distances and their nested model. The comparative analysis of estimation accuracy and the measured and predicted pollution status showed that the method combining geostatistics with Moran's I analysis was better than traditional geostatistics. Thus, Moran's I analysis is a useful complement for geostatistics to improve the spatial interpolation accuracy of heavy metals.

Modeling dolomitized carbonate-ramp reservoirs: A case study of the Seminole San Andres unit. Part 2 -- Seismic modeling, reservoir geostatistics, and reservoir simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, F.P.; Dai, J.; Kerans, C.

1998-11-01

In part 1 of this paper, the authors discussed the rock-fabric/petrophysical classes for dolomitized carbonate-ramp rocks, the effects of rock fabric and pore type on petrophysical properties, petrophysical models for analyzing wireline logs, the critical scales for defining geologic framework, and 3-D geologic modeling. Part 2 focuses on geophysical and engineering characterizations, including seismic modeling, reservoir geostatistics, stochastic modeling, and reservoir simulation. Synthetic seismograms of 30 to 200 Hz were generated to study the level of seismic resolution required to capture the high-frequency geologic features in dolomitized carbonate-ramp reservoirs. Outcrop data were collected to investigate effects of sampling interval andmore » scale-up of block size on geostatistical parameters. Semivariogram analysis of outcrop data showed that the sill of log permeability decreases and the correlation length increases with an increase of horizontal block size. Permeability models were generated using conventional linear interpolation, stochastic realizations without stratigraphic constraints, and stochastic realizations with stratigraphic constraints. Simulations of a fine-scale Lawyer Canyon outcrop model were used to study the factors affecting waterflooding performance. Simulation results show that waterflooding performance depends strongly on the geometry and stacking pattern of the rock-fabric units and on the location of production and injection wells.« less

Use of geostatistics for remediation planning to transcend urban political boundaries.

PubMed

Milillo, Tammy M; Sinha, Gaurav; Gardella, Joseph A

2012-11-01

Soil remediation plans are often dictated by areas of jurisdiction or property lines instead of scientific information. This study exemplifies how geostatistically interpolated surfaces can substantially improve remediation planning. Ordinary kriging, ordinary co-kriging, and inverse distance weighting spatial interpolation methods were compared for analyzing surface and sub-surface soil sample data originally collected by the US EPA and researchers at the University at Buffalo in Hickory Woods, an industrial-residential neighborhood in Buffalo, NY, where both lead and arsenic contamination is present. Past clean-up efforts estimated contamination levels from point samples, but parcel and agency jurisdiction boundaries were used to define remediation sites, rather than geostatistical models estimating the spatial behavior of the contaminants in the soil. Residents were understandably dissatisfied with the arbitrariness of the remediation plan. In this study we show how geostatistical mapping and participatory assessment can make soil remediation scientifically defensible, socially acceptable, and economically feasible. Copyright © 2012 Elsevier Ltd. All rights reserved.

A study of finite mixture model: Bayesian approach on financial time series data

NASA Astrophysics Data System (ADS)

Phoong, Seuk-Yen; Ismail, Mohd Tahir

2014-07-01

Recently, statistician have emphasized on the fitting finite mixture model by using Bayesian method. Finite mixture model is a mixture of distributions in modeling a statistical distribution meanwhile Bayesian method is a statistical method that use to fit the mixture model. Bayesian method is being used widely because it has asymptotic properties which provide remarkable result. In addition, Bayesian method also shows consistency characteristic which means the parameter estimates are close to the predictive distributions. In the present paper, the number of components for mixture model is studied by using Bayesian Information Criterion. Identify the number of component is important because it may lead to an invalid result. Later, the Bayesian method is utilized to fit the k-component mixture model in order to explore the relationship between rubber price and stock market price for Malaysia, Thailand, Philippines and Indonesia. Lastly, the results showed that there is a negative effect among rubber price and stock market price for all selected countries.

Dynamic Bayesian Networks for Student Modeling

ERIC Educational Resources Information Center

Kaser, Tanja; Klingler, Severin; Schwing, Alexander G.; Gross, Markus

2017-01-01

Intelligent tutoring systems adapt the curriculum to the needs of the individual student. Therefore, an accurate representation and prediction of student knowledge is essential. Bayesian Knowledge Tracing (BKT) is a popular approach for student modeling. The structure of BKT models, however, makes it impossible to represent the hierarchy and…

Geostatistics and spatial analysis in biological anthropology.

PubMed

Relethford, John H

2008-05-01

A variety of methods have been used to make evolutionary inferences based on the spatial distribution of biological data, including reconstructing population history and detection of the geographic pattern of natural selection. This article provides an examination of geostatistical analysis, a method used widely in geology but which has not often been applied in biological anthropology. Geostatistical analysis begins with the examination of a variogram, a plot showing the relationship between a biological distance measure and the geographic distance between data points and which provides information on the extent and pattern of spatial correlation. The results of variogram analysis are used for interpolating values of unknown data points in order to construct a contour map, a process known as kriging. The methods of geostatistical analysis and discussion of potential problems are applied to a large data set of anthropometric measures for 197 populations in Ireland. The geostatistical analysis reveals two major sources of spatial variation. One pattern, seen for overall body and craniofacial size, shows an east-west cline most likely reflecting the combined effects of past population dispersal and settlement. The second pattern is seen for craniofacial height and shows an isolation by distance pattern reflecting rapid spatial changes in the midlands region of Ireland, perhaps attributable to the genetic impact of the Vikings. The correspondence of these results with other analyses of these data and the additional insights generated from variogram analysis and kriging illustrate the potential utility of geostatistical analysis in biological anthropology. (c) 2008 Wiley-Liss, Inc.

Model Comparison of Bayesian Semiparametric and Parametric Structural Equation Models

ERIC Educational Resources Information Center

Song, Xin-Yuan; Xia, Ye-Mao; Pan, Jun-Hao; Lee, Sik-Yum

2011-01-01

Structural equation models have wide applications. One of the most important issues in analyzing structural equation models is model comparison. This article proposes a Bayesian model comparison statistic, namely the "L[subscript nu]"-measure for both semiparametric and parametric structural equation models. For illustration purposes, we consider…

BUMPER: the Bayesian User-friendly Model for Palaeo-Environmental Reconstruction

NASA Astrophysics Data System (ADS)

Holden, Phil; Birks, John; Brooks, Steve; Bush, Mark; Hwang, Grace; Matthews-Bird, Frazer; Valencia, Bryan; van Woesik, Robert

2017-04-01

We describe the Bayesian User-friendly Model for Palaeo-Environmental Reconstruction (BUMPER), a Bayesian transfer function for inferring past climate and other environmental variables from microfossil assemblages. The principal motivation for a Bayesian approach is that the palaeoenvironment is treated probabilistically, and can be updated as additional data become available. Bayesian approaches therefore provide a reconstruction-specific quantification of the uncertainty in the data and in the model parameters. BUMPER is fully self-calibrating, straightforward to apply, and computationally fast, requiring 2 seconds to build a 100-taxon model from a 100-site training-set on a standard personal computer. We apply the model's probabilistic framework to generate thousands of artificial training-sets under ideal assumptions. We then use these to demonstrate both the general applicability of the model and the sensitivity of reconstructions to the characteristics of the training-set, considering assemblage richness, taxon tolerances, and the number of training sites. We demonstrate general applicability to real data, considering three different organism types (chironomids, diatoms, pollen) and different reconstructed variables. In all of these applications an identically configured model is used, the only change being the input files that provide the training-set environment and taxon-count data.

Fast model updating coupling Bayesian inference and PGD model reduction

NASA Astrophysics Data System (ADS)

Rubio, Paul-Baptiste; Louf, François; Chamoin, Ludovic

2018-04-01

The paper focuses on a coupled Bayesian-Proper Generalized Decomposition (PGD) approach for the real-time identification and updating of numerical models. The purpose is to use the most general case of Bayesian inference theory in order to address inverse problems and to deal with different sources of uncertainties (measurement and model errors, stochastic parameters). In order to do so with a reasonable CPU cost, the idea is to replace the direct model called for Monte-Carlo sampling by a PGD reduced model, and in some cases directly compute the probability density functions from the obtained analytical formulation. This procedure is first applied to a welding control example with the updating of a deterministic parameter. In the second application, the identification of a stochastic parameter is studied through a glued assembly example.

Technical note: Bayesian calibration of dynamic ruminant nutrition models.

PubMed

Reed, K F; Arhonditsis, G B; France, J; Kebreab, E

2016-08-01

Mechanistic models of ruminant digestion and metabolism have advanced our understanding of the processes underlying ruminant animal physiology. Deterministic modeling practices ignore the inherent variation within and among individual animals and thus have no way to assess how sources of error influence model outputs. We introduce Bayesian calibration of mathematical models to address the need for robust mechanistic modeling tools that can accommodate error analysis by remaining within the bounds of data-based parameter estimation. For the purpose of prediction, the Bayesian approach generates a posterior predictive distribution that represents the current estimate of the value of the response variable, taking into account both the uncertainty about the parameters and model residual variability. Predictions are expressed as probability distributions, thereby conveying significantly more information than point estimates in regard to uncertainty. Our study illustrates some of the technical advantages of Bayesian calibration and discusses the future perspectives in the context of animal nutrition modeling. Copyright © 2016 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Geostatistical Borehole Image-Based Mapping of Karst-Carbonate Aquifer Pores.

PubMed

Sukop, Michael C; Cunningham, Kevin J

2016-03-01

Quantification of the character and spatial distribution of porosity in carbonate aquifers is important as input into computer models used in the calculation of intrinsic permeability and for next-generation, high-resolution groundwater flow simulations. Digital, optical, borehole-wall image data from three closely spaced boreholes in the karst-carbonate Biscayne aquifer in southeastern Florida are used in geostatistical experiments to assess the capabilities of various methods to create realistic two-dimensional models of vuggy megaporosity and matrix-porosity distribution in the limestone that composes the aquifer. When the borehole image data alone were used as the model training image, multiple-point geostatistics failed to detect the known spatial autocorrelation of vuggy megaporosity and matrix porosity among the three boreholes, which were only 10 m apart. Variogram analysis and subsequent Gaussian simulation produced results that showed a realistic conceptualization of horizontal continuity of strata dominated by vuggy megaporosity and matrix porosity among the three boreholes. © 2015, National Ground Water Association.

Geostatistical borehole image-based mapping of karst-carbonate aquifer pores

USGS Publications Warehouse

Michael Sukop,; Cunningham, Kevin J.

2016-01-01

Quantification of the character and spatial distribution of porosity in carbonate aquifers is important as input into computer models used in the calculation of intrinsic permeability and for next-generation, high-resolution groundwater flow simulations. Digital, optical, borehole-wall image data from three closely spaced boreholes in the karst-carbonate Biscayne aquifer in southeastern Florida are used in geostatistical experiments to assess the capabilities of various methods to create realistic two-dimensional models of vuggy megaporosity and matrix-porosity distribution in the limestone that composes the aquifer. When the borehole image data alone were used as the model training image, multiple-point geostatistics failed to detect the known spatial autocorrelation of vuggy megaporosity and matrix porosity among the three boreholes, which were only 10 m apart. Variogram analysis and subsequent Gaussian simulation produced results that showed a realistic conceptualization of horizontal continuity of strata dominated by vuggy megaporosity and matrix porosity among the three boreholes.

Geostatistical Model-Based Estimates of Schistosomiasis Prevalence among Individuals Aged ≤20 Years in West Africa

PubMed Central

Schur, Nadine; Hürlimann, Eveline; Garba, Amadou; Traoré, Mamadou S.; Ndir, Omar; Ratard, Raoult C.; Tchuem Tchuenté, Louis-Albert; Kristensen, Thomas K.; Utzinger, Jürg; Vounatsou, Penelope

2011-01-01

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/Significance We

Bayesian Framework for Water Quality Model Uncertainty Estimation and Risk Management

EPA Science Inventory

A formal Bayesian methodology is presented for integrated model calibration and risk-based water quality management using Bayesian Monte Carlo simulation and maximum likelihood estimation (BMCML). The primary focus is on lucid integration of model calibration with risk-based wat...

Bayesian Parameter Inference and Model Selection by Population Annealing in Systems Biology

PubMed Central

Murakami, Yohei

2014-01-01

Parameter inference and model selection are very important for mathematical modeling in systems biology. Bayesian statistics can be used to conduct both parameter inference and model selection. Especially, the framework named approximate Bayesian computation is often used for parameter inference and model selection in systems biology. However, Monte Carlo methods needs to be used to compute Bayesian posterior distributions. In addition, the posterior distributions of parameters are sometimes almost uniform or very similar to their prior distributions. In such cases, it is difficult to choose one specific value of parameter with high credibility as the representative value of the distribution. To overcome the problems, we introduced one of the population Monte Carlo algorithms, population annealing. Although population annealing is usually used in statistical mechanics, we showed that population annealing can be used to compute Bayesian posterior distributions in the approximate Bayesian computation framework. To deal with un-identifiability of the representative values of parameters, we proposed to run the simulations with the parameter ensemble sampled from the posterior distribution, named “posterior parameter ensemble”. We showed that population annealing is an efficient and convenient algorithm to generate posterior parameter ensemble. We also showed that the simulations with the posterior parameter ensemble can, not only reproduce the data used for parameter inference, but also capture and predict the data which was not used for parameter inference. Lastly, we introduced the marginal likelihood in the approximate Bayesian computation framework for Bayesian model selection. We showed that population annealing enables us to compute the marginal likelihood in the approximate Bayesian computation framework and conduct model selection depending on the Bayes factor. PMID:25089832

G STL: the geostatistical template library in C++

NASA Astrophysics Data System (ADS)

Remy, Nicolas; Shtuka, Arben; Levy, Bruno; Caers, Jef

2002-10-01

The development of geostatistics has been mostly accomplished by application-oriented engineers in the past 20 years. The focus on concrete applications gave birth to many algorithms and computer programs designed to address different issues, such as estimating or simulating a variable while possibly accounting for secondary information such as seismic data, or integrating geological and geometrical data. At the core of any geostatistical data integration methodology is a well-designed algorithm. Yet, despite their obvious differences, all these algorithms share many commonalities on which to build a geostatistics programming library, lest the resulting library is poorly reusable and difficult to expand. Building on this observation, we design a comprehensive, yet flexible and easily reusable library of geostatistics algorithms in C++. The recent advent of the generic programming paradigm allows us elegantly to express the commonalities of the geostatistical algorithms into computer code. Generic programming, also referred to as "programming with concepts", provides a high level of abstraction without loss of efficiency. This last point is a major gain over object-oriented programming which often trades efficiency for abstraction. It is not enough for a numerical library to be reusable, it also has to be fast. Because generic programming is "programming with concepts", the essential step in the library design is the careful identification and thorough definition of these concepts shared by most geostatistical algorithms. Building on these definitions, a generic and expandable code can be developed. To show the advantages of such a generic library, we use G STL to build two sequential simulation programs working on two different types of grids—a surface with faults and an unstructured grid—without requiring any change to the G STL code.

Posterior Predictive Model Checking in Bayesian Networks

ERIC Educational Resources Information Center

Crawford, Aaron

2014-01-01

This simulation study compared the utility of various discrepancy measures within a posterior predictive model checking (PPMC) framework for detecting different types of data-model misfit in multidimensional Bayesian network (BN) models. The investigated conditions were motivated by an applied research program utilizing an operational complex…

Development of dynamic Bayesian models for web application test management

NASA Astrophysics Data System (ADS)

Azarnova, T. V.; Polukhin, P. V.; Bondarenko, Yu V.; Kashirina, I. L.

2018-03-01

The mathematical apparatus of dynamic Bayesian networks is an effective and technically proven tool that can be used to model complex stochastic dynamic processes. According to the results of the research, mathematical models and methods of dynamic Bayesian networks provide a high coverage of stochastic tasks associated with error testing in multiuser software products operated in a dynamically changing environment. Formalized representation of the discrete test process as a dynamic Bayesian model allows us to organize the logical connection between individual test assets for multiple time slices. This approach gives an opportunity to present testing as a discrete process with set structural components responsible for the generation of test assets. Dynamic Bayesian network-based models allow us to combine in one management area individual units and testing components with different functionalities and a direct influence on each other in the process of comprehensive testing of various groups of computer bugs. The application of the proposed models provides an opportunity to use a consistent approach to formalize test principles and procedures, methods used to treat situational error signs, and methods used to produce analytical conclusions based on test results.

Bayesian Model Averaging of Artificial Intelligence Models for Hydraulic Conductivity Estimation

NASA Astrophysics Data System (ADS)

Nadiri, A.; Chitsazan, N.; Tsai, F. T.; Asghari Moghaddam, A.

2012-12-01

This research presents a Bayesian artificial intelligence model averaging (BAIMA) method that incorporates multiple artificial intelligence (AI) models to estimate hydraulic conductivity and evaluate estimation uncertainties. Uncertainty in the AI model outputs stems from error in model input as well as non-uniqueness in selecting different AI methods. Using one single AI model tends to bias the estimation and underestimate uncertainty. BAIMA employs Bayesian model averaging (BMA) technique to address the issue of using one single AI model for estimation. BAIMA estimates hydraulic conductivity by averaging the outputs of AI models according to their model weights. In this study, the model weights were determined using the Bayesian information criterion (BIC) that follows the parsimony principle. BAIMA calculates the within-model variances to account for uncertainty propagation from input data to AI model output. Between-model variances are evaluated to account for uncertainty due to model non-uniqueness. We employed Takagi-Sugeno fuzzy logic (TS-FL), artificial neural network (ANN) and neurofuzzy (NF) to estimate hydraulic conductivity for the Tasuj plain aquifer, Iran. BAIMA combined three AI models and produced better fitting than individual models. While NF was expected to be the best AI model owing to its utilization of both TS-FL and ANN models, the NF model is nearly discarded by the parsimony principle. The TS-FL model and the ANN model showed equal importance although their hydraulic conductivity estimates were quite different. This resulted in significant between-model variances that are normally ignored by using one AI model.

Combining Geostatistics with Moran’s I Analysis for Mapping Soil Heavy Metals in Beijing, China

PubMed Central

Huo, Xiao-Ni; Li, Hong; Sun, Dan-Feng; Zhou, Lian-Di; Li, Bao-Guo

2012-01-01

Production of high quality interpolation maps of heavy metals is important for risk assessment of environmental pollution. In this paper, the spatial correlation characteristics information obtained from Moran’s I analysis was used to supplement the traditional geostatistics. According to Moran’s I analysis, four characteristics distances were obtained and used as the active lag distance to calculate the semivariance. Validation of the optimality of semivariance demonstrated that using the two distances where the Moran’s I and the standardized Moran’s I, Z(I) reached a maximum as the active lag distance can improve the fitting accuracy of semivariance. Then, spatial interpolation was produced based on the two distances and their nested model. The comparative analysis of estimation accuracy and the measured and predicted pollution status showed that the method combining geostatistics with Moran’s I analysis was better than traditional geostatistics. Thus, Moran’s I analysis is a useful complement for geostatistics to improve the spatial interpolation accuracy of heavy metals. PMID:22690179

Bayesian Recurrent Neural Network for Language Modeling.

PubMed

Chien, Jen-Tzung; Ku, Yuan-Chu

2016-02-01

A language model (LM) is calculated as the probability of a word sequence that provides the solution to word prediction for a variety of information systems. A recurrent neural network (RNN) is powerful to learn the large-span dynamics of a word sequence in the continuous space. However, the training of the RNN-LM is an ill-posed problem because of too many parameters from a large dictionary size and a high-dimensional hidden layer. This paper presents a Bayesian approach to regularize the RNN-LM and apply it for continuous speech recognition. We aim to penalize the too complicated RNN-LM by compensating for the uncertainty of the estimated model parameters, which is represented by a Gaussian prior. The objective function in a Bayesian classification network is formed as the regularized cross-entropy error function. The regularized model is constructed not only by calculating the regularized parameters according to the maximum a posteriori criterion but also by estimating the Gaussian hyperparameter by maximizing the marginal likelihood. A rapid approximation to a Hessian matrix is developed to implement the Bayesian RNN-LM (BRNN-LM) by selecting a small set of salient outer-products. The proposed BRNN-LM achieves a sparser model than the RNN-LM. Experiments on different corpora show the robustness of system performance by applying the rapid BRNN-LM under different conditions.

Bayesian methods for characterizing unknown parameters of material models

DOE PAGES

Emery, J. M.; Grigoriu, M. D.; Field Jr., R. V.

2016-02-04

A Bayesian framework is developed for characterizing the unknown parameters of probabilistic models for material properties. In this framework, the unknown parameters are viewed as random and described by their posterior distributions obtained from prior information and measurements of quantities of interest that are observable and depend on the unknown parameters. The proposed Bayesian method is applied to characterize an unknown spatial correlation of the conductivity field in the definition of a stochastic transport equation and to solve this equation by Monte Carlo simulation and stochastic reduced order models (SROMs). As a result, the Bayesian method is also employed tomore » characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.« less

Bayesian methods for characterizing unknown parameters of material models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Emery, J. M.; Grigoriu, M. D.; Field Jr., R. V.

A Bayesian framework is developed for characterizing the unknown parameters of probabilistic models for material properties. In this framework, the unknown parameters are viewed as random and described by their posterior distributions obtained from prior information and measurements of quantities of interest that are observable and depend on the unknown parameters. The proposed Bayesian method is applied to characterize an unknown spatial correlation of the conductivity field in the definition of a stochastic transport equation and to solve this equation by Monte Carlo simulation and stochastic reduced order models (SROMs). As a result, the Bayesian method is also employed tomore » characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.« less

Bayesian Models Leveraging Bioactivity and Cytotoxicity Information for Drug Discovery

PubMed Central

Ekins, Sean; Reynolds, Robert C.; Kim, Hiyun; Koo, Mi-Sun; Ekonomidis, Marilyn; Talaue, Meliza; Paget, Steve D.; Woolhiser, Lisa K.; Lenaerts, Anne J.; Bunin, Barry A.; Connell, Nancy; Freundlich, Joel S.

2013-01-01

SUMMARY Identification of unique leads represents a significant challenge in drug discovery. This hurdle is magnified in neglected diseases such as tuberculosis. We have leveraged public high-throughput screening (HTS) data, to experimentally validate virtual screening approach employing Bayesian models built with bioactivity information (single-event model) as well as bioactivity and cytotoxicity information (dual-event model). We virtually screen a commercial library and experimentally confirm actives with hit rates exceeding typical HTS results by 1-2 orders of magnitude. The first dual-event Bayesian model identified compounds with antitubercular whole-cell activity and low mammalian cell cytotoxicity from a published set of antimalarials. The most potent hit exhibits the in vitro activity and in vitro/in vivo safety profile of a drug lead. These Bayesian models offer significant economies in time and cost to drug discovery. PMID:23521795

Bayesian Inference of High-Dimensional Dynamical Ocean Models

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

A geostatistical approach to the change-of-support problem and variable-support data fusion in spatial analysis

NASA Astrophysics Data System (ADS)

Wang, Jun; Wang, Yang; Zeng, Hui

2016-01-01

A key issue to address in synthesizing spatial data with variable-support in spatial analysis and modeling is the change-of-support problem. We present an approach for solving the change-of-support and variable-support data fusion problems. This approach is based on geostatistical inverse modeling that explicitly accounts for differences in spatial support. The inverse model is applied here to produce both the best predictions of a target support and prediction uncertainties, based on one or more measurements, while honoring measurements. Spatial data covering large geographic areas often exhibit spatial nonstationarity and can lead to computational challenge due to the large data size. We developed a local-window geostatistical inverse modeling approach to accommodate these issues of spatial nonstationarity and alleviate computational burden. We conducted experiments using synthetic and real-world raster data. Synthetic data were generated and aggregated to multiple supports and downscaled back to the original support to analyze the accuracy of spatial predictions and the correctness of prediction uncertainties. Similar experiments were conducted for real-world raster data. Real-world data with variable-support were statistically fused to produce single-support predictions and associated uncertainties. The modeling results demonstrate that geostatistical inverse modeling can produce accurate predictions and associated prediction uncertainties. It is shown that the local-window geostatistical inverse modeling approach suggested offers a practical way to solve the well-known change-of-support problem and variable-support data fusion problem in spatial analysis and modeling.

Three-dimensional Bayesian geostatistical aquifer characterization at the Hanford 300 Area using tracer test data

NASA Astrophysics Data System (ADS)

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.

Application of a predictive Bayesian model to environmental accounting.

PubMed

Anex, R P; Englehardt, J D

2001-03-30

Environmental accounting techniques are intended to capture important environmental costs and benefits that are often overlooked in standard accounting practices. Environmental accounting methods themselves often ignore or inadequately represent large but highly uncertain environmental costs and costs conditioned by specific prior events. Use of a predictive Bayesian model is demonstrated for the assessment of such highly uncertain environmental and contingent costs. The predictive Bayesian approach presented generates probability distributions for the quantity of interest (rather than parameters thereof). A spreadsheet implementation of a previously proposed predictive Bayesian model, extended to represent contingent costs, is described and used to evaluate whether a firm should undertake an accelerated phase-out of its PCB containing transformers. Variability and uncertainty (due to lack of information) in transformer accident frequency and severity are assessed simultaneously using a combination of historical accident data, engineering model-based cost estimates, and subjective judgement. Model results are compared using several different risk measures. Use of the model for incorporation of environmental risk management into a company's overall risk management strategy is discussed.

Bayesian Regression with Network Prior: Optimal Bayesian Filtering Perspective

PubMed Central

Qian, Xiaoning; Dougherty, Edward R.

2017-01-01

The recently introduced intrinsically Bayesian robust filter (IBRF) provides fully optimal filtering relative to a prior distribution over an uncertainty class ofjoint random process models, whereas formerly the theory was limited to model-constrained Bayesian robust filters, for which optimization was limited to the filters that are optimal for models in the uncertainty class. This paper extends the IBRF theory to the situation where there are both a prior on the uncertainty class and sample data. The result is optimal Bayesian filtering (OBF), where optimality is relative to the posterior distribution derived from the prior and the data. The IBRF theories for effective characteristics and canonical expansions extend to the OBF setting. A salient focus of the present work is to demonstrate the advantages of Bayesian regression within the OBF setting over the classical Bayesian approach in the context otlinear Gaussian models. PMID:28824268

Modeling Non-Gaussian Time Series with Nonparametric Bayesian Model.

PubMed

Xu, Zhiguang; MacEachern, Steven; Xu, Xinyi

2015-02-01

We present a class of Bayesian copula models whose major components are the marginal (limiting) distribution of a stationary time series and the internal dynamics of the series. We argue that these are the two features with which an analyst is typically most familiar, and hence that these are natural components with which to work. For the marginal distribution, we use a nonparametric Bayesian prior distribution along with a cdf-inverse cdf transformation to obtain large support. For the internal dynamics, we rely on the traditionally successful techniques of normal-theory time series. Coupling the two components gives us a family of (Gaussian) copula transformed autoregressive models. The models provide coherent adjustments of time scales and are compatible with many extensions, including changes in volatility of the series. We describe basic properties of the models, show their ability to recover non-Gaussian marginal distributions, and use a GARCH modification of the basic model to analyze stock index return series. The models are found to provide better fit and improved short-range and long-range predictions than Gaussian competitors. The models are extensible to a large variety of fields, including continuous time models, spatial models, models for multiple series, models driven by external covariate streams, and non-stationary models.

Bayesian network modelling of upper gastrointestinal bleeding

NASA Astrophysics Data System (ADS)

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

2013-09-01

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

Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data

ERIC Educational Resources Information Center

Lee, Sik-Yum

2006-01-01

A Bayesian approach is developed for analyzing nonlinear structural equation models with nonignorable missing data. The nonignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm is used to produce the joint Bayesian estimates of…

Bayesian models for comparative analysis integrating phylogenetic uncertainty.

PubMed

de Villemereuil, Pierre; Wells, Jessie A; Edwards, Robert D; Blomberg, Simon P

2012-06-28

Uncertainty in comparative analyses can come from at least two sources: a) phylogenetic uncertainty in the tree topology or branch lengths, and b) uncertainty due to intraspecific variation in trait values, either due to measurement error or natural individual variation. Most phylogenetic comparative methods do not account for such uncertainties. Not accounting for these sources of uncertainty leads to false perceptions of precision (confidence intervals will be too narrow) and inflated significance in hypothesis testing (e.g. p-values will be too small). Although there is some application-specific software for fitting Bayesian models accounting for phylogenetic error, more general and flexible software is desirable. We developed models to directly incorporate phylogenetic uncertainty into a range of analyses that biologists commonly perform, using a Bayesian framework and Markov Chain Monte Carlo analyses. We demonstrate applications in linear regression, quantification of phylogenetic signal, and measurement error models. Phylogenetic uncertainty was incorporated by applying a prior distribution for the phylogeny, where this distribution consisted of the posterior tree sets from Bayesian phylogenetic tree estimation programs. The models were analysed using simulated data sets, and applied to a real data set on plant traits, from rainforest plant species in Northern Australia. Analyses were performed using the free and open source software OpenBUGS and JAGS. Incorporating phylogenetic uncertainty through an empirical prior distribution of trees leads to more precise estimation of regression model parameters than using a single consensus tree and enables a more realistic estimation of confidence intervals. In addition, models incorporating measurement errors and/or individual variation, in one or both variables, are easily formulated in the Bayesian framework. We show that BUGS is a useful, flexible general purpose tool for phylogenetic comparative analyses

Bayesian models for comparative analysis integrating phylogenetic uncertainty

PubMed Central

2012-01-01

Background Uncertainty in comparative analyses can come from at least two sources: a) phylogenetic uncertainty in the tree topology or branch lengths, and b) uncertainty due to intraspecific variation in trait values, either due to measurement error or natural individual variation. Most phylogenetic comparative methods do not account for such uncertainties. Not accounting for these sources of uncertainty leads to false perceptions of precision (confidence intervals will be too narrow) and inflated significance in hypothesis testing (e.g. p-values will be too small). Although there is some application-specific software for fitting Bayesian models accounting for phylogenetic error, more general and flexible software is desirable. Methods We developed models to directly incorporate phylogenetic uncertainty into a range of analyses that biologists commonly perform, using a Bayesian framework and Markov Chain Monte Carlo analyses. Results We demonstrate applications in linear regression, quantification of phylogenetic signal, and measurement error models. Phylogenetic uncertainty was incorporated by applying a prior distribution for the phylogeny, where this distribution consisted of the posterior tree sets from Bayesian phylogenetic tree estimation programs. The models were analysed using simulated data sets, and applied to a real data set on plant traits, from rainforest plant species in Northern Australia. Analyses were performed using the free and open source software OpenBUGS and JAGS. Conclusions Incorporating phylogenetic uncertainty through an empirical prior distribution of trees leads to more precise estimation of regression model parameters than using a single consensus tree and enables a more realistic estimation of confidence intervals. In addition, models incorporating measurement errors and/or individual variation, in one or both variables, are easily formulated in the Bayesian framework. We show that BUGS is a useful, flexible general purpose tool for

National-scale aboveground biomass geostatistical mapping with FIA inventory and GLAS data: Preparation for sparsely sampled lidar assisted forest inventory

NASA Astrophysics Data System (ADS)

Babcock, C. R.; Finley, A. O.; Andersen, H. E.; Moskal, L. M.; Morton, D. C.; Cook, B.; Nelson, R.

2017-12-01

Upcoming satellite lidar missions, such as GEDI and IceSat-2, are designed to collect laser altimetry data from space for narrow bands along orbital tracts. As a result lidar metric sets derived from these sources will not be of complete spatial coverage. This lack of complete coverage, or sparsity, means traditional regression approaches that consider lidar metrics as explanatory variables (without error) cannot be used to generate wall-to-wall maps of forest inventory variables. We implement a coregionalization framework to jointly model sparsely sampled lidar information and point-referenced forest variable measurements to create wall-to-wall maps with full probabilistic uncertainty quantification of all inputs. We inform the model with USFS Forest Inventory and Analysis (FIA) in-situ forest measurements and GLAS lidar data to spatially predict aboveground forest biomass (AGB) across the contiguous US. We cast our model within a Bayesian hierarchical framework to better model complex space-varying correlation structures among the lidar metrics and FIA data, which yields improved prediction and uncertainty assessment. To circumvent computational difficulties that arise when fitting complex geostatistical models to massive datasets, we use a Nearest Neighbor Gaussian process (NNGP) prior. Results indicate that a coregionalization modeling approach to leveraging sampled lidar data to improve AGB estimation is effective. Further, fitting the coregionalization model within a Bayesian mode of inference allows for AGB quantification across scales ranging from individual pixel estimates of AGB density to total AGB for the continental US with uncertainty. The coregionalization framework examined here is directly applicable to future spaceborne lidar acquisitions from GEDI and IceSat-2. Pairing these lidar sources with the extensive FIA forest monitoring plot network using a joint prediction framework, such as the coregionalization model explored here, offers the

Mapping, Bayesian Geostatistical Analysis and Spatial Prediction of Lymphatic Filariasis Prevalence in Africa

PubMed Central

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

Modeling Soot Oxidation and Gasification with Bayesian Statistics

DOE PAGES

Josephson, Alexander J.; Gaffin, Neal D.; Smith, Sean T.; ...

2017-08-22

This paper presents a statistical method for model calibration using data collected from literature. The method is used to calibrate parameters for global models of soot consumption in combustion systems. This consumption is broken into two different submodels: first for oxidation where soot particles are attacked by certain oxidizing agents; second for gasification where soot particles are attacked by H 2O or CO 2 molecules. Rate data were collected from 19 studies in the literature and evaluated using Bayesian statistics to calibrate the model parameters. Bayesian statistics are valued in their ability to quantify uncertainty in modeling. The calibrated consumptionmore » model with quantified uncertainty is presented here along with a discussion of associated implications. The oxidation results are found to be consistent with previous studies. Significant variation is found in the CO 2 gasification rates.« less

Modeling Soot Oxidation and Gasification with Bayesian Statistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Josephson, Alexander J.; Gaffin, Neal D.; Smith, Sean T.

This paper presents a statistical method for model calibration using data collected from literature. The method is used to calibrate parameters for global models of soot consumption in combustion systems. This consumption is broken into two different submodels: first for oxidation where soot particles are attacked by certain oxidizing agents; second for gasification where soot particles are attacked by H 2O or CO 2 molecules. Rate data were collected from 19 studies in the literature and evaluated using Bayesian statistics to calibrate the model parameters. Bayesian statistics are valued in their ability to quantify uncertainty in modeling. The calibrated consumptionmore » model with quantified uncertainty is presented here along with a discussion of associated implications. The oxidation results are found to be consistent with previous studies. Significant variation is found in the CO 2 gasification rates.« less

A Tutorial Introduction to Bayesian Models of Cognitive Development

ERIC Educational Resources Information Center

Perfors, Amy; Tenenbaum, Joshua B.; Griffiths, Thomas L.; Xu, Fei

2011-01-01

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…

Scale Mixture Models with Applications to Bayesian Inference

NASA Astrophysics Data System (ADS)

Qin, Zhaohui S.; Damien, Paul; Walker, Stephen

2003-11-01

Scale mixtures of uniform distributions are used to model non-normal data in time series and econometrics in a Bayesian framework. Heteroscedastic and skewed data models are also tackled using scale mixture of uniform distributions.

Topsoil moisture mapping using geostatistical techniques under different Mediterranean climatic conditions.

PubMed

Martínez-Murillo, J F; Hueso-González, P; Ruiz-Sinoga, J D

2017-10-01

Soil mapping has been considered as an important factor in the widening of Soil Science and giving response to many different environmental questions. Geostatistical techniques, through kriging and co-kriging techniques, have made possible to improve the understanding of eco-geomorphologic variables, e.g., soil moisture. This study is focused on mapping of topsoil moisture using geostatistical techniques under different Mediterranean climatic conditions (humid, dry and semiarid) in three small watersheds and considering topography and soil properties as key factors. A Digital Elevation Model (DEM) with a resolution of 1×1m was derived from a topographical survey as well as soils were sampled to analyzed soil properties controlling topsoil moisture, which was measured during 4-years. Afterwards, some topography attributes were derived from the DEM, the soil properties analyzed in laboratory, and the topsoil moisture was modeled for the entire watersheds applying three geostatistical techniques: i) ordinary kriging; ii) co-kriging considering as co-variate topography attributes; and iii) co-kriging ta considering as co-variates topography attributes and gravel content. The results indicated topsoil moisture was more accurately mapped in the dry and semiarid watersheds when co-kriging procedure was performed. The study is a contribution to improve the efficiency and accuracy of studies about the Mediterranean eco-geomorphologic system and soil hydrology in field conditions. Copyright © 2017 Elsevier B.V. All rights reserved.

Geostatistical simulations for radon indoor with a nested model including the housing factor.

PubMed

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. Copyright © 2015 Elsevier Ltd. All rights reserved.

Geostatistical modelling of soil-transmitted helminth infection in Cambodia: do socioeconomic factors improve predictions?

PubMed

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

Bayesian inference based on dual generalized order statistics from the exponentiated Weibull model

NASA Astrophysics Data System (ADS)

Al Sobhi, Mashail M.

2015-02-01

Bayesian estimation for the two parameters and the reliability function of the exponentiated Weibull model are obtained based on dual generalized order statistics (DGOS). Also, Bayesian prediction bounds for future DGOS from exponentiated Weibull model are obtained. The symmetric and asymmetric loss functions are considered for Bayesian computations. The Markov chain Monte Carlo (MCMC) methods are used for computing the Bayes estimates and prediction bounds. The results have been specialized to the lower record values. Comparisons are made between Bayesian and maximum likelihood estimators via Monte Carlo simulation.

[Evaluation of estimation of prevalence ratio using bayesian log-binomial regression model].

PubMed

Gao, W L; Lin, H; Liu, X N; Ren, X W; Li, J S; Shen, X P; Zhu, S L

2017-03-10

To evaluate the estimation of prevalence ratio ( PR ) by using bayesian log-binomial regression model and its application, we estimated the PR of medical care-seeking prevalence to caregivers' recognition of risk signs of diarrhea in their infants by using bayesian log-binomial regression model in Openbugs software. The results showed that caregivers' recognition of infant' s risk signs of diarrhea was associated significantly with a 13% increase of medical care-seeking. Meanwhile, we compared the differences in PR 's point estimation and its interval estimation of medical care-seeking prevalence to caregivers' recognition of risk signs of diarrhea and convergence of three models (model 1: not adjusting for the covariates; model 2: adjusting for duration of caregivers' education, model 3: adjusting for distance between village and township and child month-age based on model 2) between bayesian log-binomial regression model and conventional log-binomial regression model. The results showed that all three bayesian log-binomial regression models were convergence and the estimated PRs were 1.130(95 %CI : 1.005-1.265), 1.128(95 %CI : 1.001-1.264) and 1.132(95 %CI : 1.004-1.267), respectively. Conventional log-binomial regression model 1 and model 2 were convergence and their PRs were 1.130(95 % CI : 1.055-1.206) and 1.126(95 % CI : 1.051-1.203), respectively, but the model 3 was misconvergence, so COPY method was used to estimate PR , which was 1.125 (95 %CI : 1.051-1.200). In addition, the point estimation and interval estimation of PRs from three bayesian log-binomial regression models differed slightly from those of PRs from conventional log-binomial regression model, but they had a good consistency in estimating PR . Therefore, bayesian log-binomial regression model can effectively estimate PR with less misconvergence and have more advantages in application compared with conventional log-binomial regression model.

Geostatistics applied to gas reservoirs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meunier, G.; Coulomb, C.; Laille, J.P.

1989-09-01

The spatial distribution of many of the physical parameters connected with a gas reservoir is of primary interest to both engineers and geologists throughout the study, development, and operation of a field. It is therefore desirable for the distribution to be capable of statistical interpretation, to have a simple graphical representation, and to allow data to be entered from either two- or three-dimensional grids. To satisfy these needs while dealing with the geographical variables, new methods have been developed under the name geostatistics. This paper describes briefly the theory of geostatistics and its most recent improvements for the specific problemmore » of subsurface description. The external-drift technique has been emphasized in particular, and in addition, four case studies related to gas reservoirs are presented.« less

Forward modeling of gravity data using geostatistically generated subsurface density variations

USGS Publications Warehouse

Phelps, Geoffrey

2016-01-01

Using geostatistical models of density variations in the subsurface, constrained by geologic data, forward models of gravity anomalies can be generated by discretizing the subsurface and calculating the cumulative effect of each cell (pixel). The results of such stochastically generated forward gravity anomalies can be compared with the observed gravity anomalies to find density models that match the observed data. These models have an advantage over forward gravity anomalies generated using polygonal bodies of homogeneous density because generating numerous realizations explores a larger region of the solution space. The stochastic modeling can be thought of as dividing the forward model into two components: that due to the shape of each geologic unit and that due to the heterogeneous distribution of density within each geologic unit. The modeling demonstrates that the internally heterogeneous distribution of density within each geologic unit can contribute significantly to the resulting calculated forward gravity anomaly. Furthermore, the stochastic models match observed statistical properties of geologic units, the solution space is more broadly explored by producing a suite of successful models, and the likelihood of a particular conceptual geologic model can be compared. The Vaca Fault near Travis Air Force Base, California, can be successfully modeled as a normal or strike-slip fault, with the normal fault model being slightly more probable. It can also be modeled as a reverse fault, although this structural geologic configuration is highly unlikely given the realizations we explored.

Bayesian-MCMC-based parameter estimation of stealth aircraft RCS models

NASA Astrophysics Data System (ADS)

Xia, Wei; Dai, Xiao-Xia; Feng, Yuan

2015-12-01

When modeling a stealth aircraft with low RCS (Radar Cross Section), conventional parameter estimation methods may cause a deviation from the actual distribution, owing to the fact that the characteristic parameters are estimated via directly calculating the statistics of RCS. The Bayesian-Markov Chain Monte Carlo (Bayesian-MCMC) method is introduced herein to estimate the parameters so as to improve the fitting accuracies of fluctuation models. The parameter estimations of the lognormal and the Legendre polynomial models are reformulated in the Bayesian framework. The MCMC algorithm is then adopted to calculate the parameter estimates. Numerical results show that the distribution curves obtained by the proposed method exhibit improved consistence with the actual ones, compared with those fitted by the conventional method. The fitting accuracy could be improved by no less than 25% for both fluctuation models, which implies that the Bayesian-MCMC method might be a good candidate among the optimal parameter estimation methods for stealth aircraft RCS models. Project supported by the National Natural Science Foundation of China (Grant No. 61101173), the National Basic Research Program of China (Grant No. 613206), the National High Technology Research and Development Program of China (Grant No. 2012AA01A308), the State Scholarship Fund by the China Scholarship Council (CSC), and the Oversea Academic Training Funds, and University of Electronic Science and Technology of China (UESTC).

Bayesian model selection: Evidence estimation based on DREAM simulation and bridge sampling

NASA Astrophysics Data System (ADS)

Volpi, Elena; Schoups, Gerrit; Firmani, Giovanni; Vrugt, Jasper A.

2017-04-01

Bayesian inference has found widespread application in Earth and Environmental Systems Modeling, providing an effective tool for prediction, data assimilation, parameter estimation, uncertainty analysis and hypothesis testing. Under multiple competing hypotheses, the Bayesian approach also provides an attractive alternative to traditional information criteria (e.g. AIC, BIC) for model selection. The key variable for Bayesian model selection is the evidence (or marginal likelihood) that is the normalizing constant in the denominator of Bayes theorem; while it is fundamental for model selection, the evidence is not required for Bayesian inference. It is computed for each hypothesis (model) by averaging the likelihood function over the prior parameter distribution, rather than maximizing it as by information criteria; the larger a model evidence the more support it receives among a collection of hypothesis as the simulated values assign relatively high probability density to the observed data. Hence, the evidence naturally acts as an Occam's razor, preferring simpler and more constrained models against the selection of over-fitted ones by information criteria that incorporate only the likelihood maximum. Since it is not particularly easy to estimate the evidence in practice, Bayesian model selection via the marginal likelihood has not yet found mainstream use. We illustrate here the properties of a new estimator of the Bayesian model evidence, which provides robust and unbiased estimates of the marginal likelihood; the method is coined Gaussian Mixture Importance Sampling (GMIS). GMIS uses multidimensional numerical integration of the posterior parameter distribution via bridge sampling (a generalization of importance sampling) of a mixture distribution fitted to samples of the posterior distribution derived from the DREAM algorithm (Vrugt et al., 2008; 2009). Some illustrative examples are presented to show the robustness and superiority of the GMIS estimator with

Adjusting for sampling variability in sparse data: geostatistical approaches to disease mapping

PubMed Central

2011-01-01

Background Disease maps of crude rates from routinely collected health data indexed at a small geographical resolution pose specific statistical problems due to the sparse nature of the data. Spatial smoothers allow areas to borrow strength from neighboring regions to produce a more stable estimate of the areal value. Geostatistical smoothers are able to quantify the uncertainty in smoothed rate estimates without a high computational burden. In this paper, we introduce a uniform model extension of Bayesian Maximum Entropy (UMBME) and compare its performance to that of Poisson kriging in measures of smoothing strength and estimation accuracy as applied to simulated data and the real data example of HIV infection in North Carolina. The aim is to produce more reliable maps of disease rates in small areas to improve identification of spatial trends at the local level. Results In all data environments, Poisson kriging exhibited greater smoothing strength than UMBME. With the simulated data where the true latent rate of infection was known, Poisson kriging resulted in greater estimation accuracy with data that displayed low spatial autocorrelation, while UMBME provided more accurate estimators with data that displayed higher spatial autocorrelation. With the HIV data, UMBME performed slightly better than Poisson kriging in cross-validatory predictive checks, with both models performing better than the observed data model with no smoothing. Conclusions Smoothing methods have different advantages depending upon both internal model assumptions that affect smoothing strength and external data environments, such as spatial correlation of the observed data. Further model comparisons in different data environments are required to provide public health practitioners with guidelines needed in choosing the most appropriate smoothing method for their particular health dataset. PMID:21978359

Adjusting for sampling variability in sparse data: geostatistical approaches to disease mapping.

PubMed

Hampton, Kristen H; Serre, Marc L; Gesink, Dionne C; Pilcher, Christopher D; Miller, William C

2011-10-06

Disease maps of crude rates from routinely collected health data indexed at a small geographical resolution pose specific statistical problems due to the sparse nature of the data. Spatial smoothers allow areas to borrow strength from neighboring regions to produce a more stable estimate of the areal value. Geostatistical smoothers are able to quantify the uncertainty in smoothed rate estimates without a high computational burden. In this paper, we introduce a uniform model extension of Bayesian Maximum Entropy (UMBME) and compare its performance to that of Poisson kriging in measures of smoothing strength and estimation accuracy as applied to simulated data and the real data example of HIV infection in North Carolina. The aim is to produce more reliable maps of disease rates in small areas to improve identification of spatial trends at the local level. In all data environments, Poisson kriging exhibited greater smoothing strength than UMBME. With the simulated data where the true latent rate of infection was known, Poisson kriging resulted in greater estimation accuracy with data that displayed low spatial autocorrelation, while UMBME provided more accurate estimators with data that displayed higher spatial autocorrelation. With the HIV data, UMBME performed slightly better than Poisson kriging in cross-validatory predictive checks, with both models performing better than the observed data model with no smoothing. Smoothing methods have different advantages depending upon both internal model assumptions that affect smoothing strength and external data environments, such as spatial correlation of the observed data. Further model comparisons in different data environments are required to provide public health practitioners with guidelines needed in choosing the most appropriate smoothing method for their particular health dataset.

Hierarchical Bayesian Models of Subtask Learning

ERIC Educational Resources Information Center

Anglim, Jeromy; Wynton, Sarah K. A.

2015-01-01

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

Application of geostatistics to coal-resource characterization and mine planning. Final report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kauffman, P.W.; Walton, D.R.; Martuneac, L.

1981-12-01

Geostatistics is a proven method of ore reserve estimation in many non-coal mining areas but little has been published concerning its application to coal resources. This report presents the case for using geostatistics for coal mining applications and describes how a coal mining concern can best utilize geostatistical techniques for coal resource characterization and mine planning. An overview of the theory of geostatistics is also presented. Many of the applications discussed are documented in case studies that are a part of the report. The results of an exhaustive literature search are presented and recommendations are made for needed future researchmore » and demonstration projects.« less

Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring.

PubMed

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

Overview and technical and practical aspects for use of geostatistics in hazardous-, toxic-, and radioactive-waste-site investigations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bossong, C.R.; Karlinger, M.R.; Troutman, B.M.

1999-10-01

Technical and practical aspects of applying geostatistics are developed for individuals involved in investigation at hazardous-, toxic-, and radioactive-waste sites. Important geostatistical concepts, such as variograms and ordinary, universal, and indicator kriging, are described in general terms for introductory purposes and in more detail for practical applications. Variogram modeling using measured ground-water elevation data is described in detail to illustrate principles of stationarity, anisotropy, transformations, and cross validation. Several examples of kriging applications are described using ground-water-level elevations, bedrock elevations, and ground-water-quality data. A review of contemporary literature and selected public domain software associated with geostatistics also is provided, asmore » is a discussion of alternative methods for spatial modeling, including inverse distance weighting, triangulation, splines, trend-surface analysis, and simulation.« less

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

ERIC Educational Resources Information Center

Levy, Roy

2014-01-01

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

Theory-based Bayesian Models of Inductive Inference

DTIC Science & Technology

2010-07-19

Subjective randomness and natural scene statistics. Psychonomic Bulletin & Review . http://cocosci.berkeley.edu/tom/papers/randscenes.pdf Page 1...in press). Exemplar models as a mechanism for performing Bayesian inference. Psychonomic Bulletin & Review . http://cocosci.berkeley.edu/tom

Modeling Error Distributions of Growth Curve Models through Bayesian Methods

ERIC Educational Resources Information Center

Zhang, Zhiyong

2016-01-01

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…

The Use of Geostatistics in the Study of Floral Phenology of Vulpia geniculata (L.) Link

PubMed Central

León Ruiz, Eduardo J.; García Mozo, Herminia; Domínguez Vilches, Eugenio; Galán, Carmen

2012-01-01

Traditionally phenology studies have been focused on changes through time, but there exist many instances in ecological research where it is necessary to interpolate among spatially stratified samples. The combined use of Geographical Information Systems (GIS) and Geostatistics can be an essential tool for spatial analysis in phenological studies. Geostatistics are a family of statistics that describe correlations through space/time and they can be used for both quantifying spatial correlation and interpolating unsampled points. In the present work, estimations based upon Geostatistics and GIS mapping have enabled the construction of spatial models that reflect phenological evolution of Vulpia geniculata (L.) Link throughout the study area during sampling season. Ten sampling points, scattered troughout the city and low mountains in the “Sierra de Córdoba” were chosen to carry out the weekly phenological monitoring during flowering season. The phenological data were interpolated by applying the traditional geostatitical method of Kriging, which was used to ellaborate weekly estimations of V. geniculata phenology in unsampled areas. Finally, the application of Geostatistics and GIS to create phenological maps could be an essential complement in pollen aerobiological studies, given the increased interest in obtaining automatic aerobiological forecasting maps. PMID:22629169

The use of geostatistics in the study of floral phenology of Vulpia geniculata (L.) link.

PubMed

León Ruiz, Eduardo J; García Mozo, Herminia; Domínguez Vilches, Eugenio; Galán, Carmen

2012-01-01

Traditionally phenology studies have been focused on changes through time, but there exist many instances in ecological research where it is necessary to interpolate among spatially stratified samples. The combined use of Geographical Information Systems (GIS) and Geostatistics can be an essential tool for spatial analysis in phenological studies. Geostatistics are a family of statistics that describe correlations through space/time and they can be used for both quantifying spatial correlation and interpolating unsampled points. In the present work, estimations based upon Geostatistics and GIS mapping have enabled the construction of spatial models that reflect phenological evolution of Vulpia geniculata (L.) Link throughout the study area during sampling season. Ten sampling points, scattered throughout the city and low mountains in the "Sierra de Córdoba" were chosen to carry out the weekly phenological monitoring during flowering season. The phenological data were interpolated by applying the traditional geostatitical method of Kriging, which was used to elaborate weekly estimations of V. geniculata phenology in unsampled areas. Finally, the application of Geostatistics and GIS to create phenological maps could be an essential complement in pollen aerobiological studies, given the increased interest in obtaining automatic aerobiological forecasting maps.

A Bayesian Alternative for Multi-objective Ecohydrological Model Specification

NASA Astrophysics Data System (ADS)

Tang, Y.; Marshall, L. A.; Sharma, A.; Ajami, H.

2015-12-01

Process-based ecohydrological models combine the study of hydrological, physical, biogeochemical and ecological processes of the catchments, which are usually more complex and parametric than conceptual hydrological models. Thus, appropriate calibration objectives and model uncertainty analysis are essential for ecohydrological modeling. In recent years, Bayesian inference has become one of the most popular tools for quantifying the uncertainties in hydrological modeling with the development of Markov Chain Monte Carlo (MCMC) techniques. Our study aims to develop appropriate prior distributions and likelihood functions that minimize the model uncertainties and bias within a Bayesian ecohydrological framework. In our study, a formal Bayesian approach is implemented in an ecohydrological model which combines a hydrological model (HyMOD) and a dynamic vegetation model (DVM). Simulations focused on one objective likelihood (Streamflow/LAI) and multi-objective likelihoods (Streamflow and LAI) with different weights are compared. Uniform, weakly informative and strongly informative prior distributions are used in different simulations. The Kullback-leibler divergence (KLD) is used to measure the dis(similarity) between different priors and corresponding posterior distributions to examine the parameter sensitivity. Results show that different prior distributions can strongly influence posterior distributions for parameters, especially when the available data is limited or parameters are insensitive to the available data. We demonstrate differences in optimized parameters and uncertainty limits in different cases based on multi-objective likelihoods vs. single objective likelihoods. We also demonstrate the importance of appropriately defining the weights of objectives in multi-objective calibration according to different data types.

Incorporating reservoir heterogeneity with geostatistics to investigate waterflood recoveries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wolcott, D.S.; Chopra, A.K.

1993-03-01

This paper presents an investigation of infill drilling performance and reservoir continuity with geostatistics and a reservoir simulator. The geostatistical technique provides many possible realizations and realistic descriptions of reservoir heterogeneity. Correlation between recovery efficiency and thickness of individual sand subunits is shown. Additional recovery from infill drilling results from thin, discontinuous subunits. The technique may be applied to variations in continuity for other sandstone reservoirs.

Cross-validation to select Bayesian hierarchical models in phylogenetics.

PubMed

Duchêne, Sebastián; Duchêne, David A; Di Giallonardo, Francesca; Eden, John-Sebastian; Geoghegan, Jemma L; Holt, Kathryn E; Ho, Simon Y W; Holmes, Edward C

2016-05-26

Recent developments in Bayesian phylogenetic models have increased the range of inferences that can be drawn from molecular sequence data. Accordingly, model selection has become an important component of phylogenetic analysis. Methods of model selection generally consider the likelihood of the data under the model in question. In the context of Bayesian phylogenetics, the most common approach involves estimating the marginal likelihood, which is typically done by integrating the likelihood across model parameters, weighted by the prior. Although this method is accurate, it is sensitive to the presence of improper priors. We explored an alternative approach based on cross-validation that is widely used in evolutionary analysis. This involves comparing models according to their predictive performance. We analysed simulated data and a range of viral and bacterial data sets using a cross-validation approach to compare a variety of molecular clock and demographic models. Our results show that cross-validation can be effective in distinguishing between strict- and relaxed-clock models and in identifying demographic models that allow growth in population size over time. In most of our empirical data analyses, the model selected using cross-validation was able to match that selected using marginal-likelihood estimation. The accuracy of cross-validation appears to improve with longer sequence data, particularly when distinguishing between relaxed-clock models. Cross-validation is a useful method for Bayesian phylogenetic model selection. This method can be readily implemented even when considering complex models where selecting an appropriate prior for all parameters may be difficult.

A comparison of machine learning and Bayesian modelling for molecular serotyping.

PubMed

Newton, Richard; Wernisch, Lorenz

2017-08-11

Streptococcus pneumoniae is a human pathogen that is a major cause of infant mortality. Identifying the pneumococcal serotype is an important step in monitoring the impact of vaccines used to protect against disease. Genomic microarrays provide an effective method for molecular serotyping. Previously we developed an empirical Bayesian model for the classification of serotypes from a molecular serotyping array. With only few samples available, a model driven approach was the only option. In the meanwhile, several thousand samples have been made available to us, providing an opportunity to investigate serotype classification by machine learning methods, which could complement the Bayesian model. We compare the performance of the original Bayesian model with two machine learning algorithms: Gradient Boosting Machines and Random Forests. We present our results as an example of a generic strategy whereby a preliminary probabilistic model is complemented or replaced by a machine learning classifier once enough data are available. Despite the availability of thousands of serotyping arrays, a problem encountered when applying machine learning methods is the lack of training data containing mixtures of serotypes; due to the large number of possible combinations. Most of the available training data comprises samples with only a single serotype. To overcome the lack of training data we implemented an iterative analysis, creating artificial training data of serotype mixtures by combining raw data from single serotype arrays. With the enhanced training set the machine learning algorithms out perform the original Bayesian model. However, for serotypes currently lacking sufficient training data the best performing implementation was a combination of the results of the Bayesian Model and the Gradient Boosting Machine. As well as being an effective method for classifying biological data, machine learning can also be used as an efficient method for revealing subtle biological

Bayesian Model Selection under Time Constraints

NASA Astrophysics Data System (ADS)

Hoege, M.; Nowak, W.; Illman, W. A.

2017-12-01

Bayesian model selection (BMS) provides a consistent framework for rating and comparing models in multi-model inference. In cases where models of vastly different complexity compete with each other, we also face vastly different computational runtimes of such models. For instance, time series of a quantity of interest can be simulated by an autoregressive process model that takes even less than a second for one run, or by a partial differential equations-based model with runtimes up to several hours or even days. The classical BMS is based on a quantity called Bayesian model evidence (BME). It determines the model weights in the selection process and resembles a trade-off between bias of a model and its complexity. However, in practice, the runtime of models is another weight relevant factor for model selection. Hence, we believe that it should be included, leading to an overall trade-off problem between bias, variance and computing effort. We approach this triple trade-off from the viewpoint of our ability to generate realizations of the models under a given computational budget. One way to obtain BME values is through sampling-based integration techniques. We argue with the fact that more expensive models can be sampled much less under time constraints than faster models (in straight proportion to their runtime). The computed evidence in favor of a more expensive model is statistically less significant than the evidence computed in favor of a faster model, since sampling-based strategies are always subject to statistical sampling error. We present a straightforward way to include this misbalance into the model weights that are the basis for model selection. Our approach follows directly from the idea of insufficient significance. It is based on a computationally cheap bootstrapping error estimate of model evidence and is easy to implement. The approach is illustrated in a small synthetic modeling study.

Geostatistics and GIS: tools for characterizing environmental contamination.

PubMed

Henshaw, Shannon L; Curriero, Frank C; Shields, Timothy M; Glass, Gregory E; Strickland, Paul T; Breysse, Patrick N

2004-08-01

Geostatistics is a set of statistical techniques used in the analysis of georeferenced data that can be applied to environmental contamination and remediation studies. In this study, the 1,1-dichloro-2,2-bis(p-chlorophenyl)ethylene (DDE) contamination at a Superfund site in western Maryland is evaluated. Concern about the site and its future clean up has triggered interest within the community because residential development surrounds the area. Spatial statistical methods, of which geostatistics is a subset, are becoming increasingly popular, in part due to the availability of geographic information system (GIS) software in a variety of application packages. In this article, the joint use of ArcGIS software and the R statistical computing environment are demonstrated as an approach for comprehensive geostatistical analyses. The spatial regression method, kriging, is used to provide predictions of DDE levels at unsampled locations both within the site and the surrounding areas where residential development is ongoing.

Semiparametric Thurstonian Models for Recurrent Choices: A Bayesian Analysis

ERIC Educational Resources Information Center

Ansari, Asim; Iyengar, Raghuram

2006-01-01

We develop semiparametric Bayesian Thurstonian models for analyzing repeated choice decisions involving multinomial, multivariate binary or multivariate ordinal data. Our modeling framework has multiple components that together yield considerable flexibility in modeling preference utilities, cross-sectional heterogeneity and parameter-driven…

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

PubMed

Houseman, E Andres; Virji, M Abbas

2017-08-01

Direct reading instruments are valuable tools for measuring exposure as they provide real-time measurements for rapid decision making. However, their use is limited to general survey applications in part due to issues related to their performance. Moreover, statistical analysis of real-time data is complicated by autocorrelation among successive measurements, non-stationary time series, and the presence of left-censoring due to limit-of-detection (LOD). A Bayesian framework is proposed that accounts for non-stationary autocorrelation and LOD issues in exposure time-series data in order to model workplace factors that affect exposure and estimate summary statistics for tasks or other covariates of interest. A spline-based approach is used to model non-stationary autocorrelation with relatively few assumptions about autocorrelation structure. Left-censoring is addressed by integrating over the left tail of the distribution. The model is fit using Markov-Chain Monte Carlo within a Bayesian paradigm. The method can flexibly account for hierarchical relationships, random effects and fixed effects of covariates. The method is implemented using the rjags package in R, and is illustrated by applying it to real-time exposure data. Estimates for task means and covariates from the Bayesian model are compared to those from conventional frequentist models including linear regression, mixed-effects, and time-series models with different autocorrelation structures. Simulations studies are also conducted to evaluate method performance. Simulation studies with percent of measurements below the LOD ranging from 0 to 50% showed lowest root mean squared errors for task means and the least biased standard deviations from the Bayesian model compared to the frequentist models across all levels of LOD. In the application, task means from the Bayesian model were similar to means from the frequentist models, while the standard deviations were different. Parameter estimates for covariates

Truth, models, model sets, AIC, and multimodel inference: a Bayesian perspective

USGS Publications Warehouse

Barker, Richard J.; Link, William A.

2015-01-01

Statistical inference begins with viewing data as realizations of stochastic processes. Mathematical models provide partial descriptions of these processes; inference is the process of using the data to obtain a more complete description of the stochastic processes. Wildlife and ecological scientists have become increasingly concerned with the conditional nature of model-based inference: what if the model is wrong? Over the last 2 decades, Akaike's Information Criterion (AIC) has been widely and increasingly used in wildlife statistics for 2 related purposes, first for model choice and second to quantify model uncertainty. We argue that for the second of these purposes, the Bayesian paradigm provides the natural framework for describing uncertainty associated with model choice and provides the most easily communicated basis for model weighting. Moreover, Bayesian arguments provide the sole justification for interpreting model weights (including AIC weights) as coherent (mathematically self consistent) model probabilities. This interpretation requires treating the model as an exact description of the data-generating mechanism. We discuss the implications of this assumption, and conclude that more emphasis is needed on model checking to provide confidence in the quality of inference.

Bayesian Semiparametric Structural Equation Models with Latent Variables

ERIC Educational Resources Information Center

Yang, Mingan; Dunson, David B.

2010-01-01

Structural equation models (SEMs) with latent variables are widely useful for sparse covariance structure modeling and for inferring relationships among latent variables. Bayesian SEMs are appealing in allowing for the incorporation of prior information and in providing exact posterior distributions of unknowns, including the latent variables. In…

Competing risk models in reliability systems, a weibull distribution model with bayesian analysis approach

NASA Astrophysics Data System (ADS)

Iskandar, Ismed; Satria Gondokaryono, Yudi

2016-02-01

In reliability theory, the most important problem is to determine the reliability of a complex system from the reliability of its components. The weakness of most reliability theories is that the systems are described and explained as simply functioning or failed. In many real situations, the failures may be from many causes depending upon the age and the environment of the system and its components. Another problem in reliability theory is one of estimating the parameters of the assumed failure models. The estimation may be based on data collected over censored or uncensored life tests. In many reliability problems, the failure data are simply quantitatively inadequate, especially in engineering design and maintenance system. The Bayesian analyses are more beneficial than the classical one in such cases. The Bayesian estimation analyses allow us to combine past knowledge or experience in the form of an apriori distribution with life test data to make inferences of the parameter of interest. In this paper, we have investigated the application of the Bayesian estimation analyses to competing risk systems. The cases are limited to the models with independent causes of failure by using the Weibull distribution as our model. A simulation is conducted for this distribution with the objectives of verifying the models and the estimators and investigating the performance of the estimators for varying sample size. The simulation data are analyzed by using Bayesian and the maximum likelihood analyses. The simulation results show that the change of the true of parameter relatively to another will change the value of standard deviation in an opposite direction. For a perfect information on the prior distribution, the estimation methods of the Bayesian analyses are better than those of the maximum likelihood. The sensitivity analyses show some amount of sensitivity over the shifts of the prior locations. They also show the robustness of the Bayesian analysis within the range

Performance prediction using geostatistics and window reservoir simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fontanilla, J.P.; Al-Khalawi, A.A.; Johnson, S.G.

1995-11-01

This paper is the first window model study in the northern area of a large carbonate reservoir in Saudi Arabia. It describes window reservoir simulation with geostatistics to model uneven water encroachment in the southwest producing area of the northern portion of the reservoir. In addition, this paper describes performance predictions that investigate the sweep efficiency of the current peripheral waterflood. A 50 x 50 x 549 (240 m. x 260 m. x 0.15 m. average grid block size) geological model was constructed with geostatistics software. Conditional simulation was used to obtain spatial distributions of porosity and volume of dolomite.more » Core data transforms were used to obtain horizontal and vertical permeability distributions. Simple averaging techniques were used to convert the 549-layer geological model to a 50 x 50 x 10 (240 m. x 260 m. x 8 m. average grid block size) window reservoir simulation model. Flux injectors and flux producers were assigned to the outermost grid blocks. Historical boundary flux rates were obtained from a coarsely-ridded full-field model. Pressure distribution, water cuts, GORs, and recent flowmeter data were history matched. Permeability correction factors and numerous parameter adjustments were required to obtain the final history match. The permeability correction factors were based on pressure transient permeability-thickness analyses. The prediction phase of the study evaluated the effects of infill drilling, the use of artificial lifts, workovers, horizontal wells, producing rate constraints, and tight zone development to formulate depletion strategies for the development of this area. The window model will also be used to investigate day-to-day reservoir management problems in this area.« less

Geostatistical Prediction of Microbial Water Quality Throughout a Stream Network Using Meteorology, Land Cover, and Spatiotemporal Autocorrelation.

PubMed

Holcomb, David A; Messier, Kyle P; Serre, Marc L; Rowny, Jakob G; Stewart, Jill R

2018-06-25

Predictive modeling is promising as an inexpensive tool to assess water quality. We developed geostatistical predictive models of microbial water quality that empirically modeled spatiotemporal autocorrelation in measured fecal coliform (FC) bacteria concentrations to improve prediction. We compared five geostatistical models featuring different autocorrelation structures, fit to 676 observations from 19 locations in North Carolina's Jordan Lake watershed using meteorological and land cover predictor variables. Though stream distance metrics (with and without flow-weighting) failed to improve prediction over the Euclidean distance metric, incorporating temporal autocorrelation substantially improved prediction over the space-only models. We predicted FC throughout the stream network daily for one year, designating locations "impaired", "unimpaired", or "unassessed" if the probability of exceeding the state standard was ≥90%, ≤10%, or >10% but <90%, respectively. We could assign impairment status to more of the stream network on days any FC were measured, suggesting frequent sample-based monitoring remains necessary, though implementing spatiotemporal predictive models may reduce the number of concurrent sampling locations required to adequately assess water quality. Together, these results suggest that prioritizing sampling at different times and conditions using geographically sparse monitoring networks is adequate to build robust and informative geostatistical models of water quality impairment.

Geostatistical enhancement of european hydrological predictions

NASA Astrophysics Data System (ADS)

Pugliese, Alessio; Castellarin, Attilio; Parajka, Juraj; Arheimer, Berit; Bagli, Stefano; Mazzoli, Paolo; Montanari, Alberto; Blöschl, Günter

2016-04-01

second phase, we develop a module, to be added to the flow-duration curve prediction framework, capable of enhancing E-HYPE-based predictions of FDCs by modelling the residuals obtained from the first phase. Among all possible methods, we apply geostatistical modelling of residuals and, alternatively, regional regression, so that residuals between empirical and E-HYPE-base predicted FDCs are described in terms of geomorphological and climatic catchment descriptors.

Delineating Hydrofacies Spatial Distribution by Integrating Ensemble Data Assimilation and Indicator Geostatistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Xuehang; Chen, Xingyuan; Ye, Ming

2015-07-01

This study develops a new framework of facies-based data assimilation for characterizing spatial distribution of hydrofacies and estimating their associated hydraulic properties. This framework couples ensemble data assimilation with transition probability-based geostatistical model via a parameterization based on a level set function. The nature of ensemble data assimilation makes the framework efficient and flexible to be integrated with various types of observation data. The transition probability-based geostatistical model keeps the updated hydrofacies distributions under geological constrains. The framework is illustrated by using a two-dimensional synthetic study that estimates hydrofacies spatial distribution and permeability in each hydrofacies from transient head data.more » Our results show that the proposed framework can characterize hydrofacies distribution and associated permeability with adequate accuracy even with limited direct measurements of hydrofacies. Our study provides a promising starting point for hydrofacies delineation in complex real problems.« less

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.

PubMed

Daunizeau, J; Friston, K J; Kiebel, S J

2009-11-01

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

Bayesian selection of misspecified models is overconfident and may cause spurious posterior probabilities for phylogenetic trees.

PubMed

Yang, Ziheng; Zhu, Tianqi

2018-02-20

The Bayesian method is noted to produce spuriously high posterior probabilities for phylogenetic trees in analysis of large datasets, but the precise reasons for this overconfidence are unknown. In general, the performance of Bayesian selection of misspecified models is poorly understood, even though this is of great scientific interest since models are never true in real data analysis. Here we characterize the asymptotic behavior of Bayesian model selection and show that when the competing models are equally wrong, Bayesian model selection exhibits surprising and polarized behaviors in large datasets, supporting one model with full force while rejecting the others. If one model is slightly less wrong than the other, the less wrong model will eventually win when the amount of data increases, but the method may become overconfident before it becomes reliable. We suggest that this extreme behavior may be a major factor for the spuriously high posterior probabilities for evolutionary trees. The philosophical implications of our results to the application of Bayesian model selection to evaluate opposing scientific hypotheses are yet to be explored, as are the behaviors of non-Bayesian methods in similar situations.

A Hierarchical Multivariate Bayesian Approach to Ensemble Model output Statistics in Atmospheric Prediction

DTIC Science & Technology

2017-09-01

efficacy of statistical post-processing methods downstream of these dynamical model components with a hierarchical multivariate Bayesian approach to...Bayesian hierarchical modeling, Markov chain Monte Carlo methods , Metropolis algorithm, machine learning, atmospheric prediction 15. NUMBER OF PAGES...scale processes. However, this dissertation explores the efficacy of statistical post-processing methods downstream of these dynamical model components

Impact of censoring on learning Bayesian networks in survival modelling.

PubMed

Stajduhar, Ivan; Dalbelo-Basić, Bojana; Bogunović, Nikola

2009-11-01

Bayesian networks are commonly used for presenting uncertainty and covariate interactions in an easily interpretable way. Because of their efficient inference and ability to represent causal relationships, they are an excellent choice for medical decision support systems in diagnosis, treatment, and prognosis. Although good procedures for learning Bayesian networks from data have been defined, their performance in learning from censored survival data has not been widely studied. In this paper, we explore how to use these procedures to learn about possible interactions between prognostic factors and their influence on the variate of interest. We study how censoring affects the probability of learning correct Bayesian network structures. Additionally, we analyse the potential usefulness of the learnt models for predicting the time-independent probability of an event of interest. We analysed the influence of censoring with a simulation on synthetic data sampled from randomly generated Bayesian networks. We used two well-known methods for learning Bayesian networks from data: a constraint-based method and a score-based method. We compared the performance of each method under different levels of censoring to those of the naive Bayes classifier and the proportional hazards model. We did additional experiments on several datasets from real-world medical domains. The machine-learning methods treated censored cases in the data as event-free. We report and compare results for several commonly used model evaluation metrics. On average, the proportional hazards method outperformed other methods in most censoring setups. As part of the simulation study, we also analysed structural similarities of the learnt networks. Heavy censoring, as opposed to no censoring, produces up to a 5% surplus and up to 10% missing total arcs. It also produces up to 50% missing arcs that should originally be connected to the variate of interest. Presented methods for learning Bayesian networks from

Bayesian state space models for dynamic genetic network construction across multiple tissues.

PubMed

Liang, Yulan; Kelemen, Arpad

2016-08-01

Construction of gene-gene interaction networks and potential pathways is a challenging and important problem in genomic research for complex diseases while estimating the dynamic changes of the temporal correlations and non-stationarity are the keys in this process. In this paper, we develop dynamic state space models with hierarchical Bayesian settings to tackle this challenge for inferring the dynamic profiles and genetic networks associated with disease treatments. We treat both the stochastic transition matrix and the observation matrix time-variant and include temporal correlation structures in the covariance matrix estimations in the multivariate Bayesian state space models. The unevenly spaced short time courses with unseen time points are treated as hidden state variables. Hierarchical Bayesian approaches with various prior and hyper-prior models with Monte Carlo Markov Chain and Gibbs sampling algorithms are used to estimate the model parameters and the hidden state variables. We apply the proposed Hierarchical Bayesian state space models to multiple tissues (liver, skeletal muscle, and kidney) Affymetrix time course data sets following corticosteroid (CS) drug administration. Both simulation and real data analysis results show that the genomic changes over time and gene-gene interaction in response to CS treatment can be well captured by the proposed models. The proposed dynamic Hierarchical Bayesian state space modeling approaches could be expanded and applied to other large scale genomic data, such as next generation sequence (NGS) combined with real time and time varying electronic health record (EHR) for more comprehensive and robust systematic and network based analysis in order to transform big biomedical data into predictions and diagnostics for precision medicine and personalized healthcare with better decision making and patient outcomes.

A Bayesian model for visual space perception

NASA Technical Reports Server (NTRS)

Curry, R. E.

1972-01-01

A model for visual space perception is proposed that contains desirable features in the theories of Gibson and Brunswik. This model is a Bayesian processor of proximal stimuli which contains three important elements: an internal model of the Markov process describing the knowledge of the distal world, the a priori distribution of the state of the Markov process, and an internal model relating state to proximal stimuli. The universality of the model is discussed and it is compared with signal detection theory models. Experimental results of Kinchla are used as a special case.

A Bayesian approach to model structural error and input variability in groundwater modeling

NASA Astrophysics Data System (ADS)

Xu, T.; Valocchi, A. J.; Lin, Y. F. F.; Liang, F.

2015-12-01

Effective water resource management typically relies on numerical models to analyze groundwater flow and solute transport processes. Model structural error (due to simplification and/or misrepresentation of the "true" environmental system) and input forcing variability (which commonly arises since some inputs are uncontrolled or estimated with high uncertainty) are ubiquitous in groundwater models. Calibration that overlooks errors in model structure and input data can lead to biased parameter estimates and compromised predictions. We present a fully Bayesian approach for a complete assessment of uncertainty for spatially distributed groundwater models. The approach explicitly recognizes stochastic input and uses data-driven error models based on nonparametric kernel methods to account for model structural error. We employ exploratory data analysis to assist in specifying informative prior for error models to improve identifiability. The inference is facilitated by an efficient sampling algorithm based on DREAM-ZS and a parameter subspace multiple-try strategy to reduce the required number of forward simulations of the groundwater model. We demonstrate the Bayesian approach through a synthetic case study of surface-ground water interaction under changing pumping conditions. It is found that explicit treatment of errors in model structure and input data (groundwater pumping rate) has substantial impact on the posterior distribution of groundwater model parameters. Using error models reduces predictive bias caused by parameter compensation. In addition, input variability increases parametric and predictive uncertainty. The Bayesian approach allows for a comparison among the contributions from various error sources, which could inform future model improvement and data collection efforts on how to best direct resources towards reducing predictive uncertainty.

Conditioning geostatistical simulations of a heterogeneous paleo-fluvial bedrock aquifer using lithologs and pumping tests

NASA Astrophysics Data System (ADS)

Niazi, A.; Bentley, L. R.; Hayashi, M.

2016-12-01

Geostatistical simulations are used to construct heterogeneous aquifer models. Optimally, such simulations should be conditioned with both lithologic and hydraulic data. We introduce an approach to condition lithologic geostatistical simulations of a paleo-fluvial bedrock aquifer consisting of relatively high permeable sandstone channels embedded in relatively low permeable mudstone using hydraulic data. The hydraulic data consist of two-hour single well pumping tests extracted from the public water well database for a 250-km2 watershed in Alberta, Canada. First, lithologic models of the entire watershed are simulated and conditioned with hard lithological data using transition probability - Markov chain geostatistics (TPROGS). Then, a segment of the simulation around a pumping well is used to populate a flow model (FEFLOW) with either sand or mudstone. The values of the hydraulic conductivity and specific storage of sand and mudstone are then adjusted to minimize the difference between simulated and actual pumping test data using the parameter estimation program PEST. If the simulated pumping test data do not adequately match the measured data, the lithologic model is updated by locally deforming the lithology distribution using the probability perturbation method and the model parameters are again updated with PEST. This procedure is repeated until the simulated and measured data agree within a pre-determined tolerance. The procedure is repeated for each well that has pumping test data. The method creates a local groundwater model that honors both the lithologic model and pumping test data and provides estimates of hydraulic conductivity and specific storage. Eventually, the simulations will be integrated into a watershed-scale groundwater model.

Using Bayesian Stable Isotope Mixing Models to Enhance Marine Ecosystem Models

EPA Science Inventory

The use of stable isotopes in food web studies has proven to be a valuable tool for ecologists. We investigated the use of Bayesian stable isotope mixing models as constraints for an ecosystem model of a temperate seagrass system on the Atlantic coast of France. δ13C and δ15N i...

A Bayesian hierarchical diffusion model decomposition of performance in Approach–Avoidance Tasks

PubMed Central

Krypotos, Angelos-Miltiadis; Beckers, Tom; Kindt, Merel; Wagenmakers, Eric-Jan

2015-01-01

Common methods for analysing response time (RT) tasks, frequently used across different disciplines of psychology, suffer from a number of limitations such as the failure to directly measure the underlying latent processes of interest and the inability to take into account the uncertainty associated with each individual's point estimate of performance. Here, we discuss a Bayesian hierarchical diffusion model and apply it to RT data. This model allows researchers to decompose performance into meaningful psychological processes and to account optimally for individual differences and commonalities, even with relatively sparse data. We highlight the advantages of the Bayesian hierarchical diffusion model decomposition by applying it to performance on Approach–Avoidance Tasks, widely used in the emotion and psychopathology literature. Model fits for two experimental data-sets demonstrate that the model performs well. The Bayesian hierarchical diffusion model overcomes important limitations of current analysis procedures and provides deeper insight in latent psychological processes of interest. PMID:25491372

Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach.

PubMed

Duarte, Belmiro P M; Wong, Weng Kee

2015-08-01

This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted.

Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach

PubMed Central

Duarte, Belmiro P. M.; Wong, Weng Kee

2014-01-01

Summary This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted. PMID:26512159

Predicting coastal cliff erosion using a Bayesian probabilistic model

USGS Publications Warehouse

Hapke, Cheryl J.; Plant, Nathaniel G.

2010-01-01

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

Usability and potential of geostatistics for spatial discrimination of multiple sclerosis lesion patterns.

PubMed

Marschallinger, Robert; Golaszewski, Stefan M; Kunz, Alexander B; Kronbichler, Martin; Ladurner, Gunther; Hofmann, Peter; Trinka, Eugen; McCoy, Mark; Kraus, Jörg

2014-01-01

In multiple sclerosis (MS) the individual disease courses are very heterogeneous among patients and biomarkers for setting the diagnosis and the estimation of the prognosis for individual patients would be very helpful. For this purpose, we are developing a multidisciplinary method and workflow for the quantitative, spatial, and spatiotemporal analysis and characterization of MS lesion patterns from MRI with geostatistics. We worked on a small data set involving three synthetic and three real-world MS lesion patterns, covering a wide range of possible MS lesion configurations. After brain normalization, MS lesions were extracted and the resulting binary 3-dimensional models of MS lesion patterns were subject to geostatistical indicator variography in three orthogonal directions. By applying geostatistical indicator variography, we were able to describe the 3-dimensional spatial structure of MS lesion patterns in a standardized manner. Fitting a model function to the empirical variograms, spatial characteristics of the MS lesion patterns could be expressed and quantified by two parameters. An orthogonal plot of these parameters enabled a well-arranged comparison of the involved MS lesion patterns. This method in development is a promising candidate to complement standard image-based statistics by incorporating spatial quantification. The work flow is generic and not limited to analyzing MS lesion patterns. It can be completely automated for the screening of radiological archives. Copyright © 2013 by the American Society of Neuroimaging.

On the Adequacy of Bayesian Evaluations of Categorization Models: Reply to Vanpaemel and Lee (2012)

ERIC Educational Resources Information Center

Wills, Andy J.; Pothos, Emmanuel M.

2012-01-01

Vanpaemel and Lee (2012) argued, and we agree, that the comparison of formal models can be facilitated by Bayesian methods. However, Bayesian methods neither precede nor supplant our proposals (Wills & Pothos, 2012), as Bayesian methods can be applied both to our proposals and to their polar opposites. Furthermore, the use of Bayesian methods to…

Bayesian Estimation of the Logistic Positive Exponent IRT Model

ERIC Educational Resources Information Center

Bolfarine, Heleno; Bazan, Jorge Luis

2010-01-01

A Bayesian inference approach using Markov Chain Monte Carlo (MCMC) is developed for the logistic positive exponent (LPE) model proposed by Samejima and for a new skewed Logistic Item Response Theory (IRT) model, named Reflection LPE model. Both models lead to asymmetric item characteristic curves (ICC) and can be appropriate because a symmetric…

On the Bayesian Nonparametric Generalization of IRT-Type Models

ERIC Educational Resources Information Center

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…

Spatial analysis of groundwater levels using Fuzzy Logic and geostatistical tools

NASA Astrophysics Data System (ADS)

Theodoridou, P. G.; Varouchakis, E. A.; Karatzas, G. P.

2017-12-01

The spatial variability evaluation of the water table of an aquifer provides useful information in water resources management plans. Geostatistical methods are often employed to map the free surface of an aquifer. In geostatistical analysis using Kriging techniques the selection of the optimal variogram is very important for the optimal method performance. This work compares three different criteria to assess the theoretical variogram that fits to the experimental one: the Least Squares Sum method, the Akaike Information Criterion and the Cressie's Indicator. Moreover, variable distance metrics such as the Euclidean, Minkowski, Manhattan, Canberra and Bray-Curtis are applied to calculate the distance between the observation and the prediction points, that affects both the variogram calculation and the Kriging estimator. A Fuzzy Logic System is then applied to define the appropriate neighbors for each estimation point used in the Kriging algorithm. The two criteria used during the Fuzzy Logic process are the distance between observation and estimation points and the groundwater level value at each observation point. The proposed techniques are applied to a data set of 250 hydraulic head measurements distributed over an alluvial aquifer. The analysis showed that the Power-law variogram model and Manhattan distance metric within ordinary kriging provide the best results when the comprehensive geostatistical analysis process is applied. On the other hand, the Fuzzy Logic approach leads to a Gaussian variogram model and significantly improves the estimation performance. The two different variogram models can be explained in terms of a fractional Brownian motion approach and of aquifer behavior at local scale. Finally, maps of hydraulic head spatial variability and of predictions uncertainty are constructed for the area with the two different approaches comparing their advantages and drawbacks.

Introduction to This Special Issue on Geostatistics and Geospatial Techniques in Remote Sensing

NASA Technical Reports Server (NTRS)

Atkinson, Peter; Quattrochi, Dale A.; Goodman, H. Michael (Technical Monitor)

2000-01-01

The germination of this special Computers & Geosciences (C&G) issue began at the Royal Geographical Society (with the Institute of British Geographers) (RGS-IBG) annual meeting in January 1997 held at the University of Exeter, UK. The snow and cold of the English winter were tempered greatly by warm and cordial discussion of how to stimulate and enhance cooperation on geostatistical and geospatial research in remote sensing 'across the big pond' between UK and US researchers. It was decided that one way forward would be to hold parallel sessions in 1998 on geostatistical and geospatial research in remote sensing at appropriate venues in both the UK and the US. Selected papers given at these sessions would be published as special issues of C&G on the UK side and Photogrammetric Engineering and Remote Sensing (PE&RS) on the US side. These issues would highlight the commonality in research on geostatistical and geospatial research in remote sensing on both sides of the Atlantic Ocean. As a consequence, a session on "Geostatistics and Geospatial Techniques for Remote Sensing of Land Surface Processes" was held at the RGS-IBG annual meeting in Guildford, Surrey, UK in January 1998, organized by the Modeling and Advanced Techniques Special Interest Group (MAT SIG) of the Remote Sensing Society (RSS). A similar session was held at the Association of American Geographers (AAG) annual meeting in Boston, Massachusetts in March 1998, sponsored by the AAG's Remote Sensing Specialty Group (RSSG). The 10 papers that make up this issue of C&G, comprise 7 papers from the UK and 3 papers from the LIS. We are both co-editors of each of the journal special issues, with the lead editor of each journal issue being from their respective side of the Atlantic. The special issue of PE&RS (vol. 65) that constitutes the other half of this co-edited journal series was published in early 1999, comprising 6 papers by US authors. We are indebted to the International Association for Mathematical

Linking big models to big data: efficient ecosystem model calibration through Bayesian model emulation

NASA Astrophysics Data System (ADS)

Fer, I.; Kelly, R.; Andrews, T.; Dietze, M.; Richardson, A. D.

2016-12-01

Our ability to forecast ecosystems is limited by how well we parameterize ecosystem models. Direct measurements for all model parameters are not always possible and inverse estimation of these parameters through Bayesian methods is computationally costly. A solution to computational challenges of Bayesian calibration is to approximate the posterior probability surface using a Gaussian Process that emulates the complex process-based model. Here we report the integration of this method within an ecoinformatics toolbox, Predictive Ecosystem Analyzer (PEcAn), and its application with two ecosystem models: SIPNET and ED2.1. SIPNET is a simple model, allowing application of MCMC methods both to the model itself and to its emulator. We used both approaches to assimilate flux (CO2 and latent heat), soil respiration, and soil carbon data from Bartlett Experimental Forest. This comparison showed that emulator is reliable in terms of convergence to the posterior distribution. A 10000-iteration MCMC analysis with SIPNET itself required more than two orders of magnitude greater computation time than an MCMC run of same length with its emulator. This difference would be greater for a more computationally demanding model. Validation of the emulator-calibrated SIPNET against both the assimilated data and out-of-sample data showed improved fit and reduced uncertainty around model predictions. We next applied the validated emulator method to the ED2, whose complexity precludes standard Bayesian data assimilation. We used the ED2 emulator to assimilate demographic data from a network of inventory plots. For validation of the calibrated ED2, we compared the model to results from Empirical Succession Mapping (ESM), a novel synthesis of successional patterns in Forest Inventory and Analysis data. Our results revealed that while the pre-assimilation ED2 formulation cannot capture the emergent demographic patterns from ESM analysis, constrained model parameters controlling demographic

A Hierarchical Bayesian Model for Crowd Emotions

PubMed Central

Urizar, Oscar J.; Baig, Mirza S.; Barakova, Emilia I.; Regazzoni, Carlo S.; Marcenaro, Lucio; Rauterberg, Matthias

2016-01-01

Estimation of emotions is an essential aspect in developing intelligent systems intended for crowded environments. However, emotion estimation in crowds remains a challenging problem due to the complexity in which human emotions are manifested and the capability of a system to perceive them in such conditions. This paper proposes a hierarchical Bayesian model to learn in unsupervised manner the behavior of individuals and of the crowd as a single entity, and explore the relation between behavior and emotions to infer emotional states. Information about the motion patterns of individuals are described using a self-organizing map, and a hierarchical Bayesian network builds probabilistic models to identify behaviors and infer the emotional state of individuals and the crowd. This model is trained and tested using data produced from simulated scenarios that resemble real-life environments. The conducted experiments tested the efficiency of our method to learn, detect and associate behaviors with emotional states yielding accuracy levels of 74% for individuals and 81% for the crowd, similar in performance with existing methods for pedestrian behavior detection but with novel concepts regarding the analysis of crowds. PMID:27458366

Geostatistical radar-raingauge combination with nonparametric correlograms: methodological considerations and application in Switzerland

NASA Astrophysics Data System (ADS)

Schiemann, R.; Erdin, R.; Willi, M.; Frei, C.; Berenguer, M.; Sempere-Torres, D.

2011-05-01

Modelling spatial covariance is an essential part of all geostatistical methods. Traditionally, parametric semivariogram models are fit from available data. More recently, it has been suggested to use nonparametric correlograms obtained from spatially complete data fields. Here, both estimation techniques are compared. Nonparametric correlograms are shown to have a substantial negative bias. Nonetheless, when combined with the sample variance of the spatial field under consideration, they yield an estimate of the semivariogram that is unbiased for small lag distances. This justifies the use of this estimation technique in geostatistical applications. Various formulations of geostatistical combination (Kriging) methods are used here for the construction of hourly precipitation grids for Switzerland based on data from a sparse realtime network of raingauges and from a spatially complete radar composite. Two variants of Ordinary Kriging (OK) are used to interpolate the sparse gauge observations. In both OK variants, the radar data are only used to determine the semivariogram model. One variant relies on a traditional parametric semivariogram estimate, whereas the other variant uses the nonparametric correlogram. The variants are tested for three cases and the impact of the semivariogram model on the Kriging prediction is illustrated. For the three test cases, the method using nonparametric correlograms performs equally well or better than the traditional method, and at the same time offers great practical advantages. Furthermore, two variants of Kriging with external drift (KED) are tested, both of which use the radar data to estimate nonparametric correlograms, and as the external drift variable. The first KED variant has been used previously for geostatistical radar-raingauge merging in Catalonia (Spain). The second variant is newly proposed here and is an extension of the first. Both variants are evaluated for the three test cases as well as an extended evaluation

Geostatistical radar-raingauge combination with nonparametric correlograms: methodological considerations and application in Switzerland

NASA Astrophysics Data System (ADS)

Schiemann, R.; Erdin, R.; Willi, M.; Frei, C.; Berenguer, M.; Sempere-Torres, D.

2010-09-01

Modelling spatial covariance is an essential part of all geostatistical methods. Traditionally, parametric semivariogram models are fit from available data. More recently, it has been suggested to use nonparametric correlograms obtained from spatially complete data fields. Here, both estimation techniques are compared. Nonparametric correlograms are shown to have a substantial negative bias. Nonetheless, when combined with the sample variance of the spatial field under consideration, they yield an estimate of the semivariogram that is unbiased for small lag distances. This justifies the use of this estimation technique in geostatistical applications. Various formulations of geostatistical combination (Kriging) methods are used here for the construction of hourly precipitation grids for Switzerland based on data from a sparse realtime network of raingauges and from a spatially complete radar composite. Two variants of Ordinary Kriging (OK) are used to interpolate the sparse gauge observations. In both OK variants, the radar data are only used to determine the semivariogram model. One variant relies on a traditional parametric semivariogram estimate, whereas the other variant uses the nonparametric correlogram. The variants are tested for three cases and the impact of the semivariogram model on the Kriging prediction is illustrated. For the three test cases, the method using nonparametric correlograms performs equally well or better than the traditional method, and at the same time offers great practical advantages. Furthermore, two variants of Kriging with external drift (KED) are tested, both of which use the radar data to estimate nonparametric correlograms, and as the external drift variable. The first KED variant has been used previously for geostatistical radar-raingauge merging in Catalonia (Spain). The second variant is newly proposed here and is an extension of the first. Both variants are evaluated for the three test cases as well as an extended evaluation

ON THE GEOSTATISTICAL APPROACH TO THE INVERSE PROBLEM. (R825689C037)

EPA Science Inventory

Abstract

The geostatistical approach to the inverse problem is discussed with emphasis on the importance of structural analysis. Although the geostatistical approach is occasionally misconstrued as mere cokriging, in fact it consists of two steps: estimation of statist...

Using river distance and existing hydrography data can improve the geostatistical estimation of fish tissue mercury at unsampled locations.

PubMed

Money, Eric S; Sackett, Dana K; Aday, D Derek; Serre, Marc L

2011-09-15

Mercury in fish tissue is a major human health concern. Consumption of mercury-contaminated fish poses risks to the general population, including potentially serious developmental defects and neurological damage in young children. Therefore, it is important to accurately identify areas that have the potential for high levels of bioaccumulated mercury. However, due to time and resource constraints, it is difficult to adequately assess fish tissue mercury on a basin wide scale. We hypothesized that, given the nature of fish movement along streams, an analytical approach that takes into account distance traveled along these streams would improve the estimation accuracy for fish tissue mercury in unsampled streams. Therefore, we used a river-based Bayesian Maximum Entropy framework (river-BME) for modern space/time geostatistics to estimate fish tissue mercury at unsampled locations in the Cape Fear and Lumber Basins in eastern North Carolina. We also compared the space/time geostatistical estimation using river-BME to the more traditional Euclidean-based BME approach, with and without the inclusion of a secondary variable. Results showed that this river-based approach reduced the estimation error of fish tissue mercury by more than 13% and that the median estimate of fish tissue mercury exceeded the EPA action level of 0.3 ppm in more than 90% of river miles for the study domain.

Precipitation estimation in mountainous terrain using multivariate geostatistics. Part I: structural analysis

USGS Publications Warehouse

Hevesi, Joseph A.; Istok, Jonathan D.; Flint, Alan L.

1992-01-01

Values of average annual precipitation (AAP) are desired for hydrologic studies within a watershed containing Yucca Mountain, Nevada, a potential site for a high-level nuclear-waste repository. Reliable values of AAP are not yet available for most areas within this watershed because of a sparsity of precipitation measurements and the need to obtain measurements over a sufficient length of time. To estimate AAP over the entire watershed, historical precipitation data and station elevations were obtained from a network of 62 stations in southern Nevada and southeastern California. Multivariate geostatistics (cokriging) was selected as an estimation method because of a significant (p = 0.05) correlation of r = .75 between the natural log of AAP and station elevation. A sample direct variogram for the transformed variable, TAAP = ln [(AAP) 1000], was fitted with an isotropic, spherical model defined by a small nugget value of 5000, a range of 190 000 ft, and a sill value equal to the sample variance of 163 151. Elevations for 1531 additional locations were obtained from topographic maps to improve the accuracy of cokriged estimates. A sample direct variogram for elevation was fitted with an isotropic model consisting of a nugget value of 5500 and three nested transition structures: a Gaussian structure with a range of 61 000 ft, a spherical structure with a range of 70 000 ft, and a quasi-stationary, linear structure. The use of an isotropic, stationary model for elevation was considered valid within a sliding-neighborhood radius of 120 000 ft. The problem of fitting a positive-definite, nonlinear model of coregionalization to an inconsistent sample cross variogram for TAAP and elevation was solved by a modified use of the Cauchy-Schwarz inequality. A selected cross-variogram model consisted of two nested structures: a Gaussian structure with a range of 61 000 ft and a spherical structure with a range of 190 000 ft. Cross validation was used for model selection and for

A Bayesian modification to the Jelinski-Moranda software reliability growth model

NASA Technical Reports Server (NTRS)

Littlewood, B.; Sofer, A.

1983-01-01

The Jelinski-Moranda (JM) model for software reliability was examined. It is suggested that a major reason for the poor results given by this model is the poor performance of the maximum likelihood method (ML) of parameter estimation. A reparameterization and Bayesian analysis, involving a slight modelling change, are proposed. It is shown that this new Bayesian-Jelinski-Moranda model (BJM) is mathematically quite tractable, and several metrics of interest to practitioners are obtained. The BJM and JM models are compared by using several sets of real software failure data collected and in all cases the BJM model gives superior reliability predictions. A change in the assumption which underlay both models to present the debugging process more accurately is discussed.

The Applications of Model-Based Geostatistics in Helminth Epidemiology and Control

PubMed Central

Magalhães, Ricardo J. Soares; Clements, Archie C.A.; Patil, Anand P.; Gething, Peter W.; Brooker, Simon

2011-01-01

Funding agencies are dedicating substantial resources to tackle helminth infections. Reliable maps of the distribution of helminth infection can assist these efforts by targeting control resources to areas of greatest need. The ability to define the distribution of infection at regional, national and subnational levels has been enhanced greatly by the increased availability of good quality survey data and the use of model-based geostatistics (MBG), enabling spatial prediction in unsampled locations. A major advantage of MBG risk mapping approaches is that they provide a flexible statistical platform for handling and representing different sources of uncertainty, providing plausible and robust information on the spatial distribution of infections to inform the design and implementation of control programmes. Focussing on schistosomiasis and soil-transmitted helminthiasis, with additional examples for lymphatic filariasis and onchocerciasis, we review the progress made to date with the application of MBG tools in large-scale, real-world control programmes and propose a general framework for their application to inform integrative spatial planning of helminth disease control programmes. PMID:21295680

The applications of model-based geostatistics in helminth epidemiology and control.

PubMed

Magalhães, Ricardo J Soares; Clements, Archie C A; Patil, Anand P; Gething, Peter W; Brooker, Simon

2011-01-01

Funding agencies are dedicating substantial resources to tackle helminth infections. Reliable maps of the distribution of helminth infection can assist these efforts by targeting control resources to areas of greatest need. The ability to define the distribution of infection at regional, national and subnational levels has been enhanced greatly by the increased availability of good quality survey data and the use of model-based geostatistics (MBG), enabling spatial prediction in unsampled locations. A major advantage of MBG risk mapping approaches is that they provide a flexible statistical platform for handling and representing different sources of uncertainty, providing plausible and robust information on the spatial distribution of infections to inform the design and implementation of control programmes. Focussing on schistosomiasis and soil-transmitted helminthiasis, with additional examples for lymphatic filariasis and onchocerciasis, we review the progress made to date with the application of MBG tools in large-scale, real-world control programmes and propose a general framework for their application to inform integrative spatial planning of helminth disease control programmes. Copyright © 2011 Elsevier Ltd. All rights reserved.

A Bayesian Multilevel Model for Microcystin Prediction in ...

EPA Pesticide Factsheets

The frequency of cyanobacteria blooms in North American lakes is increasing. A major concernwith rising cyanobacteria blooms is microcystin, a common cyanobacterial hepatotoxin. Toexplore the conditions that promote high microcystin concentrations, we analyzed the US EPANational Lake Assessment (NLA) dataset collected in the summer of 2007. The NLA datasetis reported for nine eco-regions. We used the results of random forest modeling as a means ofvariable selection from which we developed a Bayesian multilevel model of microcystin concentrations.Model parameters under a multilevel modeling framework are eco-region specific, butthey are also assumed to be exchangeable across eco-regions for broad continental scaling. Theexchangeability assumption ensures that both the common patterns and eco-region specific featureswill be reflected in the model. Furthermore, the method incorporates appropriate estimatesof uncertainty. Our preliminary results show associations between microcystin and turbidity, totalnutrients, and N:P ratios. The NLA 2012 will be used for Bayesian updating. The results willhelp develop management strategies to alleviate microcystin impacts and improve lake quality. This work provides a probabilistic framework for predicting microcystin presences in lakes. It would allow for insights to be made about how changes in nutrient concentrations could potentially change toxin levels.

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

PubMed Central

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

2016-01-01

Cognitive determinants of probabilistic inference were examined using hierarchical Bayesian modeling techniques. A classic urn-ball paradigm served as experimental strategy, involving a factorial two (prior probabilities) by two (likelihoods) design. Five computational models of cognitive processes were compared with the observed behavior. Parameter-free Bayesian posterior probabilities and parameter-free base rate neglect provided inadequate models of probabilistic inference. The introduction of distorted subjective probabilities yielded more robust and generalizable results. A general class of (inverted) S-shaped probability weighting functions had been proposed; however, the possibility of large differences in probability distortions not only across experimental conditions, but also across individuals, seems critical for the model's success. It also seems advantageous to consider individual differences in parameters of probability weighting as being sampled from weakly informative prior distributions of individual parameter values. Thus, the results from hierarchical Bayesian modeling converge with previous results in revealing that probability weighting parameters show considerable task dependency and individual differences. Methodologically, this work exemplifies the usefulness of hierarchical Bayesian modeling techniques for cognitive psychology. Theoretically, human probabilistic inference might be best described as the application of individualized strategic policies for Bayesian belief revision. PMID:27303323

A Bayesian estimation of a stochastic predator-prey model of economic fluctuations

NASA Astrophysics Data System (ADS)

Dibeh, Ghassan; Luchinsky, Dmitry G.; Luchinskaya, Daria D.; Smelyanskiy, Vadim N.

2007-06-01

In this paper, we develop a Bayesian framework for the empirical estimation of the parameters of one of the best known nonlinear models of the business cycle: The Marx-inspired model of a growth cycle introduced by R. M. Goodwin. The model predicts a series of closed cycles representing the dynamics of labor's share and the employment rate in the capitalist economy. The Bayesian framework is used to empirically estimate a modified Goodwin model. The original model is extended in two ways. First, we allow for exogenous periodic variations of the otherwise steady growth rates of the labor force and productivity per worker. Second, we allow for stochastic variations of those parameters. The resultant modified Goodwin model is a stochastic predator-prey model with periodic forcing. The model is then estimated using a newly developed Bayesian estimation method on data sets representing growth cycles in France and Italy during the years 1960-2005. Results show that inference of the parameters of the stochastic Goodwin model can be achieved. The comparison of the dynamics of the Goodwin model with the inferred values of parameters demonstrates quantitative agreement with the growth cycle empirical data.

Estimating virus occurrence using Bayesian modeling in multiple drinking water systems of the United States

USGS Publications Warehouse

Varughese, Eunice A.; Brinkman, Nichole E; Anneken, Emily M; Cashdollar, Jennifer S; Fout, G. Shay; Furlong, Edward T.; Kolpin, Dana W.; Glassmeyer, Susan T.; Keely, Scott P

2017-01-01

incorporated into a Bayesian model to more accurately determine viral load in both source and treated water. Results of the Bayesian model indicated that viruses are present in source water and treated water. By using a Bayesian framework that incorporates inhibition, as well as many other parameters that affect viral detection, this study offers an approach for more accurately estimating the occurrence of viral pathogens in environmental waters.

The Bayesian reader: explaining word recognition as an optimal Bayesian decision process.

PubMed

Norris, Dennis

2006-04-01

This article presents a theory of visual word recognition that assumes that, in the tasks of word identification, lexical decision, and semantic categorization, human readers behave as optimal Bayesian decision makers. This leads to the development of a computational model of word recognition, the Bayesian reader. The Bayesian reader successfully simulates some of the most significant data on human reading. The model accounts for the nature of the function relating word frequency to reaction time and identification threshold, the effects of neighborhood density and its interaction with frequency, and the variation in the pattern of neighborhood density effects seen in different experimental tasks. Both the general behavior of the model and the way the model predicts different patterns of results in different tasks follow entirely from the assumption that human readers approximate optimal Bayesian decision makers. ((c) 2006 APA, all rights reserved).

Incorporating geologic information into hydraulic tomography: A general framework based on geostatistical approach

NASA Astrophysics Data System (ADS)

Zha, Yuanyuan; Yeh, Tian-Chyi J.; Illman, Walter A.; Onoe, Hironori; Mok, Chin Man W.; Wen, Jet-Chau; Huang, Shao-Yang; Wang, Wenke

2017-04-01

Hydraulic tomography (HT) has become a mature aquifer test technology over the last two decades. It collects nonredundant information of aquifer heterogeneity by sequentially stressing the aquifer at different wells and collecting aquifer responses at other wells during each stress. The collected information is then interpreted by inverse models. Among these models, the geostatistical approaches, built upon the Bayesian framework, first conceptualize hydraulic properties to be estimated as random fields, which are characterized by means and covariance functions. They then use the spatial statistics as prior information with the aquifer response data to estimate the spatial distribution of the hydraulic properties at a site. Since the spatial statistics describe the generic spatial structures of the geologic media at the site rather than site-specific ones (e.g., known spatial distributions of facies, faults, or paleochannels), the estimates are often not optimal. To improve the estimates, we introduce a general statistical framework, which allows the inclusion of site-specific spatial patterns of geologic features. Subsequently, we test this approach with synthetic numerical experiments. Results show that this approach, using conditional mean and covariance that reflect site-specific large-scale geologic features, indeed improves the HT estimates. Afterward, this approach is applied to HT surveys at a kilometer-scale-fractured granite field site with a distinct fault zone. We find that by including fault information from outcrops and boreholes for HT analysis, the estimated hydraulic properties are improved. The improved estimates subsequently lead to better prediction of flow during a different pumping test at the site.

Bayesian hierarchical model of ceftriaxone resistance proportions among Salmonella serotype Heidelberg infections.

PubMed

Gu, Weidong; Medalla, Felicita; Hoekstra, Robert M

2018-02-01

The National Antimicrobial Resistance Monitoring System (NARMS) at the Centers for Disease Control and Prevention tracks resistance among Salmonella infections. The annual number of Salmonella isolates of a particular serotype from states may be small, making direct estimation of resistance proportions unreliable. We developed a Bayesian hierarchical model to improve estimation by borrowing strength from relevant sampling units. We illustrate the models with different specifications of spatio-temporal interaction using 2004-2013 NARMS data for ceftriaxone-resistant Salmonella serotype Heidelberg. Our results show that Bayesian estimates of resistance proportions were smoother than observed values, and the difference between predicted and observed proportions was inversely related to the number of submitted isolates. The model with interaction allowed for tracking of annual changes in resistance proportions at the state level. We demonstrated that Bayesian hierarchical models provide a useful tool to examine spatio-temporal patterns of small sample size such as those found in NARMS. Published by Elsevier Ltd.

Invited commentary: Lost in estimation--searching for alternatives to markov chains to fit complex Bayesian models.

PubMed

Molitor, John

2012-03-01

Bayesian methods have seen an increase in popularity in a wide variety of scientific fields, including epidemiology. One of the main reasons for their widespread application is the power of the Markov chain Monte Carlo (MCMC) techniques generally used to fit these models. As a result, researchers often implicitly associate Bayesian models with MCMC estimation procedures. However, Bayesian models do not always require Markov-chain-based methods for parameter estimation. This is important, as MCMC estimation methods, while generally quite powerful, are complex and computationally expensive and suffer from convergence problems related to the manner in which they generate correlated samples used to estimate probability distributions for parameters of interest. In this issue of the Journal, Cole et al. (Am J Epidemiol. 2012;175(5):368-375) present an interesting paper that discusses non-Markov-chain-based approaches to fitting Bayesian models. These methods, though limited, can overcome some of the problems associated with MCMC techniques and promise to provide simpler approaches to fitting Bayesian models. Applied researchers will find these estimation approaches intuitively appealing and will gain a deeper understanding of Bayesian models through their use. However, readers should be aware that other non-Markov-chain-based methods are currently in active development and have been widely published in other fields.

Robust spatialization of soil water content at the scale of an agricultural field using geophysical and geostatistical methods

NASA Astrophysics Data System (ADS)

Henine, Hocine; Tournebize, Julien; Laurent, Gourdol; Christophe, Hissler; Cournede, Paul-Henry; Clement, Remi

2017-04-01

Research on the Critical Zone (CZ) is a prerequisite for undertaking issues related to ecosystemic services that human societies rely on (nutrient cycles, water supply and quality). However, while the upper part of CZ (vegetation, soil, surface water) is readily accessible, knowledge of the subsurface remains limited, due to the point-scale character of conventional direct observations. While the potential for geophysical methods to overcome this limitation is recognized, the translation of the geophysical information into physical properties or states of interest remains a challenge (e.g. the translation of soil electrical resistivity into soil water content). In this study, we propose a geostatistical framework using the Bayesian Maximum Entropy (BME) approach to assimilate geophysical and point-scale data. We especially focus on the prediction of the spatial distribution of soil water content using (1) TDR point-scale measurements of soil water content, which are considered as accurate data, and (2) soil water content data derived from electrical resistivity measurements, which are uncertain data but spatially dense. We used a synthetic dataset obtained with a vertical 2D domain to evaluate the performance of this geostatistical approach. Spatio-temporal simulations of soil water content were carried out using Hydrus-software for different scenarios: homogeneous or heterogeneous hydraulic conductivity distribution, and continuous or punctual infiltration pattern. From the simulations of soil water content, conceptual soil resistivity models were built using a forward modeling approach and point sampling of water content values, vertically ranged, were done. These two datasets are similar to field measurements of soil electrical resistivity (using electrical resistivity tomography, ERT) and soil water content (using TDR probes) obtained at the Boissy-le-Chatel site, in Orgeval catchment (East of Paris, France). We then integrated them into a specialization

A Bayesian Approach for Analyzing Longitudinal Structural Equation Models

ERIC Educational Resources Information Center

Song, Xin-Yuan; Lu, Zhao-Hua; Hser, Yih-Ing; Lee, Sik-Yum

2011-01-01

This article considers a Bayesian approach for analyzing a longitudinal 2-level nonlinear structural equation model with covariates, and mixed continuous and ordered categorical variables. The first-level model is formulated for measures taken at each time point nested within individuals for investigating their characteristics that are dynamically…

Bayesian Estimation of the DINA Model with Gibbs Sampling

ERIC Educational Resources Information Center

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,…

Precise Network Modeling of Systems Genetics Data Using the Bayesian Network Webserver.

PubMed

Ziebarth, Jesse D; Cui, Yan

2017-01-01

The Bayesian Network Webserver (BNW, http://compbio.uthsc.edu/BNW ) is an integrated platform for Bayesian network modeling of biological datasets. It provides a web-based network modeling environment that seamlessly integrates advanced algorithms for probabilistic causal modeling and reasoning with Bayesian networks. BNW is designed for precise modeling of relatively small networks that contain less than 20 nodes. The structure learning algorithms used by BNW guarantee the discovery of the best (most probable) network structure given the data. To facilitate network modeling across multiple biological levels, BNW provides a very flexible interface that allows users to assign network nodes into different tiers and define the relationships between and within the tiers. This function is particularly useful for modeling systems genetics datasets that often consist of multiscalar heterogeneous genotype-to-phenotype data. BNW enables users to, within seconds or minutes, go from having a simply formatted input file containing a dataset to using a network model to make predictions about the interactions between variables and the potential effects of experimental interventions. In this chapter, we will introduce the functions of BNW and show how to model systems genetics datasets with BNW.

Metrics for evaluating performance and uncertainty of Bayesian network models

Treesearch

Bruce G. Marcot

2012-01-01

This paper presents a selected set of existing and new metrics for gauging Bayesian network model performance and uncertainty. Selected existing and new metrics are discussed for conducting model sensitivity analysis (variance reduction, entropy reduction, case file simulation); evaluating scenarios (influence analysis); depicting model complexity (numbers of model...

Assessment of spatial distribution of fallout radionuclides through geostatistics concept.

PubMed

Mabit, L; Bernard, C

2007-01-01

After introducing geostatistics concept and its utility in environmental science and especially in Fallout Radionuclide (FRN) spatialisation, a case study for cesium-137 ((137)Cs) redistribution at the field scale using geostatistics is presented. On a Canadian agricultural field, geostatistics coupled with a Geographic Information System (GIS) was used to test three different techniques of interpolation [Ordinary Kriging (OK), Inverse Distance Weighting power one (IDW1) and two (IDW2)] to create a (137)Cs map and to establish a radioisotope budget. Following the optimization of variographic parameters, an experimental semivariogram was developed to determine the spatial dependence of (137)Cs. It was adjusted to a spherical isotropic model with a range of 30 m and a very small nugget effect. This (137)Cs semivariogram showed a good autocorrelation (R(2)=0.91) and was well structured ('nugget-to-sill' ratio of 4%). It also revealed that the sampling strategy was adequate to reveal the spatial correlation of (137)Cs. The spatial redistribution of (137)Cs was estimated by Ordinary Kriging and IDW to produce contour maps. A radioisotope budget was established for the 2.16 ha agricultural field under investigation. It was estimated that around 2 x 10(7)Bq of (137)Cs were missing (around 30% of the total initial fallout) and were exported by physical processes (runoff and erosion processes) from the area under investigation. The cross-validation analysis showed that in the case of spatially structured data, OK is a better interpolation method than IDW1 or IDW2 for the assessment of potential radioactive contamination and/or pollution.

Geospatial interpolation and mapping of tropospheric ozone pollution using geostatistics.

PubMed

Kethireddy, Swatantra R; Tchounwou, Paul B; Ahmad, Hafiz A; Yerramilli, Anjaneyulu; Young, John H

2014-01-10

Tropospheric ozone (O3) pollution is a major problem worldwide, including in the United States of America (USA), particularly during the summer months. Ozone oxidative capacity and its impact on human health have attracted the attention of the scientific community. In the USA, sparse spatial observations for O3 may not provide a reliable source of data over a geo-environmental region. Geostatistical Analyst in ArcGIS has the capability to interpolate values in unmonitored geo-spaces of interest. In this study of eastern Texas O3 pollution, hourly episodes for spring and summer 2012 were selectively identified. To visualize the O3 distribution, geostatistical techniques were employed in ArcMap. Using ordinary Kriging, geostatistical layers of O3 for all the studied hours were predicted and mapped at a spatial resolution of 1 kilometer. A decent level of prediction accuracy was achieved and was confirmed from cross-validation results. The mean prediction error was close to 0, the root mean-standardized-prediction error was close to 1, and the root mean square and average standard errors were small. O3 pollution map data can be further used in analysis and modeling studies. Kriging results and O3 decadal trends indicate that the populace in Houston-Sugar Land-Baytown, Dallas-Fort Worth-Arlington, Beaumont-Port Arthur, San Antonio, and Longview are repeatedly exposed to high levels of O3-related pollution, and are prone to the corresponding respiratory and cardiovascular health effects. Optimization of the monitoring network proves to be an added advantage for the accurate prediction of exposure levels.

Advances in Applications of Hierarchical Bayesian Methods with Hydrological Models

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Development of an Anisotropic Geological-Based Land Use Regression and Bayesian Maximum Entropy Model for Estimating Groundwater Radon across Northing Carolina

NASA Astrophysics Data System (ADS)

Messier, K. P.; Serre, M. L.

2015-12-01

Radon (222Rn) is a naturally occurring chemically inert, colorless, and odorless radioactive gas produced from the decay of uranium (238U), which is ubiquitous in rocks and soils worldwide. Exposure to 222Rn is likely the second leading cause of lung cancer after cigarette smoking via inhalation; however, exposure through untreated groundwater is also a contributing factor to both inhalation and ingestion routes. A land use regression (LUR) model for groundwater 222Rn with anisotropic geological and 238U based explanatory variables is developed, which helps elucidate the factors contributing to elevated 222Rn across North Carolina. Geological and uranium based variables are constructed in elliptical buffers surrounding each observation such that they capture the lateral geometric anisotropy present in groundwater 222Rn. Moreover, geological features are defined at three different geological spatial scales to allow the model to distinguish between large area and small area effects of geology on groundwater 222Rn. The LUR is also integrated into the Bayesian Maximum Entropy (BME) geostatistical framework to increase accuracy and produce a point-level LUR-BME model of groundwater 222Rn across North Carolina including prediction uncertainty. The LUR-BME model of groundwater 222Rn results in a leave-one out cross-validation of 0.46 (Pearson correlation coefficient= 0.68), effectively predicting within the spatial covariance range. Modeled results of 222Rn concentrations show variability among Intrusive Felsic geological formations likely due to average bedrock 238U defined on the basis of overlying stream-sediment 238U concentrations that is a widely distributed consistently analyzed point-source data.

Robust geostatistical analysis of spatial data

NASA Astrophysics Data System (ADS)

Papritz, Andreas; Künsch, Hans Rudolf; Schwierz, Cornelia; Stahel, Werner A.

2013-04-01

Most of the geostatistical software tools rely on non-robust algorithms. This is unfortunate, because outlying observations are rather the rule than the exception, in particular in environmental data sets. Outliers affect the modelling of the large-scale spatial trend, the estimation of the spatial dependence of the residual variation and the predictions by kriging. Identifying outliers manually is cumbersome and requires expertise because one needs parameter estimates to decide which observation is a potential outlier. Moreover, inference after the rejection of some observations is problematic. A better approach is to use robust algorithms that prevent automatically that outlying observations have undue influence. Former studies on robust geostatistics focused on robust estimation of the sample variogram and ordinary kriging without external drift. Furthermore, Richardson and Welsh (1995) proposed a robustified version of (restricted) maximum likelihood ([RE]ML) estimation for the variance components of a linear mixed model, which was later used by Marchant and Lark (2007) for robust REML estimation of the variogram. We propose here a novel method for robust REML estimation of the variogram of a Gaussian random field that is possibly contaminated by independent errors from a long-tailed distribution. It is based on robustification of estimating equations for the Gaussian REML estimation (Welsh and Richardson, 1997). Besides robust estimates of the parameters of the external drift and of the variogram, the method also provides standard errors for the estimated parameters, robustified kriging predictions at both sampled and non-sampled locations and kriging variances. Apart from presenting our modelling framework, we shall present selected simulation results by which we explored the properties of the new method. This will be complemented by an analysis a data set on heavy metal contamination of the soil in the vicinity of a metal smelter. Marchant, B.P. and Lark, R

Exploring prediction uncertainty of spatial data in geostatistical and machine learning Approaches

NASA Astrophysics Data System (ADS)

Klump, J. F.; Fouedjio, F.

2017-12-01

Geostatistical methods such as kriging with external drift as well as machine learning techniques such as quantile regression forest have been intensively used for modelling spatial data. In addition to providing predictions for target variables, both approaches are able to deliver a quantification of the uncertainty associated with the prediction at a target location. Geostatistical approaches are, by essence, adequate for providing such prediction uncertainties and their behaviour is well understood. However, they often require significant data pre-processing and rely on assumptions that are rarely met in practice. Machine learning algorithms such as random forest regression, on the other hand, require less data pre-processing and are non-parametric. This makes the application of machine learning algorithms to geostatistical problems an attractive proposition. The objective of this study is to compare kriging with external drift and quantile regression forest with respect to their ability to deliver reliable prediction uncertainties of spatial data. In our comparison we use both simulated and real world datasets. Apart from classical performance indicators, comparisons make use of accuracy plots, probability interval width plots, and the visual examinations of the uncertainty maps provided by the two approaches. By comparing random forest regression to kriging we found that both methods produced comparable maps of estimated values for our variables of interest. However, the measure of uncertainty provided by random forest seems to be quite different to the measure of uncertainty provided by kriging. In particular, the lack of spatial context can give misleading results in areas without ground truth data. These preliminary results raise questions about assessing the risks associated with decisions based on the predictions from geostatistical and machine learning algorithms in a spatial context, e.g. mineral exploration.

Geostatistical mapping of effluent-affected sediment distribution on the Palos Verdes shelf

USGS Publications Warehouse

Murray, C.J.; Lee, H.J.; Hampton, M.A.

2002-01-01

Geostatistical techniques were used to study the spatial continuity of the thickness of effluent-affected sediment in the offshore Palos Verdes Margin area. The thickness data were measured directly from cores and indirectly from high-frequency subbottom profiles collected over the Palos Verdes Margin. Strong spatial continuity of the sediment thickness data was identified, with a maximum range of correlation in excess of 1.4 km. The spatial correlation showed a marked anisotropy, and was more than twice as continuous in the alongshore direction as in the cross-shelf direction. Sequential indicator simulation employing models fit to the thickness data variograms was used to map the distribution of the sediment, and to quantify the uncertainty in those estimates. A strong correlation between sediment thickness data and measurements of the mass of the contaminant p,p???-DDE per unit area was identified. A calibration based on the bivariate distribution of the thickness and p,p???-DDE data was applied using Markov-Bayes indicator simulation to extend the geostatistical study and map the contamination levels in the sediment. Integrating the map grids produced by the geostatistical study of the two variables indicated that 7.8 million m3 of effluent-affected sediment exist in the map area, containing approximately 61-72 Mg (metric tons) of p,p???-DDE. Most of the contaminated sediment (about 85% of the sediment and 89% of the p,p???-DDE) occurs in water depths < 100 m. The geostatistical study also indicated that the samples available for mapping are well distributed and the uncertainty of the estimates of the thickness and contamination level of the sediments is lowest in areas where the contaminated sediment is most prevalent. ?? 2002 Elsevier Science Ltd. All rights reserved.

A comprehensive probabilistic analysis model of oil pipelines network based on Bayesian network

NASA Astrophysics Data System (ADS)

Zhang, C.; Qin, T. X.; Jiang, B.; Huang, C.

2018-02-01

Oil pipelines network is one of the most important facilities of energy transportation. But oil pipelines network accident may result in serious disasters. Some analysis models for these accidents have been established mainly based on three methods, including event-tree, accident simulation and Bayesian network. Among these methods, Bayesian network is suitable for probabilistic analysis. But not all the important influencing factors are considered and the deployment rule of the factors has not been established. This paper proposed a probabilistic analysis model of oil pipelines network based on Bayesian network. Most of the important influencing factors, including the key environment condition and emergency response are considered in this model. Moreover, the paper also introduces a deployment rule for these factors. The model can be used in probabilistic analysis and sensitive analysis of oil pipelines network accident.

Identification of high-permeability subsurface structures with multiple point geostatistics and normal score ensemble Kalman filter

NASA Astrophysics Data System (ADS)

Zovi, Francesco; Camporese, Matteo; Hendricks Franssen, Harrie-Jan; Huisman, Johan Alexander; Salandin, Paolo

2017-05-01

Alluvial aquifers are often characterized by the presence of braided high-permeable paleo-riverbeds, which constitute an interconnected preferential flow network whose localization is of fundamental importance to predict flow and transport dynamics. Classic geostatistical approaches based on two-point correlation (i.e., the variogram) cannot describe such particular shapes. In contrast, multiple point geostatistics can describe almost any kind of shape using the empirical probability distribution derived from a training image. However, even with a correct training image the exact positions of the channels are uncertain. State information like groundwater levels can constrain the channel positions using inverse modeling or data assimilation, but the method should be able to handle non-Gaussianity of the parameter distribution. Here the normal score ensemble Kalman filter (NS-EnKF) was chosen as the inverse conditioning algorithm to tackle this issue. Multiple point geostatistics and NS-EnKF have already been tested in synthetic examples, but in this study they are used for the first time in a real-world case study. The test site is an alluvial unconfined aquifer in northeastern Italy with an extension of approximately 3 km2. A satellite training image showing the braid shapes of the nearby river and electrical resistivity tomography (ERT) images were used as conditioning data to provide information on channel shape, size, and position. Measured groundwater levels were assimilated with the NS-EnKF to update the spatially distributed groundwater parameters (hydraulic conductivity and storage coefficients). Results from the study show that the inversion based on multiple point geostatistics does not outperform the one with a multiGaussian model and that the information from the ERT images did not improve site characterization. These results were further evaluated with a synthetic study that mimics the experimental site. The synthetic results showed that only for a much

Bayesian Finite Mixtures for Nonlinear Modeling of Educational Data.

ERIC Educational Resources Information Center

Tirri, Henry; And Others

A Bayesian approach for finding latent classes in data is discussed. The approach uses finite mixture models to describe the underlying structure in the data and demonstrate that the possibility of using full joint probability models raises interesting new prospects for exploratory data analysis. The concepts and methods discussed are illustrated…

Bayesian cross-validation for model evaluation and selection, with application to the North American Breeding Bird Survey

USGS Publications Warehouse

Link, William; Sauer, John R.

2016-01-01

The analysis of ecological data has changed in two important ways over the last 15 years. The development and easy availability of Bayesian computational methods has allowed and encouraged the fitting of complex hierarchical models. At the same time, there has been increasing emphasis on acknowledging and accounting for model uncertainty. Unfortunately, the ability to fit complex models has outstripped the development of tools for model selection and model evaluation: familiar model selection tools such as Akaike's information criterion and the deviance information criterion are widely known to be inadequate for hierarchical models. In addition, little attention has been paid to the evaluation of model adequacy in context of hierarchical modeling, i.e., to the evaluation of fit for a single model. In this paper, we describe Bayesian cross-validation, which provides tools for model selection and evaluation. We describe the Bayesian predictive information criterion and a Bayesian approximation to the BPIC known as the Watanabe-Akaike information criterion. We illustrate the use of these tools for model selection, and the use of Bayesian cross-validation as a tool for model evaluation, using three large data sets from the North American Breeding Bird Survey.

Inferring Markov chains: Bayesian estimation, model comparison, entropy rate, and out-of-class modeling.

PubMed

Strelioff, Christopher C; Crutchfield, James P; Hübler, Alfred W

2007-07-01

Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer kth order Markov chains, for arbitrary k , from finite data by applying Bayesian methods to both parameter estimation and model-order selection. Extending existing results for multinomial models of discrete data, we connect inference to statistical mechanics through information-theoretic (type theory) techniques. We establish a direct relationship between Bayesian evidence and the partition function which allows for straightforward calculation of the expectation and variance of the conditional relative entropy and the source entropy rate. Finally, we introduce a method that uses finite data-size scaling with model-order comparison to infer the structure of out-of-class processes.

Bayesian exponential random graph modelling of interhospital patient referral networks.

PubMed

Caimo, Alberto; Pallotti, Francesca; Lomi, Alessandro

2017-08-15

Using original data that we have collected on referral relations between 110 hospitals serving a large regional community, we show how recently derived Bayesian exponential random graph models may be adopted to illuminate core empirical issues in research on relational coordination among healthcare organisations. We show how a rigorous Bayesian computation approach supports a fully probabilistic analytical framework that alleviates well-known problems in the estimation of model parameters of exponential random graph models. We also show how the main structural features of interhospital patient referral networks that prior studies have described can be reproduced with accuracy by specifying the system of local dependencies that produce - but at the same time are induced by - decentralised collaborative arrangements between hospitals. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Bayesian analysis of physiologically based toxicokinetic and toxicodynamic models.

PubMed

Hack, C Eric

2006-04-17

Physiologically based toxicokinetic (PBTK) and toxicodynamic (TD) models of bromate in animals and humans would improve our ability to accurately estimate the toxic doses in humans based on available animal studies. These mathematical models are often highly parameterized and must be calibrated in order for the model predictions of internal dose to adequately fit the experimentally measured doses. Highly parameterized models are difficult to calibrate and it is difficult to obtain accurate estimates of uncertainty or variability in model parameters with commonly used frequentist calibration methods, such as maximum likelihood estimation (MLE) or least squared error approaches. The Bayesian approach called Markov chain Monte Carlo (MCMC) analysis can be used to successfully calibrate these complex models. Prior knowledge about the biological system and associated model parameters is easily incorporated in this approach in the form of prior parameter distributions, and the distributions are refined or updated using experimental data to generate posterior distributions of parameter estimates. The goal of this paper is to give the non-mathematician a brief description of the Bayesian approach and Markov chain Monte Carlo analysis, how this technique is used in risk assessment, and the issues associated with this approach.

A Bayesian Multilevel Model for Microcystin Prediction in ...

EPA Pesticide Factsheets

The frequency of cyanobacteria blooms in North American lakes is increasing. A major concern with rising cyanobacteria blooms is microcystin, a common cyanobacterial hepatotoxin. To explore the conditions that promote high microcystin concentrations, we analyzed the US EPA National Lake Assessment (NLA) dataset collected in the summer of 2007. The NLA dataset is reported for nine eco-regions. We used the results of random forest modeling as a means ofvariable selection from which we developed a Bayesian multilevel model of microcystin concentrations. Model parameters under a multilevel modeling framework are eco-region specific, butthey are also assumed to be exchangeable across eco-regions for broad continental scaling. The exchangeability assumption ensures that both the common patterns and eco-region specific features will be reflected in the model. Furthermore, the method incorporates appropriate estimates of uncertainty. Our preliminary results show associations between microcystin and turbidity, total nutrients, and N:P ratios. Upon release of a comparable 2012 NLA dataset, we will apply Bayesian updating. The results will help develop management strategies to alleviate microcystin impacts and improve lake quality. This work provides a probabilistic framework for predicting microcystin presences in lakes. It would allow for insights to be made about how changes in nutrient concentrations could potentially change toxin levels.

Quantum-Like Bayesian Networks for Modeling Decision Making

PubMed Central

Moreira, Catarina; Wichert, Andreas

2016-01-01

In this work, we explore an alternative quantum structure to perform quantum probabilistic inferences to accommodate the paradoxical findings of the Sure Thing Principle. We propose a Quantum-Like Bayesian Network, which consists in replacing classical probabilities by quantum probability amplitudes. However, since this approach suffers from the problem of exponential growth of quantum parameters, we also propose a similarity heuristic that automatically fits quantum parameters through vector similarities. This makes the proposed model general and predictive in contrast to the current state of the art models, which cannot be generalized for more complex decision scenarios and that only provide an explanatory nature for the observed paradoxes. In the end, the model that we propose consists in a nonparametric method for estimating inference effects from a statistical point of view. It is a statistical model that is simpler than the previous quantum dynamic and quantum-like models proposed in the literature. We tested the proposed network with several empirical data from the literature, mainly from the Prisoner's Dilemma game and the Two Stage Gambling game. The results obtained show that the proposed quantum Bayesian Network is a general method that can accommodate violations of the laws of classical probability theory and make accurate predictions regarding human decision-making in these scenarios. PMID:26858669

A surrogate-based sensitivity quantification and Bayesian inversion of a regional groundwater flow model

NASA Astrophysics Data System (ADS)

Chen, Mingjie; Izady, Azizallah; Abdalla, Osman A.; Amerjeed, Mansoor

2018-02-01

Bayesian inference using Markov Chain Monte Carlo (MCMC) provides an explicit framework for stochastic calibration of hydrogeologic models accounting for uncertainties; however, the MCMC sampling entails a large number of model calls, and could easily become computationally unwieldy if the high-fidelity hydrogeologic model simulation is time consuming. This study proposes a surrogate-based Bayesian framework to address this notorious issue, and illustrates the methodology by inverse modeling a regional MODFLOW model. The high-fidelity groundwater model is approximated by a fast statistical model using Bagging Multivariate Adaptive Regression Spline (BMARS) algorithm, and hence the MCMC sampling can be efficiently performed. In this study, the MODFLOW model is developed to simulate the groundwater flow in an arid region of Oman consisting of mountain-coast aquifers, and used to run representative simulations to generate training dataset for BMARS model construction. A BMARS-based Sobol' method is also employed to efficiently calculate input parameter sensitivities, which are used to evaluate and rank their importance for the groundwater flow model system. According to sensitivity analysis, insensitive parameters are screened out of Bayesian inversion of the MODFLOW model, further saving computing efforts. The posterior probability distribution of input parameters is efficiently inferred from the prescribed prior distribution using observed head data, demonstrating that the presented BMARS-based Bayesian framework is an efficient tool to reduce parameter uncertainties of a groundwater system.

Common quandaries and their practical solutions in Bayesian network modeling

Treesearch

Bruce G. Marcot

2017-01-01

Use and popularity of Bayesian network (BN) modeling has greatly expanded in recent years, but many common problems remain. Here, I summarize key problems in BN model construction and interpretation,along with suggested practical solutions. Problems in BN model construction include parameterizing probability values, variable definition, complex network structures,...

A Bayesian Nonparametric Approach to Test Equating

ERIC Educational Resources Information Center

Karabatsos, George; Walker, Stephen G.

2009-01-01

A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are…

Climatic Models Ensemble-based Mid-21st Century Runoff Projections: A Bayesian Framework

NASA Astrophysics Data System (ADS)

Achieng, K. O.; Zhu, J.

2017-12-01

There are a number of North American Regional Climate Change Assessment Program (NARCCAP) climatic models that have been used to project surface runoff in the mid-21st century. Statistical model selection techniques are often used to select the model that best fits data. However, model selection techniques often lead to different conclusions. In this study, ten models are averaged in Bayesian paradigm to project runoff. Bayesian Model Averaging (BMA) is used to project and identify effect of model uncertainty on future runoff projections. Baseflow separation - a two-digital filter which is also called Eckhardt filter - is used to separate USGS streamflow (total runoff) into two components: baseflow and surface runoff. We use this surface runoff as the a priori runoff when conducting BMA of runoff simulated from the ten RCM models. The primary objective of this study is to evaluate how well RCM multi-model ensembles simulate surface runoff, in a Bayesian framework. Specifically, we investigate and discuss the following questions: How well do ten RCM models ensemble jointly simulate surface runoff by averaging over all the models using BMA, given a priori surface runoff? What are the effects of model uncertainty on surface runoff simulation?

Prospective evaluation of a Bayesian model to predict organizational change.

PubMed

Molfenter, Todd; Gustafson, Dave; Kilo, Chuck; Bhattacharya, Abhik; Olsson, Jesper

2005-01-01

This research examines a subjective Bayesian model's ability to predict organizational change outcomes and sustainability of those outcomes for project teams participating in a multi-organizational improvement collaborative.

Construction of monitoring model and algorithm design on passenger security during shipping based on improved Bayesian network.

PubMed

Wang, Jiali; Zhang, Qingnian; Ji, Wenfeng

2014-01-01

A large number of data is needed by the computation of the objective Bayesian network, but the data is hard to get in actual computation. The calculation method of Bayesian network was improved in this paper, and the fuzzy-precise Bayesian network was obtained. Then, the fuzzy-precise Bayesian network was used to reason Bayesian network model when the data is limited. The security of passengers during shipping is affected by various factors, and it is hard to predict and control. The index system that has the impact on the passenger safety during shipping was established on basis of the multifield coupling theory in this paper. Meanwhile, the fuzzy-precise Bayesian network was applied to monitor the security of passengers in the shipping process. The model was applied to monitor the passenger safety during shipping of a shipping company in Hainan, and the effectiveness of this model was examined. This research work provides guidance for guaranteeing security of passengers during shipping.

Construction of Monitoring Model and Algorithm Design on Passenger Security during Shipping Based on Improved Bayesian Network

PubMed Central

Wang, Jiali; Zhang, Qingnian; Ji, Wenfeng

2014-01-01

A large number of data is needed by the computation of the objective Bayesian network, but the data is hard to get in actual computation. The calculation method of Bayesian network was improved in this paper, and the fuzzy-precise Bayesian network was obtained. Then, the fuzzy-precise Bayesian network was used to reason Bayesian network model when the data is limited. The security of passengers during shipping is affected by various factors, and it is hard to predict and control. The index system that has the impact on the passenger safety during shipping was established on basis of the multifield coupling theory in this paper. Meanwhile, the fuzzy-precise Bayesian network was applied to monitor the security of passengers in the shipping process. The model was applied to monitor the passenger safety during shipping of a shipping company in Hainan, and the effectiveness of this model was examined. This research work provides guidance for guaranteeing security of passengers during shipping. PMID:25254227

GIS, geostatistics, metadata banking, and tree-based models for data analysis and mapping in environmental monitoring and epidemiology.

PubMed

Schröder, Winfried

2006-05-01

By the example of environmental monitoring, some applications of geographic information systems (GIS), geostatistics, metadata banking, and Classification and Regression Trees (CART) are presented. These tools are recommended for mapping statistically estimated hot spots of vectors and pathogens. GIS were introduced as tools for spatially modelling the real world. The modelling can be done by mapping objects according to the spatial information content of data. Additionally, this can be supported by geostatistical and multivariate statistical modelling. This is demonstrated by the example of modelling marine habitats of benthic communities and of terrestrial ecoregions. Such ecoregionalisations may be used to predict phenomena based on the statistical relation between measurements of an interesting phenomenon such as, e.g., the incidence of medically relevant species and correlated characteristics of the ecoregions. The combination of meteorological data and data on plant phenology can enhance the spatial resolution of the information on climate change. To this end, meteorological and phenological data have to be correlated. To enable this, both data sets which are from disparate monitoring networks have to be spatially connected by means of geostatistical estimation. This is demonstrated by the example of transformation of site-specific data on plant phenology into surface data. The analysis allows for spatial comparison of the phenology during the two periods 1961-1990 and 1991-2002 covering whole Germany. The changes in both plant phenology and air temperature were proved to be statistically significant. Thus, they can be combined by GIS overlay technique to enhance the spatial resolution of the information on the climate change and use them for the prediction of vector incidences at the regional scale. The localisation of such risk hot spots can be done by geometrically merging surface data on promoting factors. This is demonstrated by the example of the

Bayesian Sensitivity Analysis of Statistical Models with Missing Data

PubMed Central

ZHU, HONGTU; IBRAHIM, JOSEPH G.; TANG, NIANSHENG

2013-01-01

Methods for handling missing data depend strongly on the mechanism that generated the missing values, such as missing completely at random (MCAR) or missing at random (MAR), as well as other distributional and modeling assumptions at various stages. It is well known that the resulting estimates and tests may be sensitive to these assumptions as well as to outlying observations. In this paper, we introduce various perturbations to modeling assumptions and individual observations, and then develop a formal sensitivity analysis to assess these perturbations in the Bayesian analysis of statistical models with missing data. We develop a geometric framework, called the Bayesian perturbation manifold, to characterize the intrinsic structure of these perturbations. We propose several intrinsic influence measures to perform sensitivity analysis and quantify the effect of various perturbations to statistical models. We use the proposed sensitivity analysis procedure to systematically investigate the tenability of the non-ignorable missing at random (NMAR) assumption. Simulation studies are conducted to evaluate our methods, and a dataset is analyzed to illustrate the use of our diagnostic measures. PMID:24753718

Bayesian models based on test statistics for multiple hypothesis testing problems.

PubMed

Ji, Yuan; Lu, Yiling; Mills, Gordon B

2008-04-01

We propose a Bayesian method for the problem of multiple hypothesis testing that is routinely encountered in bioinformatics research, such as the differential gene expression analysis. Our algorithm is based on modeling the distributions of test statistics under both null and alternative hypotheses. We substantially reduce the complexity of the process of defining posterior model probabilities by modeling the test statistics directly instead of modeling the full data. Computationally, we apply a Bayesian FDR approach to control the number of rejections of null hypotheses. To check if our model assumptions for the test statistics are valid for various bioinformatics experiments, we also propose a simple graphical model-assessment tool. Using extensive simulations, we demonstrate the performance of our models and the utility of the model-assessment tool. In the end, we apply the proposed methodology to an siRNA screening and a gene expression experiment.

Bayesian spatiotemporal model of fMRI data using transfer functions.

PubMed

Quirós, Alicia; Diez, Raquel Montes; Wilson, Simon P

2010-09-01

This research describes a new Bayesian spatiotemporal model to analyse BOLD fMRI studies. In the temporal dimension, we describe the shape of the hemodynamic response function (HRF) with a transfer function model. The spatial continuity and local homogeneity of the evoked responses are modelled by a Gaussian Markov random field prior on the parameter indicating activations. The proposal constitutes an extension of the spatiotemporal model presented in a previous approach [Quirós, A., Montes Diez, R. and Gamerman, D., 2010. Bayesian spatiotemporal model of fMRI data, Neuroimage, 49: 442-456], offering more flexibility in the estimation of the HRF and computational advantages in the resulting MCMC algorithm. Simulations from the model are performed in order to ascertain the performance of the sampling scheme and the ability of the posterior to estimate model parameters, as well as to check the model sensitivity to signal to noise ratio. Results are shown on synthetic data and on a real data set from a block-design fMRI experiment. Copyright (c) 2010 Elsevier Inc. All rights reserved.

A Comparison of General Diagnostic Models (GDM) and Bayesian Networks Using a Middle School Mathematics Test

ERIC Educational Resources Information Center

Wu, Haiyan

2013-01-01

General diagnostic models (GDMs) and Bayesian networks are mathematical frameworks that cover a wide variety of psychometric models. Both extend latent class models, and while GDMs also extend item response theory (IRT) models, Bayesian networks can be parameterized using discretized IRT. The purpose of this study is to examine similarities and…

Bayesian model checking: A comparison of tests

NASA Astrophysics Data System (ADS)

Lucy, L. B.

2018-06-01

Two procedures for checking Bayesian models are compared using a simple test problem based on the local Hubble expansion. Over four orders of magnitude, p-values derived from a global goodness-of-fit criterion for posterior probability density functions agree closely with posterior predictive p-values. The former can therefore serve as an effective proxy for the difficult-to-calculate posterior predictive p-values.

BAYESIAN METHODS FOR REGIONAL-SCALE EUTROPHICATION MODELS. (R830887)

EPA Science Inventory

We demonstrate a Bayesian classification and regression tree (CART) approach to link multiple environmental stressors to biological responses and quantify uncertainty in model predictions. Such an approach can: (1) report prediction uncertainty, (2) be consistent with the amou...

Robust Bayesian Experimental Design for Conceptual Model Discrimination

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

Multivariate Bayesian modeling of known and unknown causes of events--an application to biosurveillance.

PubMed

Shen, Yanna; Cooper, Gregory F

2012-09-01

This paper investigates Bayesian modeling of known and unknown causes of events in the context of disease-outbreak detection. We introduce a multivariate Bayesian approach that models multiple evidential features of every person in the population. This approach models and detects (1) known diseases (e.g., influenza and anthrax) by using informative prior probabilities and (2) unknown diseases (e.g., a new, highly contagious respiratory virus that has never been seen before) by using relatively non-informative prior probabilities. We report the results of simulation experiments which support that this modeling method can improve the detection of new disease outbreaks in a population. A contribution of this paper is that it introduces a multivariate Bayesian approach for jointly modeling both known and unknown causes of events. Such modeling has general applicability in domains where the space of known causes is incomplete. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.

GEOSTATISTICAL SAMPLING DESIGNS FOR HAZARDOUS WASTE SITES

EPA Science Inventory

This chapter discusses field sampling design for environmental sites and hazardous waste sites with respect to random variable sampling theory, Gy's sampling theory, and geostatistical (kriging) sampling theory. The literature often presents these sampling methods as an adversari...

Number-Knower Levels in Young Children: Insights from Bayesian Modeling

ERIC Educational Resources Information Center

Lee, Michael D.; Sarnecka, Barbara W.

2011-01-01

Lee and Sarnecka (2010) developed a Bayesian model of young children's behavior on the Give-N test of number knowledge. This paper presents two new extensions of the model, and applies the model to new data. In the first extension, the model is used to evaluate competing theories about the conceptual knowledge underlying children's behavior. One,…

A simulation study on Bayesian Ridge regression models for several collinearity levels

NASA Astrophysics Data System (ADS)

Efendi, Achmad; Effrihan

2017-12-01

When analyzing data with multiple regression model if there are collinearities, then one or several predictor variables are usually omitted from the model. However, there sometimes some reasons, for instance medical or economic reasons, the predictors are all important and should be included in the model. Ridge regression model is not uncommon in some researches to use to cope with collinearity. Through this modeling, weights for predictor variables are used for estimating parameters. The next estimation process could follow the concept of likelihood. Furthermore, for the estimation nowadays the Bayesian version could be an alternative. This estimation method does not match likelihood one in terms of popularity due to some difficulties; computation and so forth. Nevertheless, with the growing improvement of computational methodology recently, this caveat should not at the moment become a problem. This paper discusses about simulation process for evaluating the characteristic of Bayesian Ridge regression parameter estimates. There are several simulation settings based on variety of collinearity levels and sample sizes. The results show that Bayesian method gives better performance for relatively small sample sizes, and for other settings the method does perform relatively similar to the likelihood method.

Bayesian Action–Perception Computational Model: Interaction of Production and Recognition of Cursive Letters

PubMed Central

Gilet, Estelle; Diard, Julien; Bessière, Pierre

2011-01-01

In this paper, we study the collaboration of perception and action representations involved in cursive letter recognition and production. We propose a mathematical formulation for the whole perception–action loop, based on probabilistic modeling and Bayesian inference, which we call the Bayesian Action–Perception (BAP) model. Being a model of both perception and action processes, the purpose of this model is to study the interaction of these processes. More precisely, the model includes a feedback loop from motor production, which implements an internal simulation of movement. Motor knowledge can therefore be involved during perception tasks. In this paper, we formally define the BAP model and show how it solves the following six varied cognitive tasks using Bayesian inference: i) letter recognition (purely sensory), ii) writer recognition, iii) letter production (with different effectors), iv) copying of trajectories, v) copying of letters, and vi) letter recognition (with internal simulation of movements). We present computer simulations of each of these cognitive tasks, and discuss experimental predictions and theoretical developments. PMID:21674043

Qualitative and quantitative comparison of geostatistical techniques of porosity prediction from the seismic and logging data: a case study from the Blackfoot Field, Alberta, Canada

NASA Astrophysics Data System (ADS)

Maurya, S. P.; Singh, K. H.; Singh, N. P.

2018-05-01

In present study, three recently developed geostatistical methods, single attribute analysis, multi-attribute analysis and probabilistic neural network algorithm have been used to predict porosity in inter well region for Blackfoot field, Alberta, Canada, an offshore oil field. These techniques make use of seismic attributes, generated by model based inversion and colored inversion techniques. The principle objective of the study is to find the suitable combination of seismic inversion and geostatistical techniques to predict porosity and identification of prospective zones in 3D seismic volume. The porosity estimated from these geostatistical approaches is corroborated with the well log porosity. The results suggest that all the three implemented geostatistical methods are efficient and reliable to predict the porosity but the multi-attribute and probabilistic neural network analysis provide more accurate and high resolution porosity sections. A low impedance (6000-8000 m/s g/cc) and high porosity (> 15%) zone is interpreted from inverted impedance and porosity sections respectively between 1060 and 1075 ms time interval and is characterized as reservoir. The qualitative and quantitative results demonstrate that of all the employed geostatistical methods, the probabilistic neural network along with model based inversion is the most efficient method for predicting porosity in inter well region.

Bayesian design criteria: computation, comparison, and application to a pharmacokinetic and a pharmacodynamic model.

PubMed

Merlé, Y; Mentré, F

1995-02-01

In this paper 3 criteria to design experiments for Bayesian estimation of the parameters of nonlinear models with respect to their parameters, when a prior distribution is available, are presented: the determinant of the Bayesian information matrix, the determinant of the pre-posterior covariance matrix, and the expected information provided by an experiment. A procedure to simplify the computation of these criteria is proposed in the case of continuous prior distributions and is compared with the criterion obtained from a linearization of the model about the mean of the prior distribution for the parameters. This procedure is applied to two models commonly encountered in the area of pharmacokinetics and pharmacodynamics: the one-compartment open model with bolus intravenous single-dose injection and the Emax model. They both involve two parameters. Additive as well as multiplicative gaussian measurement errors are considered with normal prior distributions. Various combinations of the variances of the prior distribution and of the measurement error are studied. Our attention is restricted to designs with limited numbers of measurements (1 or 2 measurements). This situation often occurs in practice when Bayesian estimation is performed. The optimal Bayesian designs that result vary with the variances of the parameter distribution and with the measurement error. The two-point optimal designs sometimes differ from the D-optimal designs for the mean of the prior distribution and may consist of replicating measurements. For the studied cases, the determinant of the Bayesian information matrix and its linearized form lead to the same optimal designs. In some cases, the pre-posterior covariance matrix can be far from its lower bound, namely, the inverse of the Bayesian information matrix, especially for the Emax model and a multiplicative measurement error. The expected information provided by the experiment and the determinant of the pre-posterior covariance matrix

Bayesian Statistical Inference in Ion-Channel Models with Exact Missed Event Correction.

PubMed

Epstein, Michael; Calderhead, Ben; Girolami, Mark A; Sivilotti, Lucia G

2016-07-26

The stochastic behavior of single ion channels is most often described as an aggregated continuous-time Markov process with discrete states. For ligand-gated channels each state can represent a different conformation of the channel protein or a different number of bound ligands. Single-channel recordings show only whether the channel is open or shut: states of equal conductance are aggregated, so transitions between them have to be inferred indirectly. The requirement to filter noise from the raw signal further complicates the modeling process, as it limits the time resolution of the data. The consequence of the reduced bandwidth is that openings or shuttings that are shorter than the resolution cannot be observed; these are known as missed events. Postulated models fitted using filtered data must therefore explicitly account for missed events to avoid bias in the estimation of rate parameters and therefore assess parameter identifiability accurately. In this article, we present the first, to our knowledge, Bayesian modeling of ion-channels with exact missed events correction. Bayesian analysis represents uncertain knowledge of the true value of model parameters by considering these parameters as random variables. This allows us to gain a full appreciation of parameter identifiability and uncertainty when estimating values for model parameters. However, Bayesian inference is particularly challenging in this context as the correction for missed events increases the computational complexity of the model likelihood. Nonetheless, we successfully implemented a two-step Markov chain Monte Carlo method that we called "BICME", which performs Bayesian inference in models of realistic complexity. The method is demonstrated on synthetic and real single-channel data from muscle nicotinic acetylcholine channels. We show that parameter uncertainty can be characterized more accurately than with maximum-likelihood methods. Our code for performing inference in these ion channel

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

NASA Astrophysics Data System (ADS)

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

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

Bayesian modeling of the mass and density of asteroids

NASA Astrophysics Data System (ADS)

Dotson, Jessie L.; Mathias, Donovan

2017-10-01

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

Bayesian structured additive regression modeling of epidemic data: application to cholera

PubMed Central

2012-01-01

Background A significant interest in spatial epidemiology lies in identifying associated risk factors which enhances the risk of infection. Most studies, however, make no, or limited use of the spatial structure of the data, as well as possible nonlinear effects of the risk factors. Methods We develop a Bayesian Structured Additive Regression model for cholera epidemic data. Model estimation and inference is based on fully Bayesian approach via Markov Chain Monte Carlo (MCMC) simulations. The model is applied to cholera epidemic data in the Kumasi Metropolis, Ghana. Proximity to refuse dumps, density of refuse dumps, and proximity to potential cholera reservoirs were modeled as continuous functions; presence of slum settlers and population density were modeled as fixed effects, whereas spatial references to the communities were modeled as structured and unstructured spatial effects. Results We observe that the risk of cholera is associated with slum settlements and high population density. The risk of cholera is equal and lower for communities with fewer refuse dumps, but variable and higher for communities with more refuse dumps. The risk is also lower for communities distant from refuse dumps and potential cholera reservoirs. The results also indicate distinct spatial variation in the risk of cholera infection. Conclusion The study highlights the usefulness of Bayesian semi-parametric regression model analyzing public health data. These findings could serve as novel information to help health planners and policy makers in making effective decisions to control or prevent cholera epidemics. PMID:22866662

Bayesian parameter estimation for nonlinear modelling of biological pathways.

PubMed

Ghasemi, Omid; Lindsey, Merry L; Yang, Tianyi; Nguyen, Nguyen; Huang, Yufei; Jin, Yu-Fang

2011-01-01

The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC) method. We applied this approach to the biological pathways involved in the left ventricle (LV) response to myocardial infarction (MI) and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly parameterized dynamic systems. Our proposed

Model selection on solid ground: Rigorous comparison of nine ways to evaluate Bayesian model evidence

PubMed Central

Schöniger, Anneli; Wöhling, Thomas; Samaniego, Luis; Nowak, Wolfgang

2014-01-01

Bayesian model selection or averaging objectively ranks a number of plausible, competing conceptual models based on Bayes' theorem. It implicitly performs an optimal trade-off between performance in fitting available data and minimum model complexity. The procedure requires determining Bayesian model evidence (BME), which is the likelihood of the observed data integrated over each model's parameter space. The computation of this integral is highly challenging because it is as high-dimensional as the number of model parameters. Three classes of techniques to compute BME are available, each with its own challenges and limitations: (1) Exact and fast analytical solutions are limited by strong assumptions. (2) Numerical evaluation quickly becomes unfeasible for expensive models. (3) Approximations known as information criteria (ICs) such as the AIC, BIC, or KIC (Akaike, Bayesian, or Kashyap information criterion, respectively) yield contradicting results with regard to model ranking. Our study features a theory-based intercomparison of these techniques. We further assess their accuracy in a simplistic synthetic example where for some scenarios an exact analytical solution exists. In more challenging scenarios, we use a brute-force Monte Carlo integration method as reference. We continue this analysis with a real-world application of hydrological model selection. This is a first-time benchmarking of the various methods for BME evaluation against true solutions. Results show that BME values from ICs are often heavily biased and that the choice of approximation method substantially influences the accuracy of model ranking. For reliable model selection, bias-free numerical methods should be preferred over ICs whenever computationally feasible. PMID:25745272

Robust Bayesian clustering.

PubMed

Archambeau, Cédric; Verleysen, Michel

2007-01-01

A new variational Bayesian learning algorithm for Student-t mixture models is introduced. This algorithm leads to (i) robust density estimation, (ii) robust clustering and (iii) robust automatic model selection. Gaussian mixture models are learning machines which are based on a divide-and-conquer approach. They are commonly used for density estimation and clustering tasks, but are sensitive to outliers. The Student-t distribution has heavier tails than the Gaussian distribution and is therefore less sensitive to any departure of the empirical distribution from Gaussianity. As a consequence, the Student-t distribution is suitable for constructing robust mixture models. In this work, we formalize the Bayesian Student-t mixture model as a latent variable model in a different way from Svensén and Bishop [Svensén, M., & Bishop, C. M. (2005). Robust Bayesian mixture modelling. Neurocomputing, 64, 235-252]. The main difference resides in the fact that it is not necessary to assume a factorized approximation of the posterior distribution on the latent indicator variables and the latent scale variables in order to obtain a tractable solution. Not neglecting the correlations between these unobserved random variables leads to a Bayesian model having an increased robustness. Furthermore, it is expected that the lower bound on the log-evidence is tighter. Based on this bound, the model complexity, i.e. the number of components in the mixture, can be inferred with a higher confidence.

Kinematic Structural Modelling in Bayesian Networks

NASA Astrophysics Data System (ADS)

Schaaf, Alexander; de la Varga, Miguel; Florian Wellmann, J.

2017-04-01

We commonly capture our knowledge about the spatial distribution of distinct geological lithologies in the form of 3-D geological models. Several methods exist to create these models, each with its own strengths and limitations. We present here an approach to combine the functionalities of two modeling approaches - implicit interpolation and kinematic modelling methods - into one framework, while explicitly considering parameter uncertainties and thus model uncertainty. In recent work, we proposed an approach to implement implicit modelling algorithms into Bayesian networks. This was done to address the issues of input data uncertainty and integration of geological information from varying sources in the form of geological likelihood functions. However, one general shortcoming of implicit methods is that they usually do not take any physical constraints into consideration, which can result in unrealistic model outcomes and artifacts. On the other hand, kinematic structural modelling intends to reconstruct the history of a geological system based on physically driven kinematic events. This type of modelling incorporates simplified, physical laws into the model, at the cost of a substantial increment of usable uncertain parameters. In the work presented here, we show an integration of these two different modelling methodologies, taking advantage of the strengths of both of them. First, we treat the two types of models separately, capturing the information contained in the kinematic models and their specific parameters in the form of likelihood functions, in order to use them in the implicit modelling scheme. We then go further and combine the two modelling approaches into one single Bayesian network. This enables the direct flow of information between the parameters of the kinematic modelling step and the implicit modelling step and links the exclusive input data and likelihoods of the two different modelling algorithms into one probabilistic inference framework. In

Bayesian truncation errors in chiral effective field theory: model checking and accounting for correlations

NASA Astrophysics Data System (ADS)

Melendez, Jordan; Wesolowski, Sarah; Furnstahl, Dick

2017-09-01

Chiral effective field theory (EFT) predictions are necessarily truncated at some order in the EFT expansion, which induces an error that must be quantified for robust statistical comparisons to experiment. A Bayesian model yields posterior probability distribution functions for these errors based on expectations of naturalness encoded in Bayesian priors and the observed order-by-order convergence pattern of the EFT. As a general example of a statistical approach to truncation errors, the model was applied to chiral EFT for neutron-proton scattering using various semi-local potentials of Epelbaum, Krebs, and Meißner (EKM). Here we discuss how our model can learn correlation information from the data and how to perform Bayesian model checking to validate that the EFT is working as advertised. Supported in part by NSF PHY-1614460 and DOE NUCLEI SciDAC DE-SC0008533.

Bayesian Inversion of 2D Models from Airborne Transient EM Data

NASA Astrophysics Data System (ADS)

Blatter, D. B.; Key, K.; Ray, A.

2016-12-01

The inherent non-uniqueness in most geophysical inverse problems leads to an infinite number of Earth models that fit observed data to within an adequate tolerance. To resolve this ambiguity, traditional inversion methods based on optimization techniques such as the Gauss-Newton and conjugate gradient methods rely on an additional regularization constraint on the properties that an acceptable model can possess, such as having minimal roughness. While allowing such an inversion scheme to converge on a solution, regularization makes it difficult to estimate the uncertainty associated with the model parameters. This is because regularization biases the inversion process toward certain models that satisfy the regularization constraint and away from others that don't, even when both may suitably fit the data. By contrast, a Bayesian inversion framework aims to produce not a single `most acceptable' model but an estimate of the posterior likelihood of the model parameters, given the observed data. In this work, we develop a 2D Bayesian framework for the inversion of transient electromagnetic (TEM) data. Our method relies on a reversible-jump Markov Chain Monte Carlo (RJ-MCMC) Bayesian inverse method with parallel tempering. Previous gradient-based inversion work in this area used a spatially constrained scheme wherein individual (1D) soundings were inverted together and non-uniqueness was tackled by using lateral and vertical smoothness constraints. By contrast, our work uses a 2D model space of Voronoi cells whose parameterization (including number of cells) is fully data-driven. To make the problem work practically, we approximate the forward solution for each TEM sounding using a local 1D approximation where the model is obtained from the 2D model by retrieving a vertical profile through the Voronoi cells. The implicit parsimony of the Bayesian inversion process leads to the simplest models that adequately explain the data, obviating the need for explicit smoothness

Fast genomic predictions via Bayesian G-BLUP and multilocus models of threshold traits including censored Gaussian data.

PubMed

Kärkkäinen, Hanni P; Sillanpää, Mikko J

2013-09-04

Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed.

Fast Genomic Predictions via Bayesian G-BLUP and Multilocus Models of Threshold Traits Including Censored Gaussian Data

PubMed Central

Kärkkäinen, Hanni P.; Sillanpää, Mikko J.

2013-01-01

Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed. PMID:23821618

Assessing global vegetation activity using spatio-temporal Bayesian modelling

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring

Treesearch

Carlos Carroll; Devin S. Johnson; Jeffrey R. Dunk; William J. Zielinski

2010-01-01

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...

Merging Digital Surface Models Implementing Bayesian Approaches

NASA Astrophysics Data System (ADS)

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.

Advances in Bayesian Modeling in Educational Research

ERIC Educational Resources Information Center

Levy, Roy

2016-01-01

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

Geostatistics for spatial genetic structures: study of wild populations of perennial ryegrass.

PubMed

Monestiez, P; Goulard, M; Charmet, G

1994-04-01

Methods based on geostatistics were applied to quantitative traits of agricultural interest measured on a collection of 547 wild populations of perennial ryegrass in France. The mathematical background of these methods, which resembles spatial autocorrelation analysis, is briefly described. When a single variable is studied, the spatial structure analysis is similar to spatial autocorrelation analysis, and a spatial prediction method, called "kriging", gives a filtered map of the spatial pattern over all the sampled area. When complex interactions of agronomic traits with different evaluation sites define a multivariate structure for the spatial analysis, geostatistical methods allow the spatial variations to be broken down into two main spatial structures with ranges of 120 km and 300 km, respectively. The predicted maps that corresponded to each range were interpreted as a result of the isolation-by-distance model and as a consequence of selection by environmental factors. Practical collecting methodology for breeders may be derived from such spatial structures.

APPLICATION OF BAYESIAN MONTE CARLO ANALYSIS TO A LAGRANGIAN PHOTOCHEMICAL AIR QUALITY MODEL. (R824792)

EPA Science Inventory

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 ...

Bayesian Probability Theory

NASA Astrophysics Data System (ADS)

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

2014-06-01

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

Bayesian data analysis for newcomers.

PubMed

Kruschke, John K; Liddell, Torrin M

2018-02-01

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

On-line Bayesian model updating for structural health monitoring

NASA Astrophysics Data System (ADS)

Rocchetta, Roberto; Broggi, Matteo; Huchet, Quentin; Patelli, Edoardo

2018-03-01

Fatigue induced cracks is a dangerous failure mechanism which affects mechanical components subject to alternating load cycles. System health monitoring should be adopted to identify cracks which can jeopardise the structure. Real-time damage detection may fail in the identification of the cracks due to different sources of uncertainty which have been poorly assessed or even fully neglected. In this paper, a novel efficient and robust procedure is used for the detection of cracks locations and lengths in mechanical components. A Bayesian model updating framework is employed, which allows accounting for relevant sources of uncertainty. The idea underpinning the approach is to identify the most probable crack consistent with the experimental measurements. To tackle the computational cost of the Bayesian approach an emulator is adopted for replacing the computationally costly Finite Element model. To improve the overall robustness of the procedure, different numerical likelihoods, measurement noises and imprecision in the value of model parameters are analysed and their effects quantified. The accuracy of the stochastic updating and the efficiency of the numerical procedure are discussed. An experimental aluminium frame and on a numerical model of a typical car suspension arm are used to demonstrate the applicability of the approach.

Emulation: A fast stochastic Bayesian method to eliminate model space

NASA Astrophysics Data System (ADS)

Roberts, Alan; Hobbs, Richard; Goldstein, Michael

2010-05-01

Joint inversion of large 3D datasets has been the goal of geophysicists ever since the datasets first started to be produced. There are two broad approaches to this kind of problem, traditional deterministic inversion schemes and more recently developed Bayesian search methods, such as MCMC (Markov Chain Monte Carlo). However, using both these kinds of schemes has proved prohibitively expensive, both in computing power and time cost, due to the normally very large model space which needs to be searched using forward model simulators which take considerable time to run. At the heart of strategies aimed at accomplishing this kind of inversion is the question of how to reliably and practicably reduce the size of the model space in which the inversion is to be carried out. Here we present a practical Bayesian method, known as emulation, which can address this issue. Emulation is a Bayesian technique used with considerable success in a number of technical fields, such as in astronomy, where the evolution of the universe has been modelled using this technique, and in the petroleum industry where history matching is carried out of hydrocarbon reservoirs. The method of emulation involves building a fast-to-compute uncertainty-calibrated approximation to a forward model simulator. We do this by modelling the output data from a number of forward simulator runs by a computationally cheap function, and then fitting the coefficients defining this function to the model parameters. By calibrating the error of the emulator output with respect to the full simulator output, we can use this to screen out large areas of model space which contain only implausible models. For example, starting with what may be considered a geologically reasonable prior model space of 10000 models, using the emulator we can quickly show that only models which lie within 10% of that model space actually produce output data which is plausibly similar in character to an observed dataset. We can thus much

Numerical Demons in Monte Carlo Estimation of Bayesian Model Evidence with Application to Soil Respiration Models

NASA Astrophysics Data System (ADS)

Elshall, A. S.; Ye, M.; Niu, G. Y.; Barron-Gafford, G.

2016-12-01

Bayesian multimodel inference is increasingly being used in hydrology. Estimating Bayesian model evidence (BME) is of central importance in many Bayesian multimodel analysis such as Bayesian model averaging and model selection. BME is the overall probability of the model in reproducing the data, accounting for the trade-off between the goodness-of-fit and the model complexity. Yet estimating BME is challenging, especially for high dimensional problems with complex sampling space. Estimating BME using the Monte Carlo numerical methods is preferred, as the methods yield higher accuracy than semi-analytical solutions (e.g. Laplace approximations, BIC, KIC, etc.). However, numerical methods are prone the numerical demons arising from underflow of round off errors. Although few studies alluded to this issue, to our knowledge this is the first study that illustrates these numerical demons. We show that the precision arithmetic can become a threshold on likelihood values and Metropolis acceptance ratio, which results in trimming parameter regions (when likelihood function is less than the smallest floating point number that a computer can represent) and corrupting of the empirical measures of the random states of the MCMC sampler (when using log-likelihood function). We consider two of the most powerful numerical estimators of BME that are the path sampling method of thermodynamic integration (TI) and the importance sampling method of steppingstone sampling (SS). We also consider the two most widely used numerical estimators, which are the prior sampling arithmetic mean (AS) and posterior sampling harmonic mean (HM). We investigate the vulnerability of these four estimators to the numerical demons. Interesting, the most biased estimator, namely the HM, turned out to be the least vulnerable. While it is generally assumed that AM is a bias-free estimator that will always approximate the true BME by investing in computational effort, we show that arithmetic underflow can

A geostatistical approach to predicting sulfur content in the Pittsburgh coal bed

USGS Publications Warehouse

Watson, W.D.; Ruppert, L.F.; Bragg, L.J.; Tewalt, S.J.

2001-01-01

The US Geological Survey (USGS) is completing a national assessment of coal resources in the five top coal-producing regions in the US. Point-located data provide measurements on coal thickness and sulfur content. The sample data and their geologic interpretation represent the most regionally complete and up-to-date assessment of what is known about top-producing US coal beds. The sample data are analyzed using a combination of geologic and Geographic Information System (GIS) models to estimate tonnages and qualities of the coal beds. Traditionally, GIS practitioners use contouring to represent geographical patterns of "similar" data values. The tonnage and grade of coal resources are then assessed by using the contour lines as references for interpolation. An assessment taken to this point is only indicative of resource quantity and quality. Data users may benefit from a statistical approach that would allow them to better understand the uncertainty and limitations of the sample data. To develop a quantitative approach, geostatistics were applied to the data on coal sulfur content from samples taken in the Pittsburgh coal bed (located in the eastern US, in the southwestern part of the state of Pennsylvania, and in adjoining areas in the states of Ohio and West Virginia). Geostatistical methods that account for regional and local trends were applied to blocks 2.7 mi (4.3 km) on a side. The data and geostatistics support conclusions concerning the average sulfur content and its degree of reliability at regional- and economic-block scale over the large, contiguous part of the Pittsburgh outcrop, but not to a mine scale. To validate the method, a comparison was made with the sulfur contents in sample data taken from 53 coal mines located in the study area. The comparison showed a high degree of similarity between the sulfur content in the mine samples and the sulfur content represented by the geostatistically derived contours. Published by Elsevier Science B.V.

Automated Bayesian model development for frequency detection in biological time series.

PubMed

Granqvist, Emma; Oldroyd, Giles E D; Morris, Richard J

2011-06-24

A first step in building a mathematical model of a biological system is often the analysis of the temporal behaviour of key quantities. Mathematical relationships between the time and frequency domain, such as Fourier Transforms and wavelets, are commonly used to extract information about the underlying signal from a given time series. This one-to-one mapping from time points to frequencies inherently assumes that both domains contain the complete knowledge of the system. However, for truncated, noisy time series with background trends this unique mapping breaks down and the question reduces to an inference problem of identifying the most probable frequencies. In this paper we build on the method of Bayesian Spectrum Analysis and demonstrate its advantages over conventional methods by applying it to a number of test cases, including two types of biological time series. Firstly, oscillations of calcium in plant root cells in response to microbial symbionts are non-stationary and noisy, posing challenges to data analysis. Secondly, circadian rhythms in gene expression measured over only two cycles highlights the problem of time series with limited length. The results show that the Bayesian frequency detection approach can provide useful results in specific areas where Fourier analysis can be uninformative or misleading. We demonstrate further benefits of the Bayesian approach for time series analysis, such as direct comparison of different hypotheses, inherent estimation of noise levels and parameter precision, and a flexible framework for modelling the data without pre-processing. Modelling in systems biology often builds on the study of time-dependent phenomena. Fourier Transforms are a convenient tool for analysing the frequency domain of time series. However, there are well-known limitations of this method, such as the introduction of spurious frequencies when handling short and noisy time series, and the requirement for uniformly sampled data. Biological time

Automated Bayesian model development for frequency detection in biological time series

PubMed Central

2011-01-01

Background A first step in building a mathematical model of a biological system is often the analysis of the temporal behaviour of key quantities. Mathematical relationships between the time and frequency domain, such as Fourier Transforms and wavelets, are commonly used to extract information about the underlying signal from a given time series. This one-to-one mapping from time points to frequencies inherently assumes that both domains contain the complete knowledge of the system. However, for truncated, noisy time series with background trends this unique mapping breaks down and the question reduces to an inference problem of identifying the most probable frequencies. Results In this paper we build on the method of Bayesian Spectrum Analysis and demonstrate its advantages over conventional methods by applying it to a number of test cases, including two types of biological time series. Firstly, oscillations of calcium in plant root cells in response to microbial symbionts are non-stationary and noisy, posing challenges to data analysis. Secondly, circadian rhythms in gene expression measured over only two cycles highlights the problem of time series with limited length. The results show that the Bayesian frequency detection approach can provide useful results in specific areas where Fourier analysis can be uninformative or misleading. We demonstrate further benefits of the Bayesian approach for time series analysis, such as direct comparison of different hypotheses, inherent estimation of noise levels and parameter precision, and a flexible framework for modelling the data without pre-processing. Conclusions Modelling in systems biology often builds on the study of time-dependent phenomena. Fourier Transforms are a convenient tool for analysing the frequency domain of time series. However, there are well-known limitations of this method, such as the introduction of spurious frequencies when handling short and noisy time series, and the requirement for uniformly

Bayesian spatio-temporal modeling of particulate matter concentrations in Peninsular Malaysia

NASA Astrophysics Data System (ADS)

Manga, Edna; Awang, Norhashidah

2016-06-01

This article presents an application of a Bayesian spatio-temporal Gaussian process (GP) model on particulate matter concentrations from Peninsular Malaysia. We analyze daily PM10 concentration levels from 35 monitoring sites in June and July 2011. The spatiotemporal model set in a Bayesian hierarchical framework allows for inclusion of informative covariates, meteorological variables and spatiotemporal interactions. Posterior density estimates of the model parameters are obtained by Markov chain Monte Carlo methods. Preliminary data analysis indicate information on PM10 levels at sites classified as industrial locations could explain part of the space time variations. We include the site-type indicator in our modeling efforts. Results of the parameter estimates for the fitted GP model show significant spatio-temporal structure and positive effect of the location-type explanatory variable. We also compute some validation criteria for the out of sample sites that show the adequacy of the model for predicting PM10 at unmonitored sites.

Bayesian flood forecasting methods: A review

NASA Astrophysics Data System (ADS)

Han, Shasha; Coulibaly, Paulin

2017-08-01

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

Bayesian network modeling applied to coastal geomorphology: lessons learned from a decade of experimentation and application

NASA Astrophysics Data System (ADS)

Plant, N. G.; Thieler, E. R.; Gutierrez, B.; Lentz, E. E.; Zeigler, S. L.; Van Dongeren, A.; Fienen, M. N.

2016-12-01

We evaluate the strengths and weaknesses of Bayesian networks that have been used to address scientific and decision-support questions related to coastal geomorphology. We will provide an overview of coastal geomorphology research that has used Bayesian networks and describe what this approach can do and when it works (or fails to work). Over the past decade, Bayesian networks have been formulated to analyze the multi-variate structure and evolution of coastal morphology and associated human and ecological impacts. The approach relates observable system variables to each other by estimating discrete correlations. The resulting Bayesian-networks make predictions that propagate errors, conduct inference via Bayes rule, or both. In scientific applications, the model results are useful for hypothesis testing, using confidence estimates to gage the strength of tests while applications to coastal resource management are aimed at decision-support, where the probabilities of desired ecosystems outcomes are evaluated. The range of Bayesian-network applications to coastal morphology includes emulation of high-resolution wave transformation models to make oceanographic predictions, morphologic response to storms and/or sea-level rise, groundwater response to sea-level rise and morphologic variability, habitat suitability for endangered species, and assessment of monetary or human-life risk associated with storms. All of these examples are based on vast observational data sets, numerical model output, or both. We will discuss the progression of our experiments, which has included testing whether the Bayesian-network approach can be implemented and is appropriate for addressing basic and applied scientific problems and evaluating the hindcast and forecast skill of these implementations. We will present and discuss calibration/validation tests that are used to assess the robustness of Bayesian-network models and we will compare these results to tests of other models. This will

Bayesian Modeling of Exposure and Airflow Using Two-Zone Models

PubMed Central

Zhang, Yufen; Banerjee, Sudipto; Yang, Rui; Lungu, Claudiu; Ramachandran, Gurumurthy

2009-01-01

Mathematical modeling is being increasingly used as a means for assessing occupational exposures. However, predicting exposure in real settings is constrained by lack of quantitative knowledge of exposure determinants. Validation of models in occupational settings is, therefore, a challenge. Not only do the model parameters need to be known, the models also need to predict the output with some degree of accuracy. In this paper, a Bayesian statistical framework is used for estimating model parameters and exposure concentrations for a two-zone model. The model predicts concentrations in a zone near the source and far away from the source as functions of the toluene generation rate, air ventilation rate through the chamber, and the airflow between near and far fields. The framework combines prior or expert information on the physical model along with the observed data. The framework is applied to simulated data as well as data obtained from the experiments conducted in a chamber. Toluene vapors are generated from a source under different conditions of airflow direction, the presence of a mannequin, and simulated body heat of the mannequin. The Bayesian framework accounts for uncertainty in measurement as well as in the unknown rate of airflow between the near and far fields. The results show that estimates of the interzonal airflow are always close to the estimated equilibrium solutions, which implies that the method works efficiently. The predictions of near-field concentration for both the simulated and real data show nice concordance with the true values, indicating that the two-zone model assumptions agree with the reality to a large extent and the model is suitable for predicting the contaminant concentration. Comparison of the estimated model and its margin of error with the experimental data thus enables validation of the physical model assumptions. The approach illustrates how exposure models and information on model parameters together with the knowledge of

Philosophy and the practice of Bayesian statistics

PubMed Central

Gelman, Andrew; Shalizi, Cosma Rohilla

2015-01-01

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework. PMID:22364575

Bayesian non-parametric inference for stochastic epidemic models using Gaussian Processes.

PubMed

Xu, Xiaoguang; Kypraios, Theodore; O'Neill, Philip D

2016-10-01

This paper considers novel Bayesian non-parametric methods for stochastic epidemic models. Many standard modeling and data analysis methods use underlying assumptions (e.g. concerning the rate at which new cases of disease will occur) which are rarely challenged or tested in practice. To relax these assumptions, we develop a Bayesian non-parametric approach using Gaussian Processes, specifically to estimate the infection process. The methods are illustrated with both simulated and real data sets, the former illustrating that the methods can recover the true infection process quite well in practice, and the latter illustrating that the methods can be successfully applied in different settings. © The Author 2016. Published by Oxford University Press.

Approximate Bayesian computation for spatial SEIR(S) epidemic models.

PubMed

Brown, Grant D; Porter, Aaron T; Oleson, Jacob J; Hinman, Jessica A

2018-02-01

Approximate Bayesia n Computation (ABC) provides an attractive approach to estimation in complex Bayesian inferential problems for which evaluation of the kernel of the posterior distribution is impossible or computationally expensive. These highly parallelizable techniques have been successfully applied to many fields, particularly in cases where more traditional approaches such as Markov chain Monte Carlo (MCMC) are impractical. In this work, we demonstrate the application of approximate Bayesian inference to spatially heterogeneous Susceptible-Exposed-Infectious-Removed (SEIR) stochastic epidemic models. These models have a tractable posterior distribution, however MCMC techniques nevertheless become computationally infeasible for moderately sized problems. We discuss the practical implementation of these techniques via the open source ABSEIR package for R. The performance of ABC relative to traditional MCMC methods in a small problem is explored under simulation, as well as in the spatially heterogeneous context of the 2014 epidemic of Chikungunya in the Americas. Copyright © 2017 Elsevier Ltd. All rights reserved.

Geostatistics for environmental and geotechnical applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rouhani, S.; Srivastava, R.M.; Desbarats, A.J.

1996-12-31

This conference was held January 26--27, 1995 in Phoenix, Arizona. The purpose of this conference was to provide a multidisciplinary forum for exchange of state-of-the-art information on the technology of geostatistics and its applicability for environmental studies, especially site characterization. Individual papers have been processed separately for inclusion in the appropriate data bases.

Robust geostatistical analysis of spatial data

NASA Astrophysics Data System (ADS)

Papritz, A.; Künsch, H. R.; Schwierz, C.; Stahel, W. A.

2012-04-01

Most of the geostatistical software tools rely on non-robust algorithms. This is unfortunate, because outlying observations are rather the rule than the exception, in particular in environmental data sets. Outlying observations may results from errors (e.g. in data transcription) or from local perturbations in the processes that are responsible for a given pattern of spatial variation. As an example, the spatial distribution of some trace metal in the soils of a region may be distorted by emissions of local anthropogenic sources. Outliers affect the modelling of the large-scale spatial variation, the so-called external drift or trend, the estimation of the spatial dependence of the residual variation and the predictions by kriging. Identifying outliers manually is cumbersome and requires expertise because one needs parameter estimates to decide which observation is a potential outlier. Moreover, inference after the rejection of some observations is problematic. A better approach is to use robust algorithms that prevent automatically that outlying observations have undue influence. Former studies on robust geostatistics focused on robust estimation of the sample variogram and ordinary kriging without external drift. Furthermore, Richardson and Welsh (1995) [2] proposed a robustified version of (restricted) maximum likelihood ([RE]ML) estimation for the variance components of a linear mixed model, which was later used by Marchant and Lark (2007) [1] for robust REML estimation of the variogram. We propose here a novel method for robust REML estimation of the variogram of a Gaussian random field that is possibly contaminated by independent errors from a long-tailed distribution. It is based on robustification of estimating equations for the Gaussian REML estimation. Besides robust estimates of the parameters of the external drift and of the variogram, the method also provides standard errors for the estimated parameters, robustified kriging predictions at both sampled

Small Sample Properties of Bayesian Multivariate Autoregressive Time Series Models

ERIC Educational Resources Information Center

Price, Larry R.

2012-01-01

The aim of this study was to compare the small sample (N = 1, 3, 5, 10, 15) performance of a Bayesian multivariate vector autoregressive (BVAR-SEM) time series model relative to frequentist power and parameter estimation bias. A multivariate autoregressive model was developed based on correlated autoregressive time series vectors of varying…

Geostatistical noise filtering of geophysical images : application to unexploded ordnance (UXO) sites.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saito, Hirotaka; McKenna, Sean Andrew; Coburn, Timothy C.

2004-07-01

Geostatistical and non-geostatistical noise filtering methodologies, factorial kriging and a low-pass filter, and a region growing method are applied to analytic signal magnetometer images at two UXO contaminated sites to delineate UXO target areas. Overall delineation performance is improved by removing background noise. Factorial kriging slightly outperforms the low-pass filter but there is no distinct difference between them in terms of finding anomalies of interest.

Optimal speech motor control and token-to-token variability: a Bayesian modeling approach.

PubMed

Patri, Jean-François; Diard, Julien; Perrier, Pascal

2015-12-01

The remarkable capacity of the speech motor system to adapt to various speech conditions is due to an excess of degrees of freedom, which enables producing similar acoustical properties with different sets of control strategies. To explain how the central nervous system selects one of the possible strategies, a common approach, in line with optimal motor control theories, is to model speech motor planning as the solution of an optimality problem based on cost functions. Despite the success of this approach, one of its drawbacks is the intrinsic contradiction between the concept of optimality and the observed experimental intra-speaker token-to-token variability. The present paper proposes an alternative approach by formulating feedforward optimal control in a probabilistic Bayesian modeling framework. This is illustrated by controlling a biomechanical model of the vocal tract for speech production and by comparing it with an existing optimal control model (GEPPETO). The essential elements of this optimal control model are presented first. From them the Bayesian model is constructed in a progressive way. Performance of the Bayesian model is evaluated based on computer simulations and compared to the optimal control model. This approach is shown to be appropriate for solving the speech planning problem while accounting for variability in a principled way.

Estimation of Groundwater Radon in North Carolina Using Land Use Regression and Bayesian Maximum Entropy.

PubMed

Messier, Kyle P; Campbell, Ted; Bradley, Philip J; Serre, Marc L

2015-08-18

Radon ((222)Rn) is a naturally occurring chemically inert, colorless, and odorless radioactive gas produced from the decay of uranium ((238)U), which is ubiquitous in rocks and soils worldwide. Exposure to (222)Rn is likely the second leading cause of lung cancer after cigarette smoking via inhalation; however, exposure through untreated groundwater is also a contributing factor to both inhalation and ingestion routes. A land use regression (LUR) model for groundwater (222)Rn with anisotropic geological and (238)U based explanatory variables is developed, which helps elucidate the factors contributing to elevated (222)Rn across North Carolina. The LUR is also integrated into the Bayesian Maximum Entropy (BME) geostatistical framework to increase accuracy and produce a point-level LUR-BME model of groundwater (222)Rn across North Carolina including prediction uncertainty. The LUR-BME model of groundwater (222)Rn results in a leave-one out cross-validation r(2) of 0.46 (Pearson correlation coefficient = 0.68), effectively predicting within the spatial covariance range. Modeled results of (222)Rn concentrations show variability among intrusive felsic geological formations likely due to average bedrock (238)U defined on the basis of overlying stream-sediment (238)U concentrations that is a widely distributed consistently analyzed point-source data.

Bayesian multimodel inference for dose-response studies

USGS Publications Warehouse

Link, W.A.; Albers, P.H.

2007-01-01

Statistical inference in dose?response studies is model-based: The analyst posits a mathematical model of the relation between exposure and response, estimates parameters of the model, and reports conclusions conditional on the model. Such analyses rarely include any accounting for the uncertainties associated with model selection. The Bayesian inferential system provides a convenient framework for model selection and multimodel inference. In this paper we briefly describe the Bayesian paradigm and Bayesian multimodel inference. We then present a family of models for multinomial dose?response data and apply Bayesian multimodel inferential methods to the analysis of data on the reproductive success of American kestrels (Falco sparveriuss) exposed to various sublethal dietary concentrations of methylmercury.

Bayesian model calibration of computational models in velocimetry diagnosed dynamic compression experiments.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, Justin; Hund, Lauren

2017-02-01

Dynamic compression experiments are being performed on complicated materials using increasingly complex drivers. The data produced in these experiments are beginning to reach a regime where traditional analysis techniques break down; requiring the solution of an inverse problem. A common measurement in dynamic experiments is an interface velocity as a function of time, and often this functional output can be simulated using a hydrodynamics code. Bayesian model calibration is a statistical framework to estimate inputs into a computational model in the presence of multiple uncertainties, making it well suited to measurements of this type. In this article, we apply Bayesianmore » model calibration to high pressure (250 GPa) ramp compression measurements in tantalum. We address several issues speci c to this calibration including the functional nature of the output as well as parameter and model discrepancy identi ability. Speci cally, we propose scaling the likelihood function by an e ective sample size rather than modeling the autocorrelation function to accommodate the functional output and propose sensitivity analyses using the notion of `modularization' to assess the impact of experiment-speci c nuisance input parameters on estimates of material properties. We conclude that the proposed Bayesian model calibration procedure results in simple, fast, and valid inferences on the equation of state parameters for tantalum.« less

A local approach for focussed Bayesian fusion

NASA Astrophysics Data System (ADS)

Sander, Jennifer; Heizmann, Michael; Goussev, Igor; Beyerer, Jürgen

2009-04-01

Local Bayesian fusion approaches aim to reduce high storage and computational costs of Bayesian fusion which is separated from fixed modeling assumptions. Using the small world formalism, we argue why this proceeding is conform with Bayesian theory. Then, we concentrate on the realization of local Bayesian fusion by focussing the fusion process solely on local regions that are task relevant with a high probability. The resulting local models correspond then to restricted versions of the original one. In a previous publication, we used bounds for the probability of misleading evidence to show the validity of the pre-evaluation of task specific knowledge and prior information which we perform to build local models. In this paper, we prove the validity of this proceeding using information theoretic arguments. For additional efficiency, local Bayesian fusion can be realized in a distributed manner. Here, several local Bayesian fusion tasks are evaluated and unified after the actual fusion process. For the practical realization of distributed local Bayesian fusion, software agents are predestinated. There is a natural analogy between the resulting agent based architecture and criminal investigations in real life. We show how this analogy can be used to improve the efficiency of distributed local Bayesian fusion additionally. Using a landscape model, we present an experimental study of distributed local Bayesian fusion in the field of reconnaissance, which highlights its high potential.

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

NASA Astrophysics Data System (ADS)

Parkinson, David; Liddle, Andrew R.

2010-11-01

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

HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python.

PubMed

Wiecki, Thomas V; Sofer, Imri; Frank, Michael J

2013-01-01

The diffusion model is a commonly used tool to infer latent psychological processes underlying decision-making, and to link them to neural mechanisms based on response times. Although efficient open source software has been made available to quantitatively fit the model to data, current estimation methods require an abundance of response time measurements to recover meaningful parameters, and only provide point estimates of each parameter. In contrast, hierarchical Bayesian parameter estimation methods are useful for enhancing statistical power, allowing for simultaneous estimation of individual subject parameters and the group distribution that they are drawn from, while also providing measures of uncertainty in these parameters in the posterior distribution. Here, we present a novel Python-based toolbox called HDDM (hierarchical drift diffusion model), which allows fast and flexible estimation of the the drift-diffusion model and the related linear ballistic accumulator model. HDDM requires fewer data per subject/condition than non-hierarchical methods, allows for full Bayesian data analysis, and can handle outliers in the data. Finally, HDDM supports the estimation of how trial-by-trial measurements (e.g., fMRI) influence decision-making parameters. This paper will first describe the theoretical background of the drift diffusion model and Bayesian inference. We then illustrate usage of the toolbox on a real-world data set from our lab. Finally, parameter recovery studies show that HDDM beats alternative fitting methods like the χ(2)-quantile method as well as maximum likelihood estimation. The software and documentation can be downloaded at: http://ski.clps.brown.edu/hddm_docs/

Basics of Bayesian methods.

PubMed

Ghosh, Sujit K

2010-01-01

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

Path integration mediated systematic search: a Bayesian model.

PubMed

Vickerstaff, Robert J; Merkle, Tobias

2012-08-21

The systematic search behaviour is a backup system that increases the chances of desert ants finding their nest entrance after foraging when the path integrator has failed to guide them home accurately enough. Here we present a mathematical model of the systematic search that is based on extensive behavioural studies in North African desert ants Cataglyphis fortis. First, a simple search heuristic utilising Bayesian inference and a probability density function is developed. This model, which optimises the short-term nest detection probability, is then compared to three simpler search heuristics and to recorded search patterns of Cataglyphis ants. To compare the different searches a method to quantify search efficiency is established as well as an estimate of the error rate in the ants' path integrator. We demonstrate that the Bayesian search heuristic is able to automatically adapt to increasing levels of positional uncertainty to produce broader search patterns, just as desert ants do, and that it outperforms the three other search heuristics tested. The searches produced by it are also arguably the most similar in appearance to the ant's searches. Copyright © 2012 Elsevier Ltd. All rights reserved.

Refining value-at-risk estimates using a Bayesian Markov-switching GJR-GARCH copula-EVT model.

PubMed

Sampid, Marius Galabe; Hasim, Haslifah M; Dai, Hongsheng

2018-01-01

In this paper, we propose a model for forecasting Value-at-Risk (VaR) using a Bayesian Markov-switching GJR-GARCH(1,1) model with skewed Student's-t innovation, copula functions and extreme value theory. A Bayesian Markov-switching GJR-GARCH(1,1) model that identifies non-constant volatility over time and allows the GARCH parameters to vary over time following a Markov process, is combined with copula functions and EVT to formulate the Bayesian Markov-switching GJR-GARCH(1,1) copula-EVT VaR model, which is then used to forecast the level of risk on financial asset returns. We further propose a new method for threshold selection in EVT analysis, which we term the hybrid method. Empirical and back-testing results show that the proposed VaR models capture VaR reasonably well in periods of calm and in periods of crisis.

A Bayesian Multinomial Probit MODEL FOR THE ANALYSIS OF PANEL CHOICE DATA.

PubMed

Fong, Duncan K H; Kim, Sunghoon; Chen, Zhe; DeSarbo, Wayne S

2016-03-01

A new Bayesian multinomial probit model is proposed for the analysis of panel choice data. Using a parameter expansion technique, we are able to devise a Markov Chain Monte Carlo algorithm to compute our Bayesian estimates efficiently. We also show that the proposed procedure enables the estimation of individual level coefficients for the single-period multinomial probit model even when the available prior information is vague. We apply our new procedure to consumer purchase data and reanalyze a well-known scanner panel dataset that reveals new substantive insights. In addition, we delineate a number of advantageous features of our proposed procedure over several benchmark models. Finally, through a simulation analysis employing a fractional factorial design, we demonstrate that the results from our proposed model are quite robust with respect to differing factors across various conditions.

Sampling design optimisation for rainfall prediction using a non-stationary geostatistical model

NASA Astrophysics Data System (ADS)

Wadoux, Alexandre M. J.-C.; Brus, Dick J.; Rico-Ramirez, Miguel A.; Heuvelink, Gerard B. M.

2017-09-01

The accuracy of spatial predictions of rainfall by merging rain-gauge and radar data is partly determined by the sampling design of the rain-gauge network. Optimising the locations of the rain-gauges may increase the accuracy of the predictions. Existing spatial sampling design optimisation methods are based on minimisation of the spatially averaged prediction error variance under the assumption of intrinsic stationarity. Over the past years, substantial progress has been made to deal with non-stationary spatial processes in kriging. Various well-documented geostatistical models relax the assumption of stationarity in the mean, while recent studies show the importance of considering non-stationarity in the variance for environmental processes occurring in complex landscapes. We optimised the sampling locations of rain-gauges using an extension of the Kriging with External Drift (KED) model for prediction of rainfall fields. The model incorporates both non-stationarity in the mean and in the variance, which are modelled as functions of external covariates such as radar imagery, distance to radar station and radar beam blockage. Spatial predictions are made repeatedly over time, each time recalibrating the model. The space-time averaged KED variance was minimised by Spatial Simulated Annealing (SSA). The methodology was tested using a case study predicting daily rainfall in the north of England for a one-year period. Results show that (i) the proposed non-stationary variance model outperforms the stationary variance model, and (ii) a small but significant decrease of the rainfall prediction error variance is obtained with the optimised rain-gauge network. In particular, it pays off to place rain-gauges at locations where the radar imagery is inaccurate, while keeping the distribution over the study area sufficiently uniform.

A Bayesian Network Approach to Modeling Learning Progressions and Task Performance. CRESST Report 776

ERIC Educational Resources Information Center

West, Patti; Rutstein, Daisy Wise; Mislevy, Robert J.; Liu, Junhui; Choi, Younyoung; Levy, Roy; Crawford, Aaron; DiCerbo, Kristen E.; Chappel, Kristina; Behrens, John T.

2010-01-01

A major issue in the study of learning progressions (LPs) is linking student performance on assessment tasks to the progressions. This report describes the challenges faced in making this linkage using Bayesian networks to model LPs in the field of computer networking. The ideas are illustrated with exemplar Bayesian networks built on Cisco…

Philosophy and the practice of Bayesian statistics.

PubMed

Gelman, Andrew; Shalizi, Cosma Rohilla

2013-02-01

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

Bayesian methods in reliability

NASA Astrophysics Data System (ADS)

Sander, P.; Badoux, R.

1991-11-01

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

Assimilating multi-source uncertainties of a parsimonious conceptual hydrological model using hierarchical Bayesian modeling

Treesearch

Wei Wu; James Clark; James Vose

2010-01-01

Hierarchical Bayesian (HB) modeling allows for multiple sources of uncertainty by factoring complex relationships into conditional distributions that can be used to draw inference and make predictions. We applied an HB model to estimate the parameters and state variables of a parsimonious hydrological model – GR4J – by coherently assimilating the uncertainties from the...

Models and simulation of 3D neuronal dendritic trees using Bayesian networks.

PubMed

López-Cruz, Pedro L; Bielza, Concha; Larrañaga, Pedro; Benavides-Piccione, Ruth; DeFelipe, Javier

2011-12-01

Neuron morphology is crucial for neuronal connectivity and brain information processing. Computational models are important tools for studying dendritic morphology and its role in brain function. We applied a class of probabilistic graphical models called Bayesian networks to generate virtual dendrites from layer III pyramidal neurons from three different regions of the neocortex of the mouse. A set of 41 morphological variables were measured from the 3D reconstructions of real dendrites and their probability distributions used in a machine learning algorithm to induce the model from the data. A simulation algorithm is also proposed to obtain new dendrites by sampling values from Bayesian networks. The main advantage of this approach is that it takes into account and automatically locates the relationships between variables in the data instead of using predefined dependencies. Therefore, the methodology can be applied to any neuronal class while at the same time exploiting class-specific properties. Also, a Bayesian network was defined for each part of the dendrite, allowing the relationships to change in the different sections and to model heterogeneous developmental factors or spatial influences. Several univariate statistical tests and a novel multivariate test based on Kullback-Leibler divergence estimation confirmed that virtual dendrites were similar to real ones. The analyses of the models showed relationships that conform to current neuroanatomical knowledge and support model correctness. At the same time, studying the relationships in the models can help to identify new interactions between variables related to dendritic morphology.

A Bayesian prediction model between a biomarker and the clinical endpoint for dichotomous variables.

PubMed

Jiang, Zhiwei; Song, Yang; Shou, Qiong; Xia, Jielai; Wang, William

2014-12-20

Early biomarkers are helpful for predicting clinical endpoints and for evaluating efficacy in clinical trials even if the biomarker cannot replace clinical outcome as a surrogate. The building and evaluation of an association model between biomarkers and clinical outcomes are two equally important concerns regarding the prediction of clinical outcome. This paper is to address both issues in a Bayesian framework. A Bayesian meta-analytic approach is proposed to build a prediction model between the biomarker and clinical endpoint for dichotomous variables. Compared with other Bayesian methods, the proposed model only requires trial-level summary data of historical trials in model building. By using extensive simulations, we evaluate the link function and the application condition of the proposed Bayesian model under scenario (i) equal positive predictive value (PPV) and negative predictive value (NPV) and (ii) higher NPV and lower PPV. In the simulations, the patient-level data is generated to evaluate the meta-analytic model. PPV and NPV are employed to describe the patient-level relationship between the biomarker and the clinical outcome. The minimum number of historical trials to be included in building the model is also considered. It is seen from the simulations that the logit link function performs better than the odds and cloglog functions under both scenarios. PPV/NPV ≥0.5 for equal PPV and NPV, and PPV + NPV ≥1 for higher NPV and lower PPV are proposed in order to predict clinical outcome accurately and precisely when the proposed model is considered. Twenty historical trials are required to be included in model building when PPV and NPV are equal. For unequal PPV and NPV, the minimum number of historical trials for model building is proposed to be five. A hypothetical example shows an application of the proposed model in global drug development. The proposed Bayesian model is able to predict well the clinical endpoint from the observed biomarker

Bayesian Inference for Generalized Linear Models for Spiking Neurons

PubMed Central

Gerwinn, Sebastian; Macke, Jakob H.; Bethge, Matthias

2010-01-01

Generalized Linear Models (GLMs) are commonly used statistical methods for modelling the relationship between neural population activity and presented stimuli. When the dimension of the parameter space is large, strong regularization has to be used in order to fit GLMs to datasets of realistic size without overfitting. By imposing properly chosen priors over parameters, Bayesian inference provides an effective and principled approach for achieving regularization. Here we show how the posterior distribution over model parameters of GLMs can be approximated by a Gaussian using the Expectation Propagation algorithm. In this way, we obtain an estimate of the posterior mean and posterior covariance, allowing us to calculate Bayesian confidence intervals that characterize the uncertainty about the optimal solution. From the posterior we also obtain a different point estimate, namely the posterior mean as opposed to the commonly used maximum a posteriori estimate. We systematically compare the different inference techniques on simulated as well as on multi-electrode recordings of retinal ganglion cells, and explore the effects of the chosen prior and the performance measure used. We find that good performance can be achieved by choosing an Laplace prior together with the posterior mean estimate. PMID:20577627

Developing a new Bayesian Risk Index for risk evaluation of soil contamination.

PubMed

Albuquerque, M T D; Gerassis, S; Sierra, C; Taboada, J; Martín, J E; Antunes, I M H R; Gallego, J R

2017-12-15

Industrial and agricultural activities heavily constrain soil quality. Potentially Toxic Elements (PTEs) are a threat to public health and the environment alike. In this regard, the identification of areas that require remediation is crucial. In the herein research a geochemical dataset (230 samples) comprising 14 elements (Cu, Pb, Zn, Ag, Ni, Mn, Fe, As, Cd, V, Cr, Ti, Al and S) was gathered throughout eight different zones distinguished by their main activity, namely, recreational, agriculture/livestock and heavy industry in the Avilés Estuary (North of Spain). Then a stratified systematic sampling method was used at short, medium, and long distances from each zone to obtain a representative picture of the total variability of the selected attributes. The information was then combined in four risk classes (Low, Moderate, High, Remediation) following reference values from several sediment quality guidelines (SQGs). A Bayesian analysis, inferred for each zone, allowed the characterization of PTEs correlations, the unsupervised learning network technique proving to be the best fit. Based on the Bayesian network structure obtained, Pb, As and Mn were selected as key contamination parameters. For these 3 elements, the conditional probability obtained was allocated to each observed point, and a simple, direct index (Bayesian Risk Index-BRI) was constructed as a linear rating of the pre-defined risk classes weighted by the previously obtained probability. Finally, the BRI underwent geostatistical modeling. One hundred Sequential Gaussian Simulations (SGS) were computed. The Mean Image and the Standard Deviation maps were obtained, allowing the definition of High/Low risk clusters (Local G clustering) and the computation of spatial uncertainty. High-risk clusters are mainly distributed within the area with the highest altitude (agriculture/livestock) showing an associated low spatial uncertainty, clearly indicating the need for remediation. Atmospheric emissions, mainly

Measuring Learning Progressions Using Bayesian Modeling in Complex Assessments

ERIC Educational Resources Information Center

Rutstein, Daisy Wise

2012-01-01

This research examines issues regarding model estimation and robustness in the use of Bayesian Inference Networks (BINs) for measuring Learning Progressions (LPs). It provides background information on LPs and how they might be used in practice. Two simulation studies are performed, along with real data examples. The first study examines the case…

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

ERIC Educational Resources Information Center

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

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

Modeling of Academic Achievement of Primary School Students in Ethiopia Using Bayesian Multilevel Approach

ERIC Educational Resources Information Center

Sebro, Negusse Yohannes; Goshu, Ayele Taye

2017-01-01

This study aims to explore Bayesian multilevel modeling to investigate variations of average academic achievement of grade eight school students. A sample of 636 students is randomly selected from 26 private and government schools by a two-stage stratified sampling design. Bayesian method is used to estimate the fixed and random effects. Input and…

Iterative updating of model error for Bayesian inversion

NASA Astrophysics Data System (ADS)

Calvetti, Daniela; Dunlop, Matthew; Somersalo, Erkki; Stuart, Andrew

2018-02-01

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when optimization algorithms are used to find a single estimate, or to speed up Markov chain Monte Carlo (MCMC) calculations in the Bayesian framework. The use of an approximate model introduces a discrepancy, or modeling error, that may have a detrimental effect on the solution of the ill-posed inverse problem, or it may severely distort the estimate of the posterior distribution. In the Bayesian paradigm, the modeling error can be considered as a random variable, and by using an estimate of the probability distribution of the unknown, one may estimate the probability distribution of the modeling error and incorporate it into the inversion. We introduce an algorithm which iterates this idea to update the distribution of the model error, leading to a sequence of posterior distributions that are demonstrated empirically to capture the underlying truth with increasing accuracy. Since the algorithm is not based on rejections, it requires only limited full model evaluations. We show analytically that, in the linear Gaussian case, the algorithm converges geometrically fast with respect to the number of iterations when the data is finite dimensional. For more general models, we introduce particle approximations of the iteratively generated sequence of distributions; we also prove that each element of the sequence converges in the large particle limit under a simplifying assumption. We show numerically that, as in the linear case, rapid convergence occurs with respect to the number of iterations. Additionally, we show through computed examples that point estimates obtained from this iterative algorithm are superior to those obtained by neglecting the model error.

Genealogical Working Distributions for Bayesian Model Testing with Phylogenetic Uncertainty

PubMed Central

Baele, Guy; Lemey, Philippe; Suchard, Marc A.

2016-01-01

Marginal likelihood estimates to compare models using Bayes factors frequently accompany Bayesian phylogenetic inference. Approaches to estimate marginal likelihoods have garnered increased attention over the past decade. In particular, the introduction of path sampling (PS) and stepping-stone sampling (SS) into Bayesian phylogenetics has tremendously improved the accuracy of model selection. These sampling techniques are now used to evaluate complex evolutionary and population genetic models on empirical data sets, but considerable computational demands hamper their widespread adoption. Further, when very diffuse, but proper priors are specified for model parameters, numerical issues complicate the exploration of the priors, a necessary step in marginal likelihood estimation using PS or SS. To avoid such instabilities, generalized SS (GSS) has recently been proposed, introducing the concept of “working distributions” to facilitate—or shorten—the integration process that underlies marginal likelihood estimation. However, the need to fix the tree topology currently limits GSS in a coalescent-based framework. Here, we extend GSS by relaxing the fixed underlying tree topology assumption. To this purpose, we introduce a “working” distribution on the space of genealogies, which enables estimating marginal likelihoods while accommodating phylogenetic uncertainty. We propose two different “working” distributions that help GSS to outperform PS and SS in terms of accuracy when comparing demographic and evolutionary models applied to synthetic data and real-world examples. Further, we show that the use of very diffuse priors can lead to a considerable overestimation in marginal likelihood when using PS and SS, while still retrieving the correct marginal likelihood using both GSS approaches. The methods used in this article are available in BEAST, a powerful user-friendly software package to perform Bayesian evolutionary analyses. PMID:26526428

Bayesian structural equation modeling: a more flexible representation of substantive theory.

PubMed

Muthén, Bengt; Asparouhov, Tihomir

2012-09-01

This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed Bayesian approach is particularly beneficial in applications where parameters are added to a conventional model such that a nonidentified model is obtained if maximum-likelihood estimation is applied. This approach is useful for measurement aspects of latent variable modeling, such as with confirmatory factor analysis, and the measurement part of structural equation modeling. Two application areas are studied, cross-loadings and residual correlations in confirmatory factor analysis. An example using a full structural equation model is also presented, showing an efficient way to find model misspecification. The approach encompasses 3 elements: model testing using posterior predictive checking, model estimation, and model modification. Monte Carlo simulations and real data are analyzed using Mplus. The real-data analyses use data from Holzinger and Swineford's (1939) classic mental abilities study, Big Five personality factor data from a British survey, and science achievement data from the National Educational Longitudinal Study of 1988.

Approximate Bayesian computation for forward modeling in cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akeret, Joël; Refregier, Alexandre; Amara, Adam

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

[Spatial distribution pattern of Chilo suppressalis analyzed by classical method and geostatistics].

PubMed

Yuan, Zheming; Fu, Wei; Li, Fangyi

2004-04-01

Two original samples of Chilo suppressalis and their grid, random and sequence samples were analyzed by classical method and geostatistics to characterize the spatial distribution pattern of C. suppressalis. The limitations of spatial distribution analysis with classical method, especially influenced by the original position of grid, were summarized rather completely. On the contrary, geostatistics characterized well the spatial distribution pattern, congregation intensity and spatial heterogeneity of C. suppressalis. According to geostatistics, the population was up to Poisson distribution in low density. As for higher density population, its distribution was up to aggregative, and the aggregation intensity and dependence range were 0.1056 and 193 cm, respectively. Spatial heterogeneity was also found in the higher density population. Its spatial correlativity in line direction was more closely than that in row direction, and the dependence ranges in line and row direction were 115 and 264 cm, respectively.

A multiple-point geostatistical approach to quantifying uncertainty for flow and transport simulation in geologically complex environments

NASA Astrophysics Data System (ADS)

Cronkite-Ratcliff, C.; Phelps, G. A.; Boucher, A.

2011-12-01

In many geologic settings, the pathways of groundwater flow are controlled by geologic heterogeneities which have complex geometries. Models of these geologic heterogeneities, and consequently, their effects on the simulated pathways of groundwater flow, are characterized by uncertainty. Multiple-point geostatistics, which uses a training image to represent complex geometric descriptions of geologic heterogeneity, provides a stochastic approach to the analysis of geologic uncertainty. Incorporating multiple-point geostatistics into numerical models provides a way to extend this analysis to the effects of geologic uncertainty on the results of flow simulations. We present two case studies to demonstrate the application of multiple-point geostatistics to numerical flow simulation in complex geologic settings with both static and dynamic conditioning data. Both cases involve the development of a training image from a complex geometric description of the geologic environment. Geologic heterogeneity is modeled stochastically by generating multiple equally-probable realizations, all consistent with the training image. Numerical flow simulation for each stochastic realization provides the basis for analyzing the effects of geologic uncertainty on simulated hydraulic response. The first case study is a hypothetical geologic scenario developed using data from the alluvial deposits in Yucca Flat, Nevada. The SNESIM algorithm is used to stochastically model geologic heterogeneity conditioned to the mapped surface geology as well as vertical drill-hole data. Numerical simulation of groundwater flow and contaminant transport through geologic models produces a distribution of hydraulic responses and contaminant concentration results. From this distribution of results, the probability of exceeding a given contaminant concentration threshold can be used as an indicator of uncertainty about the location of the contaminant plume boundary. The second case study considers a

Assessment of nitrate pollution in the Grand Morin aquifers (France): combined use of geostatistics and physically based modeling.

PubMed

Flipo, Nicolas; Jeannée, Nicolas; Poulin, Michel; Even, Stéphanie; Ledoux, Emmanuel

2007-03-01

The objective of this work is to combine several approaches to better understand nitrate fate in the Grand Morin aquifers (2700 km(2)), 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).

Robust Bayesian Analysis of Heavy-tailed Stochastic Volatility Models using Scale Mixtures of Normal Distributions

PubMed Central

Abanto-Valle, C. A.; Bandyopadhyay, D.; Lachos, V. H.; Enriquez, I.

2009-01-01

A Bayesian analysis of stochastic volatility (SV) models using the class of symmetric scale mixtures of normal (SMN) distributions is considered. In the face of non-normality, this provides an appealing robust alternative to the routine use of the normal distribution. Specific distributions examined include the normal, student-t, slash and the variance gamma distributions. Using a Bayesian paradigm, an efficient Markov chain Monte Carlo (MCMC) algorithm is introduced for parameter estimation. Moreover, the mixing parameters obtained as a by-product of the scale mixture representation can be used to identify outliers. The methods developed are applied to analyze daily stock returns data on S&P500 index. Bayesian model selection criteria as well as out-of- sample forecasting results reveal that the SV models based on heavy-tailed SMN distributions provide significant improvement in model fit as well as prediction to the S&P500 index data over the usual normal model. PMID:20730043

Reconstructing Constructivism: Causal Models, Bayesian Learning Mechanisms, and the Theory Theory

ERIC Educational Resources Information Center

Gopnik, Alison; Wellman, Henry M.

2012-01-01

We propose a new version of the "theory theory" grounded in the computational framework of probabilistic causal models and Bayesian learning. Probabilistic models allow a constructivist but rigorous and detailed approach to cognitive development. They also explain the learning of both more specific causal hypotheses and more abstract framework…

Model Diagnostics for Bayesian Networks. Research Report. ETS RR-04-17

ERIC Educational Resources Information Center

Sinharay, Sandip

2004-01-01

Assessing fit of psychometric models has always been an issue of enormous interest, but there exists no unanimously agreed upon item fit diagnostic for the models. Bayesian networks, frequently used in educational assessments (see, for example, Mislevy, Almond, Yan, & Steinberg, 2001) primarily for learning about students' knowledge and…

Bayesian prediction of placebo analgesia in an instrumental learning model

PubMed Central

Jung, Won-Mo; Lee, Ye-Seul; Wallraven, Christian; Chae, Younbyoung

2017-01-01

Placebo analgesia can be primarily explained by the Pavlovian conditioning paradigm in which a passively applied cue becomes associated with less pain. In contrast, instrumental conditioning employs an active paradigm that might be more similar to clinical settings. In the present study, an instrumental conditioning paradigm involving a modified trust game in a simulated clinical situation was used to induce placebo analgesia. Additionally, Bayesian modeling was applied to predict the placebo responses of individuals based on their choices. Twenty-four participants engaged in a medical trust game in which decisions to receive treatment from either a doctor (more effective with high cost) or a pharmacy (less effective with low cost) were made after receiving a reference pain stimulus. In the conditioning session, the participants received lower levels of pain following both choices, while high pain stimuli were administered in the test session even after making the decision. The choice-dependent pain in the conditioning session was modulated in terms of both intensity and uncertainty. Participants reported significantly less pain when they chose the doctor or the pharmacy for treatment compared to the control trials. The predicted pain ratings based on Bayesian modeling showed significant correlations with the actual reports from participants for both of the choice categories. The instrumental conditioning paradigm allowed for the active choice of optional cues and was able to induce the placebo analgesia effect. Additionally, Bayesian modeling successfully predicted pain ratings in a simulated clinical situation that fits well with placebo analgesia induced by instrumental conditioning. PMID:28225816

A Comparison of Traditional, Step-Path, and Geostatistical Techniques in the Stability Analysis of a Large Open Pit

NASA Astrophysics Data System (ADS)

Mayer, J. M.; Stead, D.

2017-04-01

With the increased drive towards deeper and more complex mine designs, geotechnical engineers are often forced to reconsider traditional deterministic design techniques in favour of probabilistic methods. These alternative techniques allow for the direct quantification of uncertainties within a risk and/or decision analysis framework. However, conventional probabilistic practices typically discretize geological materials into discrete, homogeneous domains, with attributes defined by spatially constant random variables, despite the fact that geological media display inherent heterogeneous spatial characteristics. This research directly simulates this phenomenon using a geostatistical approach, known as sequential Gaussian simulation. The method utilizes the variogram which imposes a degree of controlled spatial heterogeneity on the system. Simulations are constrained using data from the Ok Tedi mine site in Papua New Guinea and designed to randomly vary the geological strength index and uniaxial compressive strength using Monte Carlo techniques. Results suggest that conventional probabilistic techniques have a fundamental limitation compared to geostatistical approaches, as they fail to account for the spatial dependencies inherent to geotechnical datasets. This can result in erroneous model predictions, which are overly conservative when compared to the geostatistical results.

Regional flow duration curves: Geostatistical techniques versus multivariate regression

USGS Publications Warehouse

Pugliese, Alessio; Farmer, William H.; Castellarin, Attilio; Archfield, Stacey A.; Vogel, Richard M.

2016-01-01

A period-of-record flow duration curve (FDC) represents the relationship between the magnitude and frequency of daily streamflows. Prediction of FDCs is of great importance for locations characterized by sparse or missing streamflow observations. We present a detailed comparison of two methods which are capable of predicting an FDC at ungauged basins: (1) an adaptation of the geostatistical method, Top-kriging, employing a linear weighted average of dimensionless empirical FDCs, standardised with a reference streamflow value; and (2) regional multiple linear regression of streamflow quantiles, perhaps the most common method for the prediction of FDCs at ungauged sites. In particular, Top-kriging relies on a metric for expressing the similarity between catchments computed as the negative deviation of the FDC from a reference streamflow value, which we termed total negative deviation (TND). Comparisons of these two methods are made in 182 largely unregulated river catchments in the southeastern U.S. using a three-fold cross-validation algorithm. Our results reveal that the two methods perform similarly throughout flow-regimes, with average Nash-Sutcliffe Efficiencies 0.566 and 0.662, (0.883 and 0.829 on log-transformed quantiles) for the geostatistical and the linear regression models, respectively. The differences between the reproduction of FDC's occurred mostly for low flows with exceedance probability (i.e. duration) above 0.98.

SensibleSleep: A Bayesian Model for Learning Sleep Patterns from Smartphone Events

PubMed Central

Sekara, Vedran; Jonsson, Håkan; Larsen, Jakob Eg; Lehmann, Sune

2017-01-01

We propose a Bayesian model for extracting sleep patterns from smartphone events. Our method is able to identify individuals’ daily sleep periods and their evolution over time, and provides an estimation of the probability of sleep and wake transitions. The model is fitted to more than 400 participants from two different datasets, and we verify the results against ground truth from dedicated armband sleep trackers. We show that the model is able to produce reliable sleep estimates with an accuracy of 0.89, both at the individual and at the collective level. Moreover the Bayesian model is able to quantify uncertainty and encode prior knowledge about sleep patterns. Compared with existing smartphone-based systems, our method requires only screen on/off events, and is therefore much less intrusive in terms of privacy and more battery-efficient. PMID:28076375

SensibleSleep: A Bayesian Model for Learning Sleep Patterns from Smartphone Events.

PubMed

Cuttone, Andrea; Bækgaard, Per; Sekara, Vedran; Jonsson, Håkan; Larsen, Jakob Eg; Lehmann, Sune

2017-01-01

We propose a Bayesian model for extracting sleep patterns from smartphone events. Our method is able to identify individuals' daily sleep periods and their evolution over time, and provides an estimation of the probability of sleep and wake transitions. The model is fitted to more than 400 participants from two different datasets, and we verify the results against ground truth from dedicated armband sleep trackers. We show that the model is able to produce reliable sleep estimates with an accuracy of 0.89, both at the individual and at the collective level. Moreover the Bayesian model is able to quantify uncertainty and encode prior knowledge about sleep patterns. Compared with existing smartphone-based systems, our method requires only screen on/off events, and is therefore much less intrusive in terms of privacy and more battery-efficient.

Model selection and parameter estimation in structural dynamics using approximate Bayesian computation

NASA Astrophysics Data System (ADS)

Ben Abdessalem, Anis; Dervilis, Nikolaos; Wagg, David; Worden, Keith

2018-01-01

This paper will introduce the use of the approximate Bayesian computation (ABC) algorithm for model selection and parameter estimation in structural dynamics. ABC is a likelihood-free method typically used when the likelihood function is either intractable or cannot be approached in a closed form. To circumvent the evaluation of the likelihood function, simulation from a forward model is at the core of the ABC algorithm. The algorithm offers the possibility to use different metrics and summary statistics representative of the data to carry out Bayesian inference. The efficacy of the algorithm in structural dynamics is demonstrated through three different illustrative examples of nonlinear system identification: cubic and cubic-quintic models, the Bouc-Wen model and the Duffing oscillator. The obtained results suggest that ABC is a promising alternative to deal with model selection and parameter estimation issues, specifically for systems with complex behaviours.

Bayesian inference for OPC modeling

NASA Astrophysics Data System (ADS)

Burbine, Andrew; Sturtevant, John; Fryer, David; Smith, Bruce W.

2016-03-01

The use of optical proximity correction (OPC) demands increasingly accurate models of the photolithographic process. Model building and inference techniques in the data science community have seen great strides in the past two decades which make better use of available information. This paper aims to demonstrate the predictive power of Bayesian inference as a method for parameter selection in lithographic models by quantifying the uncertainty associated with model inputs and wafer data. Specifically, the method combines the model builder's prior information about each modelling assumption with the maximization of each observation's likelihood as a Student's t-distributed random variable. Through the use of a Markov chain Monte Carlo (MCMC) algorithm, a model's parameter space is explored to find the most credible parameter values. During parameter exploration, the parameters' posterior distributions are generated by applying Bayes' rule, using a likelihood function and the a priori knowledge supplied. The MCMC algorithm used, an affine invariant ensemble sampler (AIES), is implemented by initializing many walkers which semiindependently explore the space. The convergence of these walkers to global maxima of the likelihood volume determine the parameter values' highest density intervals (HDI) to reveal champion models. We show that this method of parameter selection provides insights into the data that traditional methods do not and outline continued experiments to vet the method.

A Bayesian joint probability modeling approach for seasonal forecasting of streamflows at multiple sites

NASA Astrophysics Data System (ADS)

Wang, Q. J.; Robertson, D. E.; Chiew, F. H. S.

2009-05-01

Seasonal forecasting of streamflows can be highly valuable for water resources management. In this paper, a Bayesian joint probability (BJP) modeling approach for seasonal forecasting of streamflows at multiple sites is presented. A Box-Cox transformed multivariate normal distribution is proposed to model the joint distribution of future streamflows and their predictors such as antecedent streamflows and El Niño-Southern Oscillation indices and other climate indicators. Bayesian inference of model parameters and uncertainties is implemented using Markov chain Monte Carlo sampling, leading to joint probabilistic forecasts of streamflows at multiple sites. The model provides a parametric structure for quantifying relationships between variables, including intersite correlations. The Box-Cox transformed multivariate normal distribution has considerable flexibility for modeling a wide range of predictors and predictands. The Bayesian inference formulated allows the use of data that contain nonconcurrent and missing records. The model flexibility and data-handling ability means that the BJP modeling approach is potentially of wide practical application. The paper also presents a number of statistical measures and graphical methods for verification of probabilistic forecasts of continuous variables. Results for streamflows at three river gauges in the Murrumbidgee River catchment in southeast Australia show that the BJP modeling approach has good forecast quality and that the fitted model is consistent with observed data.

Using Bayesian statistics for modeling PTSD through Latent Growth Mixture Modeling: implementation and discussion.

PubMed

Depaoli, Sarah; van de Schoot, Rens; van Loey, Nancy; Sijbrandij, Marit

2015-01-01

After traumatic events, such as disaster, war trauma, and injuries including burns (which is the focus here), the risk to develop posttraumatic stress disorder (PTSD) is approximately 10% (Breslau & Davis, 1992). Latent Growth Mixture Modeling can be used to classify individuals into distinct groups exhibiting different patterns of PTSD (Galatzer-Levy, 2015). Currently, empirical evidence points to four distinct trajectories of PTSD patterns in those who have experienced burn trauma. These trajectories are labeled as: resilient, recovery, chronic, and delayed onset trajectories (e.g., Bonanno, 2004; Bonanno, Brewin, Kaniasty, & Greca, 2010; Maercker, Gäbler, O'Neil, Schützwohl, & Müller, 2013; Pietrzak et al., 2013). The delayed onset trajectory affects only a small group of individuals, that is, about 4-5% (O'Donnell, Elliott, Lau, & Creamer, 2007). In addition to its low frequency, the later onset of this trajectory may contribute to the fact that these individuals can be easily overlooked by professionals. In this special symposium on Estimating PTSD trajectories (Van de Schoot, 2015a), we illustrate how to properly identify this small group of individuals through the Bayesian estimation framework using previous knowledge through priors (see, e.g., Depaoli & Boyajian, 2014; Van de Schoot, Broere, Perryck, Zondervan-Zwijnenburg, & Van Loey, 2015). We used latent growth mixture modeling (LGMM) (Van de Schoot, 2015b) to estimate PTSD trajectories across 4 years that followed a traumatic burn. We demonstrate and compare results from traditional (maximum likelihood) and Bayesian estimation using priors (see, Depaoli, 2012, 2013). Further, we discuss where priors come from and how to define them in the estimation process. We demonstrate that only the Bayesian approach results in the desired theory-driven solution of PTSD trajectories. Since the priors are chosen subjectively, we also present a sensitivity analysis of the Bayesian results to illustrate how to check

Open Source Bayesian Models. 1. Application to ADME/Tox and Drug Discovery Datasets.

PubMed

Clark, Alex M; Dole, Krishna; Coulon-Spektor, Anna; McNutt, Andrew; Grass, George; Freundlich, Joel S; Reynolds, Robert C; Ekins, Sean

2015-06-22

On the order of hundreds of absorption, distribution, metabolism, excretion, and toxicity (ADME/Tox) models have been described in the literature in the past decade which are more often than not inaccessible to anyone but their authors. Public accessibility is also an issue with computational models for bioactivity, and the ability to share such models still remains a major challenge limiting drug discovery. We describe the creation of a reference implementation of a Bayesian model-building software module, which we have released as an open source component that is now included in the Chemistry Development Kit (CDK) project, as well as implemented in the CDD Vault and in several mobile apps. We use this implementation to build an array of Bayesian models for ADME/Tox, in vitro and in vivo bioactivity, and other physicochemical properties. We show that these models possess cross-validation receiver operator curve values comparable to those generated previously in prior publications using alternative tools. We have now described how the implementation of Bayesian models with FCFP6 descriptors generated in the CDD Vault enables the rapid production of robust machine learning models from public data or the user's own datasets. The current study sets the stage for generating models in proprietary software (such as CDD) and exporting these models in a format that could be run in open source software using CDK components. This work also demonstrates that we can enable biocomputation across distributed private or public datasets to enhance drug discovery.

Breast carcinoma, intratumour heterogeneity and histological grading, using geostatistics.

PubMed

Sharifi-Salamatian, V; de Roquancourt, A; Rigaut, J P

2000-01-01

Tumour progression is currently believed to result from genetic instability. Chromosomal patterns specific of a type of cancer are frequent even though phenotypic spatial heterogeneity is omnipresent. The latter is the usual cause of histological grading imprecision, a well documented problem, without any fully satisfactory solution up to now. The present article addresses this problem in breast carcinoma. The assessment of a genetic marker for human tumours requires quantifiable measures of intratumoral heterogeneity. If any invariance paradigm representing a stochastic or geostatistic function could be discovered, this might help in solving the grading problem. A novel methodological approach using geostatistics to measure heterogeneity is used. Twenty tumours from the three usual (Scarff-Bloom and Richardson) grades were obtained and paraffin sections stained by MIB-1 (Ki-67) and peroxidase staining. Whole two-dimensional sections were sampled. Morphometric grids of variable sizes allowed a simple and fast recording of positions of epithelial nuclei, marked or not by MIB-1. The geostatistical method is based here upon the asymptotic behaviour of dispersion variance. Measure of asymptotic exponent of dispersion variance shows an increase from grade 1 to grade 3. Preliminary results are encouraging: grades 1 and 3 on one hand and 2 and 3 on the other hand are totally separated. The final proof of an improved grading using this measure will of course require a confrontation with the results of survival studies.

Bayesian evidence computation for model selection in non-linear geoacoustic inference problems.

PubMed

Dettmer, Jan; Dosso, Stan E; Osler, John C

2010-12-01

This paper applies a general Bayesian inference approach, based on Bayesian evidence computation, to geoacoustic inversion of interface-wave dispersion data. Quantitative model selection is carried out by computing the evidence (normalizing constants) for several model parameterizations using annealed importance sampling. The resulting posterior probability density estimate is compared to estimates obtained from Metropolis-Hastings sampling to ensure consistent results. The approach is applied to invert interface-wave dispersion data collected on the Scotian Shelf, off the east coast of Canada for the sediment shear-wave velocity profile. Results are consistent with previous work on these data but extend the analysis to a rigorous approach including model selection and uncertainty analysis. The results are also consistent with core samples and seismic reflection measurements carried out in the area.

Ridge, Lasso and Bayesian additive-dominance genomic models.

PubMed

Azevedo, Camila Ferreira; de Resende, Marcos Deon Vilela; E Silva, Fabyano Fonseca; Viana, José Marcelo Soriano; Valente, Magno Sávio Ferreira; Resende, Márcio Fernando Ribeiro; Muñoz, Patricio

2015-08-25

A complete approach for genome-wide selection (GWS) involves reliable statistical genetics models and methods. Reports on this topic are common for additive genetic models but not for additive-dominance models. The objective of this paper was (i) to compare the performance of 10 additive-dominance predictive models (including current models and proposed modifications), fitted using Bayesian, Lasso and Ridge regression approaches; and (ii) to decompose genomic heritability and accuracy in terms of three quantitative genetic information sources, namely, linkage disequilibrium (LD), co-segregation (CS) and pedigree relationships or family structure (PR). The simulation study considered two broad sense heritability levels (0.30 and 0.50, associated with narrow sense heritabilities of 0.20 and 0.35, respectively) and two genetic architectures for traits (the first consisting of small gene effects and the second consisting of a mixed inheritance model with five major genes). G-REML/G-BLUP and a modified Bayesian/Lasso (called BayesA*B* or t-BLASSO) method performed best in the prediction of genomic breeding as well as the total genotypic values of individuals in all four scenarios (two heritabilities x two genetic architectures). The BayesA*B*-type method showed a better ability to recover the dominance variance/additive variance ratio. Decomposition of genomic heritability and accuracy revealed the following descending importance order of information: LD, CS and PR not captured by markers, the last two being very close. Amongst the 10 models/methods evaluated, the G-BLUP, BAYESA*B* (-2,8) and BAYESA*B* (4,6) methods presented the best results and were found to be adequate for accurately predicting genomic breeding and total genotypic values as well as for estimating additive and dominance in additive-dominance genomic models.

Assessing Local Model Adequacy in Bayesian Hierarchical Models Using the Partitioned Deviance Information Criterion

PubMed Central

Wheeler, David C.; Hickson, DeMarc A.; Waller, Lance A.

2010-01-01

Many diagnostic tools and goodness-of-fit measures, such as the Akaike information criterion (AIC) and the Bayesian deviance information criterion (DIC), are available to evaluate the overall adequacy of linear regression models. In addition, visually assessing adequacy in models has become an essential part of any regression analysis. In this paper, we focus on a spatial consideration of the local DIC measure for model selection and goodness-of-fit evaluation. We use a partitioning of the DIC into the local DIC, leverage, and deviance residuals to assess local model fit and influence for both individual observations and groups of observations in a Bayesian framework. We use visualization of the local DIC and differences in local DIC between models to assist in model selection and to visualize the global and local impacts of adding covariates or model parameters. We demonstrate the utility of the local DIC in assessing model adequacy using HIV prevalence data from pregnant women in the Butare province of Rwanda during 1989-1993 using a range of linear model specifications, from global effects only to spatially varying coefficient models, and a set of covariates related to sexual behavior. Results of applying the diagnostic visualization approach include more refined model selection and greater understanding of the models as applied to the data. PMID:21243121

Prediction and assimilation of surf-zone processes using a Bayesian network: Part I: Forward models

USGS Publications Warehouse

Plant, Nathaniel G.; Holland, K. Todd

2011-01-01

Prediction of coastal processes, including waves, currents, and sediment transport, can be obtained from a variety of detailed geophysical-process models with many simulations showing significant skill. This capability supports a wide range of research and applied efforts that can benefit from accurate numerical predictions. However, the predictions are only as accurate as the data used to drive the models and, given the large temporal and spatial variability of the surf zone, inaccuracies in data are unavoidable such that useful predictions require corresponding estimates of uncertainty. We demonstrate how a Bayesian-network model can be used to provide accurate predictions of wave-height evolution in the surf zone given very sparse and/or inaccurate boundary-condition data. The approach is based on a formal treatment of a data-assimilation problem that takes advantage of significant reduction of the dimensionality of the model system. We demonstrate that predictions of a detailed geophysical model of the wave evolution are reproduced accurately using a Bayesian approach. In this surf-zone application, forward prediction skill was 83%, and uncertainties in the model inputs were accurately transferred to uncertainty in output variables. We also demonstrate that if modeling uncertainties were not conveyed to the Bayesian network (i.e., perfect data or model were assumed), then overly optimistic prediction uncertainties were computed. More consistent predictions and uncertainties were obtained by including model-parameter errors as a source of input uncertainty. Improved predictions (skill of 90%) were achieved because the Bayesian network simultaneously estimated optimal parameters while predicting wave heights.

Update on Bayesian Blocks: Segmented Models for Sequential Data

NASA Technical Reports Server (NTRS)

Scargle, Jeff

2017-01-01

The Bayesian Block algorithm, in wide use in astronomy and other areas, has been improved in several ways. The model for block shape has been generalized to include other than constant signal rate - e.g., linear, exponential, or other parametric models. In addition the computational efficiency has been improved, so that instead of O(N**2) the basic algorithm is O(N) in most cases. Other improvements in the theory and application of segmented representations will be described.

A Bayesian Approach for Population Pharmacokinetic Modeling of Alcohol in Japanese Individuals.

PubMed

Nemoto, Asuka; Masaaki, Matsuura; Yamaoka, Kazue

2017-01-01

Blood alcohol concentration data that were previously obtained from 34 healthy Japanese subjects with limited sampling times were reanalyzed. Characteristics of the data were that the concentrations were obtained from only the early part of the time-concentration curve. To explore significant covariates for the population pharmacokinetic analysis of alcohol by incorporating external data using a Bayesian method, and to estimate effects of the covariates. The data were analyzed using a Markov chain Monte Carlo Bayesian estimation with NONMEM 7.3 (ICON Clinical Research LLC, North Wales, Pennsylvania). Informative priors were obtained from the external study. A 1-compartment model with Michaelis-Menten elimination was used. The typical value for the apparent volume of distribution was 49.3 L at the age of 29.4 years. Volume of distribution was estimated to be 20.4 L smaller in subjects with the ALDH2*1/*2 genotype than in subjects with the ALDH2*1/*1 genotype. A population pharmacokinetic model for alcohol was updated. A Bayesian approach allowed interpretation of significant covariate relationships, even if the current dataset is not informative about all parameters. This is the first study reporting an estimate of the effect of the ALDH2 genotype in a PPK model.

Stoffenmanager exposure model: company-specific exposure assessments using a Bayesian methodology.

PubMed

van de Ven, Peter; Fransman, Wouter; Schinkel, Jody; Rubingh, Carina; Warren, Nicholas; Tielemans, Erik

2010-04-01

The web-based tool "Stoffenmanager" was initially developed to assist small- and medium-sized enterprises in the Netherlands to make qualitative risk assessments and to provide advice on control at the workplace. The tool uses a mechanistic model to arrive at a "Stoffenmanager score" for exposure. In a recent study it was shown that variability in exposure measurements given a certain Stoffenmanager score is still substantial. This article discusses an extension to the tool that uses a Bayesian methodology for quantitative workplace/scenario-specific exposure assessment. This methodology allows for real exposure data observed in the company of interest to be combined with the prior estimate (based on the Stoffenmanager model). The output of the tool is a company-specific assessment of exposure levels for a scenario for which data is available. The Bayesian approach provides a transparent way of synthesizing different types of information and is especially preferred in situations where available data is sparse, as is often the case in small- and medium sized-enterprises. Real-world examples as well as simulation studies were used to assess how different parameters such as sample size, difference between prior and data, uncertainty in prior, and variance in the data affect the eventual posterior distribution of a Bayesian exposure assessment.

A multiscale Bayesian data integration approach for mapping air dose rates around the Fukushima Daiichi Nuclear Power Plant.

PubMed

Wainwright, Haruko M; Seki, Akiyuki; Chen, Jinsong; Saito, Kimiaki

2017-02-01

This paper presents a multiscale data integration method to estimate the spatial distribution of air dose rates in the regional scale around the Fukushima Daiichi Nuclear Power Plant. We integrate various types of datasets, such as ground-based walk and car surveys, and airborne surveys, all of which have different scales, resolutions, spatial coverage, and accuracy. This method is based on geostatistics to represent spatial heterogeneous structures, and also on Bayesian hierarchical models to integrate multiscale, multi-type datasets in a consistent manner. The Bayesian method allows us to quantify the uncertainty in the estimates, and to provide the confidence intervals that are critical for robust decision-making. Although this approach is primarily data-driven, it has great flexibility to include mechanistic models for representing radiation transport or other complex correlations. We demonstrate our approach using three types of datasets collected at the same time over Fukushima City in Japan: (1) coarse-resolution airborne surveys covering the entire area, (2) car surveys along major roads, and (3) walk surveys in multiple neighborhoods. Results show that the method can successfully integrate three types of datasets and create an integrated map (including the confidence intervals) of air dose rates over the domain in high resolution. Moreover, this study provides us with various insights into the characteristics of each dataset, as well as radiocaesium distribution. In particular, the urban areas show high heterogeneity in the contaminant distribution due to human activities as well as large discrepancy among different surveys due to such heterogeneity. Copyright © 2016 Elsevier Ltd. All rights reserved.

Model Selection in Historical Research Using Approximate Bayesian Computation