A Bayesian Shrinkage Approach for AMMI Models
de Oliveira, Luciano Antonio; Nuvunga, Joel Jorge; Pamplona, Andrezza Kéllen Alves
2015-01-01
Linear-bilinear models, especially the additive main effects and multiplicative interaction (AMMI) model, are widely applicable to genotype-by-environment interaction (GEI) studies in plant breeding programs. These models allow a parsimonious modeling of GE interactions, retaining a small number of principal components in the analysis. However, one aspect of the AMMI model that is still debated is the selection criteria for determining the number of multiplicative terms required to describe the GE interaction pattern. Shrinkage estimators have been proposed as selection criteria for the GE interaction components. In this study, a Bayesian approach was combined with the AMMI model with shrinkage estimators for the principal components. A total of 55 maize genotypes were evaluated in nine different environments using a complete blocks design with three replicates. The results show that the traditional Bayesian AMMI model produces low shrinkage of singular values but avoids the usual pitfalls in determining the credible intervals in the biplot. On the other hand, Bayesian shrinkage AMMI models have difficulty with the credible interval for model parameters, but produce stronger shrinkage of the principal components, converging to GE matrices that have more shrinkage than those obtained using mixed models. This characteristic allowed more parsimonious models to be chosen, and resulted in models being selected that were similar to those obtained by the Cornelius F-test (α = 0.05) in traditional AMMI models and cross validation based on leave-one-out. This characteristic allowed more parsimonious models to be chosen and more GEI pattern retained on the first two components. The resulting model chosen by posterior distribution of singular value was also similar to those produced by the cross-validation approach in traditional AMMI models. Our method enables the estimation of credible interval for AMMI biplot plus the choice of AMMI model based on direct posterior
A Bayesian Shrinkage Approach for AMMI Models.
da Silva, Carlos Pereira; de Oliveira, Luciano Antonio; Nuvunga, Joel Jorge; Pamplona, Andrezza Kéllen Alves; Balestre, Marcio
2015-01-01
Linear-bilinear models, especially the additive main effects and multiplicative interaction (AMMI) model, are widely applicable to genotype-by-environment interaction (GEI) studies in plant breeding programs. These models allow a parsimonious modeling of GE interactions, retaining a small number of principal components in the analysis. However, one aspect of the AMMI model that is still debated is the selection criteria for determining the number of multiplicative terms required to describe the GE interaction pattern. Shrinkage estimators have been proposed as selection criteria for the GE interaction components. In this study, a Bayesian approach was combined with the AMMI model with shrinkage estimators for the principal components. A total of 55 maize genotypes were evaluated in nine different environments using a complete blocks design with three replicates. The results show that the traditional Bayesian AMMI model produces low shrinkage of singular values but avoids the usual pitfalls in determining the credible intervals in the biplot. On the other hand, Bayesian shrinkage AMMI models have difficulty with the credible interval for model parameters, but produce stronger shrinkage of the principal components, converging to GE matrices that have more shrinkage than those obtained using mixed models. This characteristic allowed more parsimonious models to be chosen, and resulted in models being selected that were similar to those obtained by the Cornelius F-test (α = 0.05) in traditional AMMI models and cross validation based on leave-one-out. This characteristic allowed more parsimonious models to be chosen and more GEI pattern retained on the first two components. The resulting model chosen by posterior distribution of singular value was also similar to those produced by the cross-validation approach in traditional AMMI models. Our method enables the estimation of credible interval for AMMI biplot plus the choice of AMMI model based on direct posterior
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.
Bayesian approach to decompression sickness model parameter estimation.
Howle, L E; Weber, P W; Nichols, J M
2017-03-01
We examine both maximum likelihood and Bayesian approaches for estimating probabilistic decompression sickness model parameters. Maximum likelihood estimation treats parameters as fixed values and determines the best estimate through repeated trials, whereas the Bayesian approach treats parameters as random variables and determines the parameter probability distributions. We would ultimately like to know the probability that a parameter lies in a certain range rather than simply make statements about the repeatability of our estimator. Although both represent powerful methods of inference, for models with complex or multi-peaked likelihoods, maximum likelihood parameter estimates can prove more difficult to interpret than the estimates of the parameter distributions provided by the Bayesian approach. For models of decompression sickness, we show that while these two estimation methods are complementary, the credible intervals generated by the Bayesian approach are more naturally suited to quantifying uncertainty in the model parameters.
Stochastic model updating utilizing Bayesian approach and Gaussian process model
NASA Astrophysics Data System (ADS)
Wan, Hua-Ping; Ren, Wei-Xin
2016-03-01
Stochastic model updating (SMU) has been increasingly applied in quantifying structural parameter uncertainty from responses variability. SMU for parameter uncertainty quantification refers to the problem of inverse uncertainty quantification (IUQ), which is a nontrivial task. Inverse problem solved with optimization usually brings about the issues of gradient computation, ill-conditionedness, and non-uniqueness. Moreover, the uncertainty present in response makes the inverse problem more complicated. In this study, Bayesian approach is adopted in SMU for parameter uncertainty quantification. The prominent strength of Bayesian approach for IUQ problem is that it solves IUQ problem in a straightforward manner, which enables it to avoid the previous issues. However, when applied to engineering structures that are modeled with a high-resolution finite element model (FEM), Bayesian approach is still computationally expensive since the commonly used Markov chain Monte Carlo (MCMC) method for Bayesian inference requires a large number of model runs to guarantee the convergence. Herein we reduce computational cost in two aspects. On the one hand, the fast-running Gaussian process model (GPM) is utilized to approximate the time-consuming high-resolution FEM. On the other hand, the advanced MCMC method using delayed rejection adaptive Metropolis (DRAM) algorithm that incorporates local adaptive strategy with global adaptive strategy is employed for Bayesian inference. In addition, we propose the use of the powerful variance-based global sensitivity analysis (GSA) in parameter selection to exclude non-influential parameters from calibration parameters, which yields a reduced-order model and thus further alleviates the computational burden. A simulated aluminum plate and a real-world complex cable-stayed pedestrian bridge are presented to illustrate the proposed framework and verify its feasibility.
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 non-parametrics and the probabilistic approach to modelling
Ghahramani, Zoubin
2013-01-01
Modelling is fundamental to many fields of science and engineering. A model can be thought of as a representation of possible data one could predict from a system. The probabilistic approach to modelling uses probability theory to express all aspects of uncertainty in the model. The probabilistic approach is synonymous with Bayesian modelling, which simply uses the rules of probability theory in order to make predictions, compare alternative models, and learn model parameters and structure from data. This simple and elegant framework is most powerful when coupled with flexible probabilistic models. Flexibility is achieved through the use of Bayesian non-parametrics. This article provides an overview of probabilistic modelling and an accessible survey of some of the main tools in Bayesian non-parametrics. The survey covers the use of Bayesian non-parametrics for modelling unknown functions, density estimation, clustering, time-series modelling, and representing sparsity, hierarchies, and covariance structure. More specifically, it gives brief non-technical overviews of Gaussian processes, Dirichlet processes, infinite hidden Markov models, Indian buffet processes, Kingman’s coalescent, Dirichlet diffusion trees and Wishart processes. PMID:23277609
Diagnosing Hybrid Systems: a Bayesian Model Selection Approach
NASA Technical Reports Server (NTRS)
McIlraith, Sheila A.
2005-01-01
In this paper we examine the problem of monitoring and diagnosing noisy complex dynamical systems that are modeled as hybrid systems-models of continuous behavior, interleaved by discrete transitions. In particular, we examine continuous systems with embedded supervisory controllers that experience abrupt, partial or full failure of component devices. Building on our previous work in this area (MBCG99;MBCG00), our specific focus in this paper ins on the mathematical formulation of the hybrid monitoring and diagnosis task as a Bayesian model tracking algorithm. The nonlinear dynamics of many hybrid systems present challenges to probabilistic tracking. Further, probabilistic tracking of a system for the purposes of diagnosis is problematic because the models of the system corresponding to failure modes are numerous and generally very unlikely. To focus tracking on these unlikely models and to reduce the number of potential models under consideration, we exploit logic-based techniques for qualitative model-based diagnosis to conjecture a limited initial set of consistent candidate models. In this paper we discuss alternative tracking techniques that are relevant to different classes of hybrid systems, focusing specifically on a method for tracking multiple models of nonlinear behavior simultaneously using factored sampling and conditional density propagation. To illustrate and motivate the approach described in this paper we examine the problem of monitoring and diganosing NASA's Sprint AERCam, a small spherical robotic camera unit with 12 thrusters that enable both linear and rotational motion.
Nonlinear regression modeling of nutrient loads in streams: A Bayesian approach
Qian, S.S.; Reckhow, K.H.; Zhai, J.; McMahon, G.
2005-01-01
A Bayesian nonlinear regression modeling method is introduced and compared with the least squares method for modeling nutrient loads in stream networks. The objective of the study is to better model spatial correlation in river basin hydrology and land use for improving the model as a forecasting tool. The Bayesian modeling approach is introduced in three steps, each with a more complicated model and data error structure. The approach is illustrated using a data set from three large river basins in eastern North Carolina. Results indicate that the Bayesian model better accounts for model and data uncertainties than does the conventional least squares approach. Applications of the Bayesian models for ambient water quality standards compliance and TMDL assessment are discussed. Copyright 2005 by the American Geophysical Union.
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…
Ice Shelf Modeling: A Cross-Polar Bayesian Statistical Approach
NASA Astrophysics Data System (ADS)
Kirchner, N.; Furrer, R.; Jakobsson, M.; Zwally, H. J.
2010-12-01
Ice streams interlink glacial terrestrial and marine environments: embedded in a grounded inland ice such as the Antarctic Ice Sheet or the paleo ice sheets covering extensive parts of the Eurasian and Amerasian Arctic respectively, ice streams are major drainage agents facilitating the discharge of substantial portions of continental ice into the ocean. At their seaward side, ice streams can either extend onto the ocean as floating ice tongues (such as the Drygalsky Ice Tongue/East Antarctica), or feed large ice shelves (as is the case for e.g. the Siple Coast and the Ross Ice Shelf/West Antarctica). The flow behavior of ice streams has been recognized to be intimately linked with configurational changes in their attached ice shelves; in particular, ice shelf disintegration is associated with rapid ice stream retreat and increased mass discharge from the continental ice mass, contributing eventually to sea level rise. Investigations of ice stream retreat mechanism are however incomplete if based on terrestrial records only: rather, the dynamics of ice shelves (and, eventually, the impact of the ocean on the latter) must be accounted for. However, since floating ice shelves leave hardly any traces behind when melting, uncertainty regarding the spatio-temporal distribution and evolution of ice shelves in times prior to instrumented and recorded observation is high, calling thus for a statistical modeling approach. Complementing ongoing large-scale numerical modeling efforts (Pollard & DeConto, 2009), we model the configuration of ice shelves by using a Bayesian Hiearchial Modeling (BHM) approach. We adopt a cross-polar perspective accounting for the fact that currently, ice shelves exist mainly along the coastline of Antarctica (and are virtually non-existing in the Arctic), while Arctic Ocean ice shelves repeatedly impacted the Arctic ocean basin during former glacial periods. Modeled Arctic ocean ice shelf configurations are compared with geological spatial
Bayesian Belief Networks Approach for Modeling Irrigation Behavior
NASA Astrophysics Data System (ADS)
Andriyas, S.; McKee, M.
2012-12-01
Canal operators need information to manage water deliveries to irrigators. Short-term irrigation demand forecasts can potentially valuable information for a canal operator who must manage an on-demand system. Such forecasts could be generated by using information about the decision-making processes of irrigators. Bayesian models of irrigation behavior can provide insight into the likely criteria which farmers use to make irrigation decisions. This paper develops a Bayesian belief network (BBN) to learn irrigation decision-making behavior of farmers and utilizes the resulting model to make forecasts of future irrigation decisions based on factor interaction and posterior probabilities. Models for studying irrigation behavior have been rarely explored in the past. The model discussed here was built from a combination of data about biotic, climatic, and edaphic conditions under which observed irrigation decisions were made. The paper includes a case study using data collected from the Canal B region of the Sevier River, near Delta, Utah. Alfalfa, barley and corn are the main crops of the location. The model has been tested with a portion of the data to affirm the model predictive capabilities. Irrigation rules were deduced in the process of learning and verified in the testing phase. It was found that most of the farmers used consistent rules throughout all years and across different types of crops. Soil moisture stress, which indicates the level of water available to the plant in the soil profile, was found to be one of the most significant likely driving forces for irrigation. Irrigations appeared to be triggered by a farmer's perception of soil stress, or by a perception of combined factors such as information about a neighbor irrigating or an apparent preference to irrigate on a weekend. Soil stress resulted in irrigation probabilities of 94.4% for alfalfa. With additional factors like weekend and irrigating when a neighbor irrigates, alfalfa irrigation
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.
A General and Flexible Approach to Estimating the Social Relations Model Using Bayesian Methods
ERIC Educational Resources Information Center
Ludtke, Oliver; Robitzsch, Alexander; Kenny, David A.; Trautwein, Ulrich
2013-01-01
The social relations model (SRM) is a conceptual, methodological, and analytical approach that is widely used to examine dyadic behaviors and interpersonal perception within groups. This article introduces a general and flexible approach to estimating the parameters of the SRM that is based on Bayesian methods using Markov chain Monte Carlo…
Medical Inpatient Journey Modeling and Clustering: A Bayesian Hidden Markov Model Based Approach
Huang, Zhengxing; Dong, Wei; Wang, Fei; Duan, Huilong
2015-01-01
Modeling and clustering medical inpatient journeys is useful to healthcare organizations for a number of reasons including inpatient journey reorganization in a more convenient way for understanding and browsing, etc. In this study, we present a probabilistic model-based approach to model and cluster medical inpatient journeys. Specifically, we exploit a Bayesian Hidden Markov Model based approach to transform medical inpatient journeys into a probabilistic space, which can be seen as a richer representation of inpatient journeys to be clustered. Then, using hierarchical clustering on the matrix of similarities, inpatient journeys can be clustered into different categories w.r.t their clinical and temporal characteristics. We evaluated the proposed approach on a real clinical data set pertaining to the unstable angina treatment process. The experimental results reveal that our method can identify and model latent treatment topics underlying in personalized inpatient journeys, and yield impressive clustering quality. PMID:26958200
ERIC Educational Resources Information Center
Lee, Sik-Yum; Song, Xin-Yuan; Cai, Jing-Heng
2010-01-01
Analysis of ordered binary and unordered binary data has received considerable attention in social and psychological research. This article introduces a Bayesian approach, which has several nice features in practical applications, for analyzing nonlinear structural equation models with dichotomous data. We demonstrate how to use the software…
A Robust Bayesian Approach for Structural Equation Models with Missing Data
ERIC Educational Resources Information Center
Lee, Sik-Yum; Xia, Ye-Mao
2008-01-01
In this paper, normal/independent distributions, including but not limited to the multivariate t distribution, the multivariate contaminated distribution, and the multivariate slash distribution, are used to develop a robust Bayesian approach for analyzing structural equation models with complete or missing data. In the context of a nonlinear…
Equifinality of formal (DREAM) and informal (GLUE) bayesian approaches in hydrologic modeling?
Vrugt, Jasper A; Robinson, Bruce A; Ter Braak, Cajo J F; Gupta, Hoshin V
2008-01-01
In recent years, a strong debate has emerged in the hydrologic literature regarding what constitutes an appropriate framework for uncertainty estimation. Particularly, there is strong disagreement whether an uncertainty framework should have its roots within a proper statistical (Bayesian) context, or whether such a framework should be based on a different philosophy and implement informal measures and weaker inference to summarize parameter and predictive distributions. In this paper, we compare a formal Bayesian approach using Markov Chain Monte Carlo (MCMC) with generalized likelihood uncertainty estimation (GLUE) for assessing uncertainty in conceptual watershed modeling. Our formal Bayesian approach is implemented using the recently developed differential evolution adaptive metropolis (DREAM) MCMC scheme with a likelihood function that explicitly considers model structural, input and parameter uncertainty. Our results demonstrate that DREAM and GLUE can generate very similar estimates of total streamflow uncertainty. This suggests that formal and informal Bayesian approaches have more common ground than the hydrologic literature and ongoing debate might suggest. The main advantage of formal approaches is, however, that they attempt to disentangle the effect of forcing, parameter and model structural error on total predictive uncertainty. This is key to improving hydrologic theory and to better understand and predict the flow of water through catchments.
A Bayesian approach to the semi-analytic model of galaxy formation
NASA Astrophysics Data System (ADS)
Lu, Yu
It is believed that a wide range of physical processes conspire to shape the observed galaxy population but it remains unsure of their detailed interactions. The semi-analytic model (SAM) of galaxy formation uses multi-dimensional parameterizations of the physical processes of galaxy formation and provides a tool to constrain these underlying physical interactions. Because of the high dimensionality and large uncertainties in the model, the parametric problem of galaxy formation can be profitably tackled with a Bayesian-inference based approach, which allows one to constrain theory with data in a statistically rigorous way. In this thesis, I present a newly developed method to build SAM upon the framework of Bayesian inference. I show that, aided by advanced Markov-Chain Monte-Carlo algorithms, the method has the power to efficiently combine information from diverse data sources, rigorously establish confidence bounds on model parameters, and provide powerful probability-based methods for hypothesis test. Using various data sets (stellar mass function, conditional stellar mass function, K-band luminosity function, and cold gas mass functions) of galaxies in the local Universe, I carry out a series of Bayesian model inferences. The results show that SAM contains huge degeneracies among its parameters, indicating that some of the conclusions drawn previously with the conventional approach may not be truly valid but need to be revisited by the Bayesian approach. Second, some of the degeneracy of the model can be broken by adopting multiple data sets that constrain different aspects of the galaxy population. Third, the inferences reveal that model has challenge to simultaneously explain some important observational results, suggesting that some key physics governing the evolution of star formation and feedback may still be missing from the model. These analyses show clearly that the Bayesian inference based SAM can be used to perform systematic and statistically
NASA Astrophysics Data System (ADS)
Xu, Tianfang; Valocchi, Albert J.
2015-11-01
Numerical groundwater flow and solute transport models are usually subject to model structural error due to simplification and/or misrepresentation of the real system, which raises questions regarding the suitability of conventional least squares regression-based (LSR) calibration. We present a new framework that explicitly describes the model structural error statistically in an inductive, data-driven way. We adopt a fully Bayesian approach that integrates Gaussian process error models into the calibration, prediction, and uncertainty analysis of groundwater flow models. We test the usefulness of the fully Bayesian approach with a synthetic case study of the impact of pumping on surface-ground water interaction. We illustrate through this example that the Bayesian parameter posterior distributions differ significantly from parameters estimated by conventional LSR, which does not account for model structural error. For the latter method, parameter compensation for model structural error leads to biased, overconfident prediction under changing pumping condition. In contrast, integrating Gaussian process error models significantly reduces predictive bias and leads to prediction intervals that are more consistent with validation data. Finally, we carry out a generalized LSR recalibration step to assimilate the Bayesian prediction while preserving mass conservation and other physical constraints, using a full error covariance matrix obtained from Bayesian results. It is found that the recalibrated model achieved lower predictive bias compared to the model calibrated using conventional LSR. The results highlight the importance of explicit treatment of model structural error especially in circumstances where subsequent decision-making and risk analysis require accurate prediction and uncertainty quantification.
A Bayesian Hidden Markov Model-based approach for anomaly detection in electronic systems
NASA Astrophysics Data System (ADS)
Dorj, E.; Chen, C.; Pecht, M.
Early detection of anomalies in any system or component prevents impending failures and enhances performance and availability. The complex architecture of electronics, the interdependency of component functionalities, and the miniaturization of most electronic systems make it difficult to detect and analyze anomalous behaviors. A Hidden Markov Model-based classification technique determines unobservable hidden behaviors of complex and remotely inaccessible electronic systems using observable signals. This paper presents a data-driven approach for anomaly detection in electronic systems based on a Bayesian Hidden Markov Model classification technique. The posterior parameters of the Hidden Markov Models are estimated using the conjugate prior method. An application of the developed Bayesian Hidden Markov Model-based anomaly detection approach is presented for detecting anomalous behavior in Insulated Gate Bipolar Transistors using experimental data. The detection results illustrate that the developed anomaly detection approach can help detect anomalous behaviors in electronic systems, which can help prevent system downtime and catastrophic failures.
Sequential Bayesian Detection: A Model-Based Approach
Sullivan, E J; Candy, J V
2007-08-13
Sequential detection theory has been known for a long time evolving in the late 1940's by Wald and followed by Middleton's classic exposition in the 1960's coupled with the concurrent enabling technology of digital computer systems and the development of sequential processors. Its development, when coupled to modern sequential model-based processors, offers a reasonable way to attack physics-based problems. In this chapter, the fundamentals of the sequential detection are reviewed from the Neyman-Pearson theoretical perspective and formulated for both linear and nonlinear (approximate) Gauss-Markov, state-space representations. We review the development of modern sequential detectors and incorporate the sequential model-based processors as an integral part of their solution. Motivated by a wealth of physics-based detection problems, we show how both linear and nonlinear processors can seamlessly be embedded into the sequential detection framework to provide a powerful approach to solving non-stationary detection problems.
Sequential Bayesian Detection: A Model-Based Approach
Candy, J V
2008-12-08
Sequential detection theory has been known for a long time evolving in the late 1940's by Wald and followed by Middleton's classic exposition in the 1960's coupled with the concurrent enabling technology of digital computer systems and the development of sequential processors. Its development, when coupled to modern sequential model-based processors, offers a reasonable way to attack physics-based problems. In this chapter, the fundamentals of the sequential detection are reviewed from the Neyman-Pearson theoretical perspective and formulated for both linear and nonlinear (approximate) Gauss-Markov, state-space representations. We review the development of modern sequential detectors and incorporate the sequential model-based processors as an integral part of their solution. Motivated by a wealth of physics-based detection problems, we show how both linear and nonlinear processors can seamlessly be embedded into the sequential detection framework to provide a powerful approach to solving non-stationary detection problems.
An Application of Bayesian Approach in Modeling Risk of Death in an Intensive Care Unit
Wong, Rowena Syn Yin; Ismail, Noor Azina
2016-01-01
Background and Objectives There are not many studies that attempt to model intensive care unit (ICU) risk of death in developing countries, especially in South East Asia. The aim of this study was to propose and describe application of a Bayesian approach in modeling in-ICU deaths in a Malaysian ICU. Methods This was a prospective study in a mixed medical-surgery ICU in a multidisciplinary tertiary referral hospital in Malaysia. Data collection included variables that were defined in Acute Physiology and Chronic Health Evaluation IV (APACHE IV) model. Bayesian Markov Chain Monte Carlo (MCMC) simulation approach was applied in the development of four multivariate logistic regression predictive models for the ICU, where the main outcome measure was in-ICU mortality risk. The performance of the models were assessed through overall model fit, discrimination and calibration measures. Results from the Bayesian models were also compared against results obtained using frequentist maximum likelihood method. Results The study involved 1,286 consecutive ICU admissions between January 1, 2009 and June 30, 2010, of which 1,111 met the inclusion criteria. Patients who were admitted to the ICU were generally younger, predominantly male, with low co-morbidity load and mostly under mechanical ventilation. The overall in-ICU mortality rate was 18.5% and the overall mean Acute Physiology Score (APS) was 68.5. All four models exhibited good discrimination, with area under receiver operating characteristic curve (AUC) values approximately 0.8. Calibration was acceptable (Hosmer-Lemeshow p-values > 0.05) for all models, except for model M3. Model M1 was identified as the model with the best overall performance in this study. Conclusion Four prediction models were proposed, where the best model was chosen based on its overall performance in this study. This study has also demonstrated the promising potential of the Bayesian MCMC approach as an alternative in the analysis and modeling of
Modelling household finances: A Bayesian approach to a multivariate two-part model.
Brown, Sarah; Ghosh, Pulak; Su, Li; Taylor, Karl
2015-09-01
We contribute to the empirical literature on household finances by introducing a Bayesian multivariate two-part model, which has been developed to further our understanding of household finances. Our flexible approach allows for the potential interdependence between the holding of assets and liabilities at the household level and also encompasses a two-part process to allow for differences in the influences on asset or liability holding and on the respective amounts held. Furthermore, the framework is dynamic in order to allow for persistence in household finances over time. Our findings endorse the joint modelling approach and provide evidence supporting the importance of dynamics. In addition, we find that certain independent variables exert different influences on the binary and continuous parts of the model thereby highlighting the flexibility of our framework and revealing a detailed picture of the nature of household finances.
Modelling household finances: A Bayesian approach to a multivariate two-part model
Brown, Sarah; Ghosh, Pulak; Su, Li; Taylor, Karl
2016-01-01
We contribute to the empirical literature on household finances by introducing a Bayesian multivariate two-part model, which has been developed to further our understanding of household finances. Our flexible approach allows for the potential interdependence between the holding of assets and liabilities at the household level and also encompasses a two-part process to allow for differences in the influences on asset or liability holding and on the respective amounts held. Furthermore, the framework is dynamic in order to allow for persistence in household finances over time. Our findings endorse the joint modelling approach and provide evidence supporting the importance of dynamics. In addition, we find that certain independent variables exert different influences on the binary and continuous parts of the model thereby highlighting the flexibility of our framework and revealing a detailed picture of the nature of household finances. PMID:27212801
Bayesian approach to color-difference models based on threshold and constant-stimuli methods.
Brusola, Fernando; Tortajada, Ignacio; Lengua, Ismael; Jordá, Begoña; Peris, Guillermo
2015-06-15
An alternative approach based on statistical Bayesian inference is presented to deal with the development of color-difference models and the precision of parameter estimation. The approach was applied to simulated data and real data, the latter published by selected authors involved with the development of color-difference formulae using traditional methods. Our results show very good agreement between the Bayesian and classical approaches. Among other benefits, our proposed methodology allows one to determine the marginal posterior distribution of each random individual parameter of the color-difference model. In this manner, it is possible to analyze the effect of individual parameters on the statistical significance calculation of a color-difference equation.
A Bayesian approach for inducing sparsity in generalized linear models with multi-category response
2015-01-01
Background The dimension and complexity of high-throughput gene expression data create many challenges for downstream analysis. Several approaches exist to reduce the number of variables with respect to small sample sizes. In this study, we utilized the Generalized Double Pareto (GDP) prior to induce sparsity in a Bayesian Generalized Linear Model (GLM) setting. The approach was evaluated using a publicly available microarray dataset containing 99 samples corresponding to four different prostate cancer subtypes. Results A hierarchical Sparse Bayesian GLM using GDP prior (SBGG) was developed to take into account the progressive nature of the response variable. We obtained an average overall classification accuracy between 82.5% and 94%, which was higher than Support Vector Machine, Random Forest or a Sparse Bayesian GLM using double exponential priors. Additionally, SBGG outperforms the other 3 methods in correctly identifying pre-metastatic stages of cancer progression, which can prove extremely valuable for therapeutic and diagnostic purposes. Importantly, using Geneset Cohesion Analysis Tool, we found that the top 100 genes produced by SBGG had an average functional cohesion p-value of 2.0E-4 compared to 0.007 to 0.131 produced by the other methods. Conclusions Using GDP in a Bayesian GLM model applied to cancer progression data results in better subclass prediction. In particular, the method identifies pre-metastatic stages of prostate cancer with substantially better accuracy and produces more functionally relevant gene sets. PMID:26423345
NASA Astrophysics Data System (ADS)
Xu, T.; Valocchi, A. J.
2014-12-01
Effective water resource management typically relies on numerical models to analyse groundwater flow and solute transport processes. These models are usually subject to model structure error due to simplification and/or misrepresentation of the real system. As a result, the model outputs may systematically deviate from measurements, thus violating a key assumption for traditional regression-based calibration and uncertainty analysis. On the other hand, model structure error induced bias can be described statistically in an inductive, data-driven way based on historical model-to-measurement misfit. We adopt a fully Bayesian approach that integrates a Gaussian process error model to account for model structure error to the calibration, prediction and uncertainty analysis of groundwater models. The posterior distributions of parameters of the groundwater model and the Gaussian process error model are jointly inferred using DREAM, an efficient Markov chain Monte Carlo sampler. We test the usefulness of the fully Bayesian approach towards a synthetic case study of surface-ground water interaction under changing pumping conditions. We first illustrate through this example that traditional least squares regression without accounting for model structure error yields biased parameter estimates due to parameter compensation as well as biased predictions. In contrast, the Bayesian approach gives less biased parameter estimates. Moreover, the integration of a Gaussian process error model significantly reduces predictive bias and leads to prediction intervals that are more consistent with observations. The results highlight the importance of explicit treatment of model structure error especially in circumstances where subsequent decision-making and risk analysis require accurate prediction and uncertainty quantification. In addition, the data-driven error modelling approach is capable of extracting more information from observation data than using a groundwater model alone.
Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach.
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.
NASA Astrophysics Data System (ADS)
Varvia, Petri; Rautiainen, Miina; Seppänen, Aku
2017-04-01
Hyperspectral remote sensing data carry information on the leaf area index (LAI) of forests, and thus in principle, LAI can be estimated based on the data by inverting a forest reflectance model. However, LAI is usually not the only unknown in a reflectance model; especially, the leaf spectral albedo and understory reflectance are also not known. If the uncertainties of these parameters are not accounted for, the inversion of a forest reflectance model can lead to biased estimates for LAI. In this paper, we study the effects of reflectance model uncertainties on LAI estimates, and further, investigate whether the LAI estimates could recover from these uncertainties with the aid of Bayesian inference. In the proposed approach, the unknown leaf albedo and understory reflectance are estimated simultaneously with LAI from hyperspectral remote sensing data. The feasibility of the approach is tested with numerical simulation studies. The results show that in the presence of unknown parameters, the Bayesian LAI estimates which account for the model uncertainties outperform the conventional estimates that are based on biased model parameters. Moreover, the results demonstrate that the Bayesian inference can also provide feasible measures for the uncertainty of the estimated LAI.
Model of Conceptual Change for INQPRO: A Bayesian Network Approach
ERIC Educational Resources Information Center
Ting, Choo-Yee; Sam, Yok-Cheng; Wong, Chee-Onn
2013-01-01
Constructing a computational model of conceptual change for a computer-based scientific inquiry learning environment is difficult due to two challenges: (i) externalizing the variables of conceptual change and its related variables is difficult. In addition, defining the causal dependencies among the variables is also not trivial. Such difficulty…
Gomez-Ramirez, Jaime; Sanz, Ricardo
2013-09-01
One of the most important scientific challenges today is the quantitative and predictive understanding of biological function. Classical mathematical and computational approaches have been enormously successful in modeling inert matter, but they may be inadequate to address inherent features of biological systems. We address the conceptual and methodological obstacles that lie in the inverse problem in biological systems modeling. We introduce a full Bayesian approach (FBA), a theoretical framework to study biological function, in which probability distributions are conditional on biophysical information that physically resides in the biological system that is studied by the scientist.
Lifting a veil on diversity: a Bayesian approach to fitting relative-abundance models.
Golicher, Duncan J; O'Hara, Robert B; Ruíz-Montoya, Lorena; Cayuela, Luis
2006-02-01
Bayesian methods incorporate prior knowledge into a statistical analysis. This prior knowledge is usually restricted to assumptions regarding the form of probability distributions of the parameters of interest, leaving their values to be determined mainly through the data. Here we show how a Bayesian approach can be applied to the problem of drawing inference regarding species abundance distributions and comparing diversity indices between sites. The classic log series and the lognormal models of relative- abundance distribution are apparently quite different in form. The first is a sampling distribution while the other is a model of abundance of the underlying population. Bayesian methods help unite these two models in a common framework. Markov chain Monte Carlo simulation can be used to fit both distributions as small hierarchical models with shared common assumptions. Sampling error can be assumed to follow a Poisson distribution. Species not found in a sample, but suspected to be present in the region or community of interest, can be given zero abundance. This not only simplifies the process of model fitting, but also provides a convenient way of calculating confidence intervals for diversity indices. The method is especially useful when a comparison of species diversity between sites with different sample sizes is the key motivation behind the research. We illustrate the potential of the approach using data on fruit-feeding butterflies in southern Mexico. We conclude that, once all assumptions have been made transparent, a single data set may provide support for the belief that diversity is negatively affected by anthropogenic forest disturbance. Bayesian methods help to apply theory regarding the distribution of abundance in ecological communities to applied conservation.
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.
A Bayesian approach to modeling diffraction profiles and application to ferroelectric materials
Iamsasri, Thanakorn; Guerrier, Jonathon; Esteves, Giovanni; ...
2017-02-01
A new statistical approach for modeling diffraction profiles is introduced, using Bayesian inference and a Markov chain Monte Carlo (MCMC) algorithm. This method is demonstrated by modeling the degenerate reflections during application of an electric field to two different ferroelectric materials: thin-film lead zirconate titanate (PZT) of composition PbZr0.3Ti0.7O3and a bulk commercial PZT polycrystalline ferroelectric. Here, the new method offers a unique uncertainty quantification of the model parameters that can be readily propagated into new calculated parameters.
A robust Bayesian approach to modeling epistemic uncertainty in common-cause failure models
Matthias C. M. Troffaes; Gero Walter; Dana Kelly
2014-05-01
In a standard Bayesian approach to the alpha-factor model for common-cause failure, a precise Dirichlet prior distribution models epistemic uncertainty in the alpha-factors. This Dirichlet prior is then updated with observed data to obtain a posterior distribution, which forms the basis for further inferences. In this paper, we adapt the imprecise Dirichlet model of Walley to represent epistemic uncertainty in the alpha-factors. In this approach, epistemic uncertainty is expressed more cautiously via lower and upper expectations for each alpha-factor, along with a learning parameter which determines how quickly the model learns from observed data. For this application, we focus on elicitation of the learning parameter, and find that values in the range of 1 to 10 seem reasonable. The approach is compared with Kelly and Atwood's minimally informative Dirichlet prior for the alpha-factor model, which incorporated precise mean values for the alpha-factors, but which was otherwise quite diffuse. Next, we explore the use of a set of Gamma priors to model epistemic uncertainty in the marginal failure rate, expressed via a lower and upper expectation for this rate, again along with a learning parameter. As zero counts are generally less of an issue here, we find that the choice of this learning parameter is less crucial. Finally, we demonstrate how both epistemic uncertainty models can be combined to arrive at lower and upper expectations for all common-cause failure rates. Thereby, we effectively provide a full sensitivity analysis of common-cause failure rates, properly reflecting epistemic uncertainty of the analyst on all levels of the common-cause failure model.
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
NASA Astrophysics Data System (ADS)
Skataric, Maja; Bose, Sandip; Zeroug, Smaine; Tilke, Peter
2017-02-01
It is not uncommon in the field of non-destructive evaluation that multiple measurements encompassing a variety of modalities are available for analysis and interpretation for determining the underlying states of nature of the materials or parts being tested. Despite and sometimes due to the richness of data, significant challenges arise in the interpretation manifested as ambiguities and inconsistencies due to various uncertain factors in the physical properties (inputs), environment, measurement device properties, human errors, and the measurement data (outputs). Most of these uncertainties cannot be described by any rigorous mathematical means, and modeling of all possibilities is usually infeasible for many real time applications. In this work, we will discuss an approach based on Hierarchical Bayesian Graphical Models (HBGM) for the improved interpretation of complex (multi-dimensional) problems with parametric uncertainties that lack usable physical models. In this setting, the input space of the physical properties is specified through prior distributions based on domain knowledge and expertise, which are represented as Gaussian mixtures to model the various possible scenarios of interest for non-destructive testing applications. Forward models are then used offline to generate the expected distribution of the proposed measurements which are used to train a hierarchical Bayesian network. In Bayesian analysis, all model parameters are treated as random variables, and inference of the parameters is made on the basis of posterior distribution given the observed data. Learned parameters of the posterior distribution obtained after the training can therefore be used to build an efficient classifier for differentiating new observed data in real time on the basis of pre-trained models. We will illustrate the implementation of the HBGM approach to ultrasonic measurements used for cement evaluation of cased wells in the oil industry.
NASA Astrophysics Data System (ADS)
Stucchi Boschi, Raquel; Qin, Mingming; Gimenez, Daniel; Cooper, Miguel
2016-04-01
Modeling is an important tool for better understanding and assessing land use impacts on landscape processes. A key point for environmental modeling is the knowledge of soil hydraulic properties. However, direct determination of soil hydraulic properties is difficult and costly, particularly in vast and remote regions such as one constituting the Amazon Biome. One way to overcome this problem is to extrapolate accurately estimated data to pedologically similar sites. The van Genuchten (VG) parametric equation is the most commonly used for modeling SWRC. The use of a Bayesian approach in combination with the Markov chain Monte Carlo to estimate the VG parameters has several advantages compared to the widely used global optimization techniques. The Bayesian approach provides posterior distributions of parameters that are independent from the initial values and allow for uncertainty analyses. The main objectives of this study were: i) to estimate hydraulic parameters from data of pasture and forest sites by the Bayesian inverse modeling approach; and ii) to investigate the extrapolation of the estimated VG parameters to a nearby toposequence with pedologically similar soils to those used for its estimate. The parameters were estimated from volumetric water content and tension observations obtained after rainfall events during a 207-day period from pasture and forest sites located in the southeastern Amazon region. These data were used to run HYDRUS-1D under a Differential Evolution Adaptive Metropolis (DREAM) scheme 10,000 times, and only the last 2,500 times were used to calculate the posterior distributions of each hydraulic parameter along with 95% confidence intervals (CI) of volumetric water content and tension time series. Then, the posterior distributions were used to generate hydraulic parameters for two nearby toposequences composed by six soil profiles, three are under forest and three are under pasture. The parameters of the nearby site were accepted when
Bayesian Model Averaging for Propensity Score Analysis.
Kaplan, David; Chen, Jianshen
2014-01-01
This article considers Bayesian model averaging as a means of addressing uncertainty in the selection of variables in the propensity score equation. We investigate an approximate Bayesian model averaging approach based on the model-averaged propensity score estimates produced by the R package BMA but that ignores uncertainty in the propensity score. We also provide a fully Bayesian model averaging approach via Markov chain Monte Carlo sampling (MCMC) to account for uncertainty in both parameters and models. A detailed study of our approach examines the differences in the causal estimate when incorporating noninformative versus informative priors in the model averaging stage. We examine these approaches under common methods of propensity score implementation. In addition, we evaluate the impact of changing the size of Occam's window used to narrow down the range of possible models. We also assess the predictive performance of both Bayesian model averaging propensity score approaches and compare it with the case without Bayesian model averaging. Overall, results show that both Bayesian model averaging propensity score approaches recover the treatment effect estimates well and generally provide larger uncertainty estimates, as expected. Both Bayesian model averaging approaches offer slightly better prediction of the propensity score compared with the Bayesian approach with a single propensity score equation. Covariate balance checks for the case study show that both Bayesian model averaging approaches offer good balance. The fully Bayesian model averaging approach also provides posterior probability intervals of the balance indices.
Crash risk analysis for Shanghai urban expressways: A Bayesian semi-parametric modeling approach.
Yu, Rongjie; Wang, Xuesong; Yang, Kui; Abdel-Aty, Mohamed
2016-10-01
Urban expressway systems have been developed rapidly in recent years in China; it has become one key part of the city roadway networks as carrying large traffic volume and providing high traveling speed. Along with the increase of traffic volume, traffic safety has become a major issue for Chinese urban expressways due to the frequent crash occurrence and the non-recurrent congestions caused by them. For the purpose of unveiling crash occurrence mechanisms and further developing Active Traffic Management (ATM) control strategies to improve traffic safety, this study developed disaggregate crash risk analysis models with loop detector traffic data and historical crash data. Bayesian random effects logistic regression models were utilized as it can account for the unobserved heterogeneity among crashes. However, previous crash risk analysis studies formulated random effects distributions in a parametric approach, which assigned them to follow normal distributions. Due to the limited information known about random effects distributions, subjective parametric setting may be incorrect. In order to construct more flexible and robust random effects to capture the unobserved heterogeneity, Bayesian semi-parametric inference technique was introduced to crash risk analysis in this study. Models with both inference techniques were developed for total crashes; semi-parametric models were proved to provide substantial better model goodness-of-fit, while the two models shared consistent coefficient estimations. Later on, Bayesian semi-parametric random effects logistic regression models were developed for weekday peak hour crashes, weekday non-peak hour crashes, and weekend non-peak hour crashes to investigate different crash occurrence scenarios. Significant factors that affect crash risk have been revealed and crash mechanisms have been concluded.
A Bayesian approach to the semi-analytic model of galaxy formation: methodology
NASA Astrophysics Data System (ADS)
Lu, Yu; Mo, H. J.; Weinberg, Martin D.; Katz, Neal
2011-09-01
We believe that a wide range of physical processes conspire to shape the observed galaxy population, but we remain unsure of their detailed interactions. The semi-analytic model (SAM) of galaxy formation uses multidimensional parametrizations of the physical processes of galaxy formation and provides a tool to constrain these underlying physical interactions. Because of the high dimensionality, the parametric problem of galaxy formation may be profitably tackled with a Bayesian-inference-based approach, which allows one to constrain theory with data in a statistically rigorous way. In this paper, we develop a SAM in the framework of Bayesian inference. We show that, with a parallel implementation of an advanced Markov chain Monte Carlo algorithm, it is now possible to rigorously sample the posterior distribution of the high-dimensional parameter space of typical SAMs. As an example, we characterize galaxy formation in the current Λ cold dark matter cosmology using the stellar mass function of galaxies as an observational constraint. We find that the posterior probability distribution is both topologically complex and degenerate in some important model parameters, suggesting that thorough explorations of the parameter space are needed to understand the models. We also demonstrate that because of the model degeneracy, adopting a narrow prior strongly restricts the model. Therefore, the inferences based on SAMs are conditional to the model adopted. Using synthetic data to mimic systematic errors in the stellar mass function, we demonstrate that an accurate observational error model is essential to meaningful inference.
Water quality modeling for load reduction under uncertainty: a Bayesian approach.
Liu, Yong; Yang, Pingjian; Hu, Cheng; Guo, Huaicheng
2008-07-01
A Bayesian approach was applied to river water quality modeling (WQM) for load and parameter estimation. A distributed-source model (DSM) was used as the basic model to support load reduction and effective water quality management in the Hun-Taizi River system, northeastern China. Water quality was surveyed at 18 sites weekly from 1995 to 2004; biological oxygen demand (BOD) and ammonia (NH(4)(+)) were selected as WQM variables. The first-order decay rate (k(i)) and load (L(i)) of the 16 river segments were estimated using the Bayesian approach. The maximum pollutant loading (L(m)) of NH(4)(+) and BOD for each river segment was determined based on DSM and the estimated parameters of k(i). The results showed that for most river segments, the historical loading was beyond the L(m) threshold; thus, reduction for organic matter and nitrogen is necessary to meet water quality goals. Then the effects of inflow pollutant concentration (C(i-1)) and water velocity (v(i)) on water quality standard compliance were used to demonstrate how the proposed model can be applied to water quality management. The results enable decision makers to decide load reductions and allocations among river segments under different C(i-1) and v(i) scenarios.
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…
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.
Jiménez, José; García, Emilio J; Llaneza, Luis; Palacios, Vicente; González, Luis Mariano; García-Domínguez, Francisco; Múñoz-Igualada, Jaime; López-Bao, José Vicente
2016-08-01
In many cases, the first step in large-carnivore management is to obtain objective, reliable, and cost-effective estimates of population parameters through procedures that are reproducible over time. However, monitoring predators over large areas is difficult, and the data have a high level of uncertainty. We devised a practical multimethod and multistate modeling approach based on Bayesian hierarchical-site-occupancy models that combined multiple survey methods to estimate different population states for use in monitoring large predators at a regional scale. We used wolves (Canis lupus) as our model species and generated reliable estimates of the number of sites with wolf reproduction (presence of pups). We used 2 wolf data sets from Spain (Western Galicia in 2013 and Asturias in 2004) to test the approach. Based on howling surveys, the naïve estimation (i.e., estimate based only on observations) of the number of sites with reproduction was 9 and 25 sites in Western Galicia and Asturias, respectively. Our model showed 33.4 (SD 9.6) and 34.4 (3.9) sites with wolf reproduction, respectively. The number of occupied sites with wolf reproduction was 0.67 (SD 0.19) and 0.76 (0.11), respectively. This approach can be used to design more cost-effective monitoring programs (i.e., to define the sampling effort needed per site). Our approach should inspire well-coordinated surveys across multiple administrative borders and populations and lead to improved decision making for management of large carnivores on a landscape level. The use of this Bayesian framework provides a simple way to visualize the degree of uncertainty around population-parameter estimates and thus provides managers and stakeholders an intuitive approach to interpreting monitoring results. Our approach can be widely applied to large spatial scales in wildlife monitoring where detection probabilities differ between population states and where several methods are being used to estimate different population
Bayesian Approach for Inconsistent Information
Stein, M.; Beer, M.; Kreinovich, V.
2013-01-01
In engineering situations, we usually have a large amount of prior knowledge that needs to be taken into account when processing data. Traditionally, the Bayesian approach is used to process data in the presence of prior knowledge. Sometimes, when we apply the traditional Bayesian techniques to engineering data, we get inconsistencies between the data and prior knowledge. These inconsistencies are usually caused by the fact that in the traditional approach, we assume that we know the exact sample values, that the prior distribution is exactly known, etc. In reality, the data is imprecise due to measurement errors, the prior knowledge is only approximately known, etc. So, a natural way to deal with the seemingly inconsistent information is to take this imprecision into account in the Bayesian approach – e.g., by using fuzzy techniques. In this paper, we describe several possible scenarios for fuzzifying the Bayesian approach. Particular attention is paid to the interaction between the estimated imprecise parameters. In this paper, to implement the corresponding fuzzy versions of the Bayesian formulas, we use straightforward computations of the related expression – which makes our computations reasonably time-consuming. Computations in the traditional (non-fuzzy) Bayesian approach are much faster – because they use algorithmically efficient reformulations of the Bayesian formulas. We expect that similar reformulations of the fuzzy Bayesian formulas will also drastically decrease the computation time and thus, enhance the practical use of the proposed methods. PMID:24089579
Onisko, Agnieszka; Druzdzel, Marek J.; Austin, R. Marshall
2016-01-01
Background: Classical statistics is a well-established approach in the analysis of medical data. While the medical community seems to be familiar with the concept of a statistical analysis and its interpretation, the Bayesian approach, argued by many of its proponents to be superior to the classical frequentist approach, is still not well-recognized in the analysis of medical data. Aim: The goal of this study is to encourage data analysts to use the Bayesian approach, such as modeling with graphical probabilistic networks, as an insightful alternative to classical statistical analysis of medical data. Materials and Methods: This paper offers a comparison of two approaches to analysis of medical time series data: (1) classical statistical approach, such as the Kaplan–Meier estimator and the Cox proportional hazards regression model, and (2) dynamic Bayesian network modeling. Our comparison is based on time series cervical cancer screening data collected at Magee-Womens Hospital, University of Pittsburgh Medical Center over 10 years. Results: The main outcomes of our comparison are cervical cancer risk assessments produced by the three approaches. However, our analysis discusses also several aspects of the comparison, such as modeling assumptions, model building, dealing with incomplete data, individualized risk assessment, results interpretation, and model validation. Conclusion: Our study shows that the Bayesian approach is (1) much more flexible in terms of modeling effort, and (2) it offers an individualized risk assessment, which is more cumbersome for classical statistical approaches. PMID:28163973
Yi, Nengjun; Shriner, Daniel; Banerjee, Samprit; Mehta, Tapan; Pomp, Daniel; Yandell, Brian S.
2007-01-01
We extend our Bayesian model selection framework for mapping epistatic QTL in experimental crosses to include environmental effects and gene–environment interactions. We propose a new, fast Markov chain Monte Carlo algorithm to explore the posterior distribution of unknowns. In addition, we take advantage of any prior knowledge about genetic architecture to increase posterior probability on more probable models. These enhancements have significant computational advantages in models with many effects. We illustrate the proposed method by detecting new epistatic and gene–sex interactions for obesity-related traits in two real data sets of mice. Our method has been implemented in the freely available package R/qtlbim (http://www.qtlbim.org) to facilitate the general usage of the Bayesian methodology for genomewide interacting QTL analysis. PMID:17483424
Xu, Chengcheng; Wang, Wei; Liu, Pan; Li, Zhibin
2015-12-01
This study aimed to develop a real-time crash risk model with limited data in China by using Bayesian meta-analysis and Bayesian inference approach. A systematic review was first conducted by using three different Bayesian meta-analyses, including the fixed effect meta-analysis, the random effect meta-analysis, and the meta-regression. The meta-analyses provided a numerical summary of the effects of traffic variables on crash risks by quantitatively synthesizing results from previous studies. The random effect meta-analysis and the meta-regression produced a more conservative estimate for the effects of traffic variables compared with the fixed effect meta-analysis. Then, the meta-analyses results were used as informative priors for developing crash risk models with limited data. Three different meta-analyses significantly affect model fit and prediction accuracy. The model based on meta-regression can increase the prediction accuracy by about 15% as compared to the model that was directly developed with limited data. Finally, the Bayesian predictive densities analysis was used to identify the outliers in the limited data. It can further improve the prediction accuracy by 5.0%.
NASA Astrophysics Data System (ADS)
Stephenson, John; Gallagher, Kerry; Holmes, Chris
2006-10-01
We present a new approach for modelling annealing of fission tracks in apatite, aiming to address various problems with existing models. We cast the model in a fully Bayesian context, which allows us explicitly to deal with data and parameter uncertainties and correlations, and also to deal with the predictive uncertainties. We focus on a well-known annealing algorithm [Laslett, G.M., Green, P.F., Duddy, I.R., Gleadow. A.J.W., 1987. Thermal annealing of fission tracks in apatite. 2. A quantitative-analysis. Chem. Geol., 65 (1), 1-13], and build a hierachical Bayesian model to incorporate both laboratory and geological timescale data as direct constraints. Relative to the original model calibration, we find a better (in terms of likelihood) model conditioned just on the reported laboratory data. We then include the uncertainty on the temperatures recorded during the laboratory annealing experiments. We again find a better model, but the predictive uncertainty when extrapolated to geological timescales is increased due to the uncertainty on the laboratory temperatures. Finally, we explictly include a data set [Vrolijk, P., Donelick, R.A., Quenq, J., Cloos. M., 1992. Testing models of fission track annealing in apatite in a simple thermal setting: site 800, leg 129. In: Larson, R., Lancelet, Y. (Eds.), Proceedings of the Ocean Drilling Program, Scientific Results, vol. 129, pp. 169-176] which provides low-temperature geological timescale constraints for the model calibration. When combined with the laboratory data, we find a model which satisfies both the low-temperature and high-temperature geological timescale benchmarks, although the fit to the original laboratory data is degraded. However, when extrapolated to geological timescales, this combined model significantly reduces the well-known rapid recent cooling artifact found in many published thermal models for geological samples.
A Bayesian approach for temporally scaling climate for modeling ecological systems
Post van der Burg, Max; Anteau, Michael J.; McCauley, Lisa A.; Wiltermuth, Mark T.
2016-01-01
With climate change becoming more of concern, many ecologists are including climate variables in their system and statistical models. The Standardized Precipitation Evapotranspiration Index (SPEI) is a drought index that has potential advantages in modeling ecological response variables, including a flexible computation of the index over different timescales. However, little development has been made in terms of the choice of timescale for SPEI. We developed a Bayesian modeling approach for estimating the timescale for SPEI and demonstrated its use in modeling wetland hydrologic dynamics in two different eras (i.e., historical [pre-1970] and contemporary [post-2003]). Our goal was to determine whether differences in climate between the two eras could explain changes in the amount of water in wetlands. Our results showed that wetland water surface areas tended to be larger in wetter conditions, but also changed less in response to climate fluctuations in the contemporary era. We also found that the average timescale parameter was greater in the historical period, compared with the contemporary period. We were not able to determine whether this shift in timescale was due to a change in the timing of wet–dry periods or whether it was due to changes in the way wetlands responded to climate. Our results suggest that perhaps some interaction between climate and hydrologic response may be at work, and further analysis is needed to determine which has a stronger influence. Despite this, we suggest that our modeling approach enabled us to estimate the relevant timescale for SPEI and make inferences from those estimates. Likewise, our approach provides a mechanism for using prior information with future data to assess whether these patterns may continue over time. We suggest that ecologists consider using temporally scalable climate indices in conjunction with Bayesian analysis for assessing the role of climate in ecological systems.
A Bayesian Hierarchical Modeling Approach to Predicting Flow in Ungauged Basins
NASA Astrophysics Data System (ADS)
Gronewold, A.; Alameddine, I.; Anderson, R. M.
2009-12-01
Recent innovative approaches to identifying and applying regression-based relationships between land use patterns (such as increasing impervious surface area and decreasing vegetative cover) and rainfall-runoff model parameters represent novel and promising improvements to predicting flow from ungauged basins. In particular, these approaches allow for predicting flows under uncertain and potentially variable future conditions due to rapid land cover changes, variable climate conditions, and other factors. Despite the broad range of literature on estimating rainfall-runoff model parameters, however, the absence of a robust set of modeling tools for identifying and quantifying uncertainties in (and correlation between) rainfall-runoff model parameters represents a significant gap in current hydrological modeling research. Here, we build upon a series of recent publications promoting novel Bayesian and probabilistic modeling strategies for quantifying rainfall-runoff model parameter estimation uncertainty. Our approach applies alternative measures of rainfall-runoff model parameter joint likelihood (including Nash-Sutcliffe efficiency, among others) to simulate samples from the joint parameter posterior probability density function. We then use these correlated samples as response variables in a Bayesian hierarchical model with land use coverage data as predictor variables in order to develop a robust land use-based tool for forecasting flow in ungauged basins while accounting for, and explicitly acknowledging, parameter estimation uncertainty. We apply this modeling strategy to low-relief coastal watersheds of Eastern North Carolina, an area representative of coastal resource waters throughout the world because of its sensitive embayments and because of the abundant (but currently threatened) natural resources it hosts. Consequently, this area is the subject of several ongoing studies and large-scale planning initiatives, including those conducted through the United
A Bayesian network approach for modeling local failure in lung cancer
NASA Astrophysics Data System (ADS)
Oh, Jung Hun; Craft, Jeffrey; Lozi, Rawan Al; Vaidya, Manushka; Meng, Yifan; Deasy, Joseph O.; Bradley, Jeffrey D.; El Naqa, Issam
2011-03-01
Locally advanced non-small cell lung cancer (NSCLC) patients suffer from a high local failure rate following radiotherapy. Despite many efforts to develop new dose-volume models for early detection of tumor local failure, there was no reported significant improvement in their application prospectively. Based on recent studies of biomarker proteins' role in hypoxia and inflammation in predicting tumor response to radiotherapy, we hypothesize that combining physical and biological factors with a suitable framework could improve the overall prediction. To test this hypothesis, we propose a graphical Bayesian network framework for predicting local failure in lung cancer. The proposed approach was tested using two different datasets of locally advanced NSCLC patients treated with radiotherapy. The first dataset was collected retrospectively, which comprises clinical and dosimetric variables only. The second dataset was collected prospectively in which in addition to clinical and dosimetric information, blood was drawn from the patients at various time points to extract candidate biomarkers as well. Our preliminary results show that the proposed method can be used as an efficient method to develop predictive models of local failure in these patients and to interpret relationships among the different variables in the models. We also demonstrate the potential use of heterogeneous physical and biological variables to improve the model prediction. With the first dataset, we achieved better performance compared with competing Bayesian-based classifiers. With the second dataset, the combined model had a slightly higher performance compared to individual physical and biological models, with the biological variables making the largest contribution. Our preliminary results highlight the potential of the proposed integrated approach for predicting post-radiotherapy local failure in NSCLC patients.
Shi, Ming; Shen, Weiming; Wang, Hong-Qiang; Chong, Yanwen
2016-12-01
Inferring gene regulatory networks (GRNs) from microarray expression data are an important but challenging issue in systems biology. In this study, the authors propose a Bayesian information criterion (BIC)-guided sparse regression approach for GRN reconstruction. This approach can adaptively model GRNs by optimising the l1-norm regularisation of sparse regression based on a modified version of BIC. The use of the regularisation strategy ensures the inferred GRNs to be as sparse as natural, while the modified BIC allows incorporating prior knowledge on expression regulation and thus avoids the overestimation of expression regulators as usual. Especially, the proposed method provides a clear interpretation of combinatorial regulations of gene expression by optimally extracting regulation coordination for a given target gene. Experimental results on both simulation data and real-world microarray data demonstrate the competent performance of discovering regulatory relationships in GRN reconstruction.
Harrison, Jay M; Breeze, Matthew L; Harrigan, George G
2011-08-01
Statistical comparisons of compositional data generated on genetically modified (GM) crops and their near-isogenic conventional (non-GM) counterparts typically rely on classical significance testing. This manuscript presents an introduction to Bayesian methods for compositional analysis along with recommendations for model validation. The approach is illustrated using protein and fat data from two herbicide tolerant GM soybeans (MON87708 and MON87708×MON89788) and a conventional comparator grown in the US in 2008 and 2009. Guidelines recommended by the US Food and Drug Administration (FDA) in conducting Bayesian analyses of clinical studies on medical devices were followed. This study is the first Bayesian approach to GM and non-GM compositional comparisons. The evaluation presented here supports a conclusion that a Bayesian approach to analyzing compositional data can provide meaningful and interpretable results. We further describe the importance of method validation and approaches to model checking if Bayesian approaches to compositional data analysis are to be considered viable by scientists involved in GM research and regulation.
NASA Astrophysics Data System (ADS)
Freni, Gabriele; Mannina, Giorgio
In urban drainage modelling, uncertainty analysis is of undoubted necessity. However, uncertainty analysis in urban water-quality modelling is still in its infancy and only few studies have been carried out. Therefore, several methodological aspects still need to be experienced and clarified especially regarding water quality modelling. The use of the Bayesian approach for uncertainty analysis has been stimulated by its rigorous theoretical framework and by the possibility of evaluating the impact of new knowledge on the modelling predictions. Nevertheless, the Bayesian approach relies on some restrictive hypotheses that are not present in less formal methods like the Generalised Likelihood Uncertainty Estimation (GLUE). One crucial point in the application of Bayesian method is the formulation of a likelihood function that is conditioned by the hypotheses made regarding model residuals. Statistical transformations, such as the use of Box-Cox equation, are generally used to ensure the homoscedasticity of residuals. However, this practice may affect the reliability of the analysis leading to a wrong uncertainty estimation. The present paper aims to explore the influence of the Box-Cox equation for environmental water quality models. To this end, five cases were considered one of which was the “real” residuals distributions (i.e. drawn from available data). The analysis was applied to the Nocella experimental catchment (Italy) which is an agricultural and semi-urbanised basin where two sewer systems, two wastewater treatment plants and a river reach were monitored during both dry and wet weather periods. The results show that the uncertainty estimation is greatly affected by residual transformation and a wrong assumption may also affect the evaluation of model uncertainty. The use of less formal methods always provide an overestimation of modelling uncertainty with respect to Bayesian method but such effect is reduced if a wrong assumption is made regarding the
Meta-analysis of diagnostic test data: a bivariate Bayesian modeling approach.
Verde, Pablo E
2010-12-30
In the last decades, the amount of published results on clinical diagnostic tests has expanded very rapidly. The counterpart to this development has been the formal evaluation and synthesis of diagnostic results. However, published results present substantial heterogeneity and they can be regarded as so far removed from the classical domain of meta-analysis, that they can provide a rather severe test of classical statistical methods. Recently, bivariate random effects meta-analytic methods, which model the pairs of sensitivities and specificities, have been presented from the classical point of view. In this work a bivariate Bayesian modeling approach is presented. This approach substantially extends the scope of classical bivariate methods by allowing the structural distribution of the random effects to depend on multiple sources of variability. Meta-analysis is summarized by the predictive posterior distributions for sensitivity and specificity. This new approach allows, also, to perform substantial model checking, model diagnostic and model selection. Statistical computations are implemented in the public domain statistical software (WinBUGS and R) and illustrated with real data examples.
Bayesian model-based approach for developing a river water quality index
NASA Astrophysics Data System (ADS)
Ali, Zalina Mohd; Ibrahim, Noor Akma; Mengersen, Kerrie; Shitan, Mahendran; Juahir, Hafizan
2014-09-01
Six main pollutants have been previously identified by expert opinion to determine river condition in Malaysia. The pollutants were Dissolved Oxygen (DO), Biochemical Oxygen Demand (BOD), Chemical Oxygen Demand (COD), Suspended Solid (SS), potential of Hydrogen (pH) and Ammonia (AN). The selected variables together with the respective weights have been applied to calculate the water quality index of all rivers in Malaysia. However, the relative weights established in DOE-WQI formula are subjective in nature and not unanimously agreed upon, as indicated by different weight being proposed for the same variables by various panels of experts. Focusing on the Langat River, a Bayesian model-based approach was introduced for the first time in this study to obtain new objective relative weights. The new weights used in WQI calculation are shown to be capable of capturing similar distributions in water quality compared with the existing DOE-WQI.
NASA Astrophysics Data System (ADS)
Zhao, Tongtiegang; Schepen, Andrew; Wang, Q. J.
2016-10-01
The Bayesian joint probability (BJP) modelling approach is used operationally to produce seasonal (three-month-total) ensemble streamflow forecasts in Australia. However, water resource managers are calling for more informative sub-seasonal forecasts. Taking advantage of BJP's capability of handling multiple predictands, ensemble forecasting of sub-seasonal to seasonal streamflows is investigated for 23 catchments around Australia. Using antecedent streamflow and climate indices as predictors, monthly forecasts are developed for the three-month period ahead. Forecast reliability and skill are evaluated for the period 1982-2011 using a rigorous leave-five-years-out cross validation strategy. BJP ensemble forecasts of monthly streamflow volumes are generally reliable in ensemble spread. Forecast skill, relative to climatology, is positive in 74% of cases in the first month, decreasing to 57% and 46% respectively for streamflow forecasts for the final two months of the season. As forecast skill diminishes with increasing lead time, the monthly forecasts approach climatology. Seasonal forecasts accumulated from monthly forecasts are found to be similarly skilful to forecasts from BJP models based on seasonal totals directly. The BJP modelling approach is demonstrated to be a viable option for producing ensemble time-series sub-seasonal to seasonal streamflow forecasts.
Analysis of Blood Transfusion Data Using Bivariate Zero-Inflated Poisson Model: A Bayesian Approach
Mohammadi, Tayeb; Sedehi, Morteza
2016-01-01
Recognizing the factors affecting the number of blood donation and blood deferral has a major impact on blood transfusion. There is a positive correlation between the variables “number of blood donation” and “number of blood deferral”: as the number of return for donation increases, so does the number of blood deferral. On the other hand, due to the fact that many donors never return to donate, there is an extra zero frequency for both of the above-mentioned variables. In this study, in order to apply the correlation and to explain the frequency of the excessive zero, the bivariate zero-inflated Poisson regression model was used for joint modeling of the number of blood donation and number of blood deferral. The data was analyzed using the Bayesian approach applying noninformative priors at the presence and absence of covariates. Estimating the parameters of the model, that is, correlation, zero-inflation parameter, and regression coefficients, was done through MCMC simulation. Eventually double-Poisson model, bivariate Poisson model, and bivariate zero-inflated Poisson model were fitted on the data and were compared using the deviance information criteria (DIC). The results showed that the bivariate zero-inflated Poisson regression model fitted the data better than the other models. PMID:27703493
Analysis of Blood Transfusion Data Using Bivariate Zero-Inflated Poisson Model: A Bayesian Approach.
Mohammadi, Tayeb; Kheiri, Soleiman; Sedehi, Morteza
2016-01-01
Recognizing the factors affecting the number of blood donation and blood deferral has a major impact on blood transfusion. There is a positive correlation between the variables "number of blood donation" and "number of blood deferral": as the number of return for donation increases, so does the number of blood deferral. On the other hand, due to the fact that many donors never return to donate, there is an extra zero frequency for both of the above-mentioned variables. In this study, in order to apply the correlation and to explain the frequency of the excessive zero, the bivariate zero-inflated Poisson regression model was used for joint modeling of the number of blood donation and number of blood deferral. The data was analyzed using the Bayesian approach applying noninformative priors at the presence and absence of covariates. Estimating the parameters of the model, that is, correlation, zero-inflation parameter, and regression coefficients, was done through MCMC simulation. Eventually double-Poisson model, bivariate Poisson model, and bivariate zero-inflated Poisson model were fitted on the data and were compared using the deviance information criteria (DIC). The results showed that the bivariate zero-inflated Poisson regression model fitted the data better than the other models.
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…
Craig, B A; Fryback, D G; Klein, R; Klein, B E
1999-06-15
To assess the costs and benefits of screening and treatment strategies, it is important to know what would have happened had there been no intervention. In today's ethical climate, however, it is almost impossible to observe this directly and therefore must be inferred from observations with intervention. In this paper, we illustrate a Bayesian approach to this situation when the observations are at separated and unequally spaced time points and the time of intervention is interval censored. We develop a discrete-time Markov model which combines a non-homogeneous Markov chain, used to model the natural progression, with mechanisms that describe the possibility of both treatment intervention and death. We apply this approach to a subpopulation of the Wisconsin Epidemiologic Study of Diabetic Retinopathy, a population-based cohort study to investigate prevalence, incidence, and progression of diabetic retinopathy. In addition, posterior predictive distributions are discussed as a prognostic tool to assist researchers in evaluating costs and benefits of treatment protocols. While we focus this approach on diabetic retinopathy cohort data, we believe this methodology can have wide application.
Construction of feasible and accurate kinetic models of metabolism: A Bayesian approach
Saa, Pedro A.; Nielsen, Lars K.
2016-01-01
Kinetic models are essential to quantitatively understand and predict the behaviour of metabolic networks. Detailed and thermodynamically feasible kinetic models of metabolism are inherently difficult to formulate and fit. They have a large number of heterogeneous parameters, are non-linear and have complex interactions. Many powerful fitting strategies are ruled out by the intractability of the likelihood function. Here, we have developed a computational framework capable of fitting feasible and accurate kinetic models using Approximate Bayesian Computation. This framework readily supports advanced modelling features such as model selection and model-based experimental design. We illustrate this approach on the tightly-regulated mammalian methionine cycle. Sampling from the posterior distribution, the proposed framework generated thermodynamically feasible parameter samples that converged on the true values, and displayed remarkable prediction accuracy in several validation tests. Furthermore, a posteriori analysis of the parameter distributions enabled appraisal of the systems properties of the network (e.g., control structure) and key metabolic regulations. Finally, the framework was used to predict missing allosteric interactions. PMID:27417285
Chan, Jennifer S K
2016-05-01
Dropouts are common in longitudinal study. If the dropout probability depends on the missing observations at or after dropout, this type of dropout is called informative (or nonignorable) dropout (ID). Failure to accommodate such dropout mechanism into the model will bias the parameter estimates. We propose a conditional autoregressive model for longitudinal binary data with an ID model such that the probabilities of positive outcomes as well as the drop-out indicator in each occasion are logit linear in some covariates and outcomes. This model adopting a marginal model for outcomes and a conditional model for dropouts is called a selection model. To allow for the heterogeneity and clustering effects, the outcome model is extended to incorporate mixture and random effects. Lastly, the model is further extended to a novel model that models the outcome and dropout jointly such that their dependency is formulated through an odds ratio function. Parameters are estimated by a Bayesian approach implemented using the user-friendly Bayesian software WinBUGS. A methadone clinic dataset is analyzed to illustrate the proposed models. Result shows that the treatment time effect is still significant but weaker after allowing for an ID process in the data. Finally the effect of drop-out on parameter estimates is evaluated through simulation studies.
Bååth, Rasmus
2016-06-01
The sensorimotor synchronization paradigm is used when studying the coordination of rhythmic motor responses with a pacing stimulus and is an important paradigm in the study of human timing and time perception. Two measures of performance frequently calculated using sensorimotor synchronization data are the average offset and variability of the stimulus-to-response asynchronies-the offsets between the stimuli and the motor responses. Here it is shown that assuming that asynchronies are normally distributed when estimating these measures can result in considerable underestimation of both the average offset and variability. This is due to a tendency for the distribution of the asynchronies to be bimodal and left skewed when the interstimulus interval is longer than 2 s. It is argued that (1) this asymmetry is the result of the distribution of the asynchronies being a mixture of two types of responses-predictive and reactive-and (2) the main interest in a sensorimotor synchronization study is the predictive responses. A Bayesian hierarchical modeling approach is proposed in which sensorimotor synchronization data are modeled as coming from a right-censored normal distribution that effectively separates the predictive responses from the reactive responses. Evaluation using both simulated data and experimental data from a study by Repp and Doggett (2007) showed that the proposed approach produces more precise estimates of the average offset and variability, with considerably less underestimation.
Jordan, Paul; Brunschwig, Hadassa; Luedin, Eric
2008-01-01
The approach of Bayesian mixed effects modeling is an appropriate method for estimating both population-specific as well as subject-specific times to steady state. In addition to pure estimation, the approach allows to determine the time until a certain fraction of individuals of a population has reached steady state with a pre-specified certainty. In this paper a mixed effects model for the parameters of a nonlinear pharmacokinetic model is used within a Bayesian framework. Model fitting by means of Markov Chain Monte Carlo methods as implemented in the Gibbs sampler as well as the extraction of estimates and probability statements of interest are described. Finally, the proposed approach is illustrated by application to trough data from a multiple dose clinical trial.
ERIC Educational Resources Information Center
Tchumtchoua, Sylvie; Dey, Dipak K.
2012-01-01
This paper proposes a semiparametric Bayesian framework for the analysis of associations among multivariate longitudinal categorical variables in high-dimensional data settings. This type of data is frequent, especially in the social and behavioral sciences. A semiparametric hierarchical factor analysis model is developed in which the…
ERIC Educational Resources Information Center
Bekele, Rahel; McPherson, Maggie
2011-01-01
This research work presents a Bayesian Performance Prediction Model that was created in order to determine the strength of personality traits in predicting the level of mathematics performance of high school students in Addis Ababa. It is an automated tool that can be used to collect information from students for the purpose of effective group…
Hu, Yi; Ward, Michael P; Xia, Congcong; Li, Rui; Sun, Liqian; Lynn, Henry; Gao, Fenghua; Wang, Qizhi; Zhang, Shiqing; Xiong, Chenglong; Zhang, Zhijie; Jiang, Qingwu
2016-04-07
Schistosomiasis remains a major public health problem and causes substantial economic impact in east China, particularly along the Yangtze River Basin. Disease forecasting and surveillance can assist in the development and implementation of more effective intervention measures to control disease. In this study, we applied a Bayesian hierarchical spatio-temporal model to describe trends in schistosomiasis risk in Anhui Province, China, using annual parasitological and environmental data for the period 1997-2010. A computationally efficient approach-Integrated Nested Laplace Approximation-was used for model inference. A zero-inflated, negative binomial model best described the spatio-temporal dynamics of schistosomiasis risk. It predicted that the disease risk would generally be low and stable except for some specific, local areas during the period 2011-2014. High-risk counties were identified in the forecasting maps: three in which the risk remained high, and two in which risk would become high. The results indicated that schistosomiasis risk has been reduced to consistently low levels throughout much of this region of China; however, some counties were identified in which progress in schistosomiasis control was less than satisfactory. Whilst maintaining overall control, specific interventions in the future should focus on these refractive counties as part of a strategy to eliminate schistosomiasis from this region.
Gentsch, Lydia; Hammerle, Albin; Sturm, Patrick; Ogée, Jérôme; Wingate, Lisa; Siegwolf, Rolf; Plüss, Peter; Baur, Thomas; Buchmann, Nina; Knohl, Alexander
2014-07-01
Field measurements of photosynthetic carbon isotope discrimination ((13)Δ) of Fagus sylvatica, conducted with branch bags and laser spectrometry, revealed a high variability of (13)Δ, both on diurnal and day-to-day timescales. We tested the prediction capability of three versions of a commonly used model for (13)Δ [called here comprehensive ((13)(Δcomp)), simplified ((13) Δsimple) and revised ((13)(Δrevised)) versions]. A Bayesian approach was used to calibrate major model parameters. Constrained estimates were found for the fractionation during CO(2) fixation in (13)(Δcomp), but not in (13)(Δsimple), and partially for the mesophyll conductance for CO(2)(gi). No constrained estimates were found for fractionations during mitochondrial and photorespiration, and for a diurnally variable apparent fractionation between current assimilates and mitochondrial respiration, specific to (13)(Δrevised). A quantification of parameter estimation uncertainties and interdependencies further helped explore model structure and behaviour. We found that (13)(Δcomp) usually outperformed (13)(Δsimple) because of the explicit consideration of gi and the photorespiratory fractionation in (13)(Δcomp) that enabled a better description of the large observed diurnal variation (≈9‰) of (13)Δ. Flux-weighted daily means of (13)Δ were also better predicted with (13)(Δcomp) than with (13)(Δsimple).
Chen, Cong; Zhang, Guohui; Tarefder, Rafiqul; Ma, Jianming; Wei, Heng; Guan, Hongzhi
2015-07-01
Rear-end crash is one of the most common types of traffic crashes in the U.S. A good understanding of its characteristics and contributing factors is of practical importance. Previously, both multinomial Logit models and Bayesian network methods have been used in crash modeling and analysis, respectively, although each of them has its own application restrictions and limitations. In this study, a hybrid approach is developed to combine multinomial logit models and Bayesian network methods for comprehensively analyzing driver injury severities in rear-end crashes based on state-wide crash data collected in New Mexico from 2010 to 2011. A multinomial logit model is developed to investigate and identify significant contributing factors for rear-end crash driver injury severities classified into three categories: no injury, injury, and fatality. Then, the identified significant factors are utilized to establish a Bayesian network to explicitly formulate statistical associations between injury severity outcomes and explanatory attributes, including driver behavior, demographic features, vehicle factors, geometric and environmental characteristics, etc. The test results demonstrate that the proposed hybrid approach performs reasonably well. The Bayesian network reference analyses indicate that the factors including truck-involvement, inferior lighting conditions, windy weather conditions, the number of vehicles involved, etc. could significantly increase driver injury severities in rear-end crashes. The developed methodology and estimation results provide insights for developing effective countermeasures to reduce rear-end crash injury severities and improve traffic system safety performance.
2008-01-01
Background Marine allopatric speciation is an enigma because pelagic larval dispersal can potentially connect disjunct populations thereby preventing reproductive and morphological divergence. Here we present a new hierarchical approximate Bayesian computation model (HABC) that tests two hypotheses of marine allopatric speciation: 1.) "soft vicariance", where a speciation involves fragmentation of a large widespread ancestral species range that was previously connected by long distance gene flow; and 2.) peripatric colonization, where speciations in peripheral archipelagos emerge from sweepstakes colonizations from central source regions. The HABC approach analyzes all the phylogeographic datasets at once in order to make across taxon-pair inferences about biogeographic processes while explicitly allowing for uncertainty in the demographic differences within each taxon-pair. Our method uses comparative phylogeographic data that consists of single locus mtDNA sequences from multiple co-distributed taxa containing pairs of central and peripheral populations. We use the method on two comparative phylogeographic data sets consisting of cowrie gastropod endemics co-distributed in the Hawaiian (11 taxon-pairs) and Marquesan archipelagos (7 taxon-pairs). Results Given the Marquesan data, we find strong evidence of simultaneous colonization across all seven cowrie gastropod endemics co-distributed in the Marquesas. In contrast, the lower sample sizes in the Hawaiian data lead to greater uncertainty associated with the Hawaiian estimates. Although, the hyper-parameter estimates point to soft vicariance in a subset of the 11 Hawaiian taxon-pairs, the hyper-prior and hyper-posterior are too similar to make a definitive conclusion. Both results are not inconsistent with what is known about the geologic history of the archipelagos. Simulations verify that our method can successfully distinguish these two histories across a wide range of conditions given sufficient sampling
NASA Astrophysics Data System (ADS)
Aguayo, M.; Marshall, H.; McNamara, J. P.; Mead, J.; Flores, A. N.
2013-12-01
Estimation of snowpack parameters such as depth, density and grain structure is a central focus of hydrology in seasonally snow-covered lands. These parameters are directly estimated by field observations, indirectly estimated from other parameters using statistical correlations, or simulated with a model. Difficulty in sampling thin layers and uncertainty in the transition between layers can cause significant uncertainty in measurements of these parameters. Snow density is one of the most important parameters to measure because it is strictly related with snow water content, an important component of the global water balance. We develop a mathematical framework to estimate snow density from measurements of temperature and thickness of snowpack layers over a particular time period, in conjunction with a physics-based model of snowpack evolution. We formulate a Bayesian approach to estimate the snowpack density profile, using a full range of possible simulations that incorporate key sources of uncertainty to build in prior snowpack knowledge. The posterior probability density function of the snow density, conditioned on snowpack temperature measurements, is computed by multiplying the likelihoods and assumed prior distribution function. Random sampling is used to generate a range of densities with same probability when prior uniform probability function is assumed. A posterior probability density function calculated directly via Bayes' theorem is used to calculate the probability of every sample generated. The forward model is a 1D, multilayer snow energy and mass balance model, which solves for snow temperature, density, and liquid water content on a finite element mesh. The surface and ground temperature data of snowpack (boundary conditions), are provided by the Center for Snow and Avalanche Studies (CSAS), Silverton CO, from snow pits made at Swamp Angel and Senator Beck study plot sites. Standard errors between field observations and results computed denote the
NASA Astrophysics Data System (ADS)
Thomsen, Nanna I.; Binning, Philip J.; McKnight, Ursula S.; Tuxen, Nina; Bjerg, Poul L.; Troldborg, Mads
2016-05-01
A key component in risk assessment of contaminated sites is in the formulation of a conceptual site model (CSM). A CSM is a simplified representation of reality and forms the basis for the mathematical modeling of contaminant fate and transport at the site. The CSM should therefore identify the most important site-specific features and processes that may affect the contaminant transport behavior at the site. However, the development of a CSM will always be associated with uncertainties due to limited data and lack of understanding of the site conditions. CSM uncertainty is often found to be a major source of model error and it should therefore be accounted for when evaluating uncertainties in risk assessments. We present a Bayesian belief network (BBN) approach for constructing CSMs and assessing their uncertainty at contaminated sites. BBNs are graphical probabilistic models that are effective for integrating quantitative and qualitative information, and thus can strengthen decisions when empirical data are lacking. The proposed BBN approach facilitates a systematic construction of multiple CSMs, and then determines the belief in each CSM using a variety of data types and/or expert opinion at different knowledge levels. The developed BBNs combine data from desktop studies and initial site investigations with expert opinion to assess which of the CSMs are more likely to reflect the actual site conditions. The method is demonstrated on a Danish field site, contaminated with chlorinated ethenes. Four different CSMs are developed by combining two contaminant source zone interpretations (presence or absence of a separate phase contamination) and two geological interpretations (fractured or unfractured clay till). The beliefs in each of the CSMs are assessed sequentially based on data from three investigation stages (a screening investigation, a more detailed investigation, and an expert consultation) to demonstrate that the belief can be updated as more information
A Nonparametric Bayesian Approach to Seismic Hazard Modeling Using the ETAS Framework
NASA Astrophysics Data System (ADS)
Ross, G.
2015-12-01
The epidemic-type aftershock sequence (ETAS) model is one of the most popular tools for modeling seismicity and quantifying risk in earthquake-prone regions. Under the ETAS model, the occurrence times of earthquakes are treated as a self-exciting Poisson process where each earthquake briefly increases the probability of subsequent earthquakes occurring soon afterwards, which captures the fact that large mainshocks tend to produce long sequences of aftershocks. A triggering kernel controls the amount by which the probability increases based on the magnitude of each earthquake, and the rate at which it then decays over time. This triggering kernel is usually chosen heuristically, to match the parametric form of the modified Omori law for aftershock decay. However recent work has questioned whether this is an appropriate choice. Since the choice of kernel has a large impact on the predictions made by the ETAS model, avoiding misspecification is crucially important. We present a novel nonparametric version of ETAS which avoids making parametric assumptions, and instead learns the correct specification from the data itself. Our approach is based on the Dirichlet process, which is a modern class of Bayesian prior distribution which allows for efficient inference over an infinite dimensional space of functions. We show how our nonparametric ETAS model can be fit to data, and present results demonstrating that the fit is greatly improved compared to the standard parametric specification. Additionally, we explain how our model can be used to perform probabilistic declustering of earthquake catalogs, to classify earthquakes as being either aftershocks or mainshocks. and to learn the causal relations between pairs of earthquakes.
Partially linear models with autoregressive scale-mixtures of normal errors: A Bayesian approach
NASA Astrophysics Data System (ADS)
Ferreira, Guillermo; Castro, Mauricio; Lachos, Victor H.
2012-10-01
Normality and independence of error terms is a typical assumption for partial linear models. However, such an assumption may be unrealistic on many fields such as economics, finance and biostatistics. In this paper, we develop a Bayesian analysis for partial linear model with first-order autoregressive errors belonging to the class of scale mixtures of normal (SMN) distributions. The proposed model provides a useful generalization of the symmetrical linear regression models with independent error, since the error distribution cover both correlated and thick-tailed distribution, and has a convenient hierarchical representation allowing to us an easily implementation of a Markov chain Monte Carlo (MCMC) scheme. In order to examine the robustness of this distribution against outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler (K-L) divergence. The proposed methodology is applied to the Cuprum Company monthly returns.
A Bayesian estimation approach for the mortality in a stage-structured demographic model.
Lanzarone, E; Pasquali, S; Gilioli, G; Marchesini, E
2017-01-27
Control interventions in sustainable pest management schemes are set according to the phenology and the population abundance of the pests. This information can be obtained using suitable mathematical models that describe the population dynamics based on individual life history responses to environmental conditions and resource availability. These responses are described by development, fecundity and survival rate functions, which can be estimated from laboratory experiments. If experimental data are not available, data on field population dynamics can be used for their estimation. This is the case of the extrinsic mortality term that appears in the mortality rate function due to biotic factors. We propose a Bayesian approach to estimate the probability density functions of the parameters in the extrinsic mortality rate function, starting from data on population abundance. The method investigates the time variability in the mortality parameters by comparing simulated and observed trajectories. The grape berry moth, a pest of great importance in European vineyards, has been considered as a case study. Simulated data have been considered to evaluate the convergence of the algorithm, while field data have been used to obtain estimates of the mortality for the grape berry moth.
Akutekwe, Arinze; Seker, Huseyin
2014-01-01
Computational and machine learning techniques have been applied in identifying biomarkers and constructing predictive models for diagnosis of hypertension. Strategies such as improved classification rules based on decision trees have been proposed. Other techniques such as Fuzzy Expert Systems (FES) and Neuro-Fuzzy Systems (NFS) have recently been applied. However, these methods lack the ability to detect temporal relationships among biomarker genes that will aid better understanding of the mechanism of hypertension disease. In this paper we apply a proposed two-stage bio-network construction approach that combines the power and computational efficiency of classification methods with the well-established predictive ability of Dynamic Bayesian Network. We demonstrate our method using the analysis of male young-onset hypertension microarray dataset. Four key genes were identified by the Least Angle Shrinkage and Selection Operator (LASSO) and three Support Vector Machine Recursive Feature Elimination (SVM-RFE) methods. Results show that cell regulation FOXQ1 may inhibit the expression of focusyltransferase-6 (FUT6) and that ABCG1 ATP-binding cassette sub-family G may also play inhibitory role against NR2E3 nuclear receptor sub-family 2 and CGB2 Chromatin Gonadotrophin.
NASA Technical Reports Server (NTRS)
Littlewood, B.; Sofer, A.
1981-01-01
Maximum likelihood estimation procedures for the Jelinski-Moranda software reliability model often give misleading answers. A reparameterization and a Bayesian analysis eliminate some of the problems incurred by MLE methods and often give better predictions on sets of real and simulated data. Practical difficulties in estimating the initial number of errors N and the failure rate of each error phi by the method of maximum likelihood are: N, the MLE of N, is occasionally infinite (i.e., the routines for calculating N and phi do not converge). It is shown that N is finite sub i only if the regression line of the interevent times t sub i vs. i has positive slope. A serious problem is that often N approximates n, the sample size, and sometimes N = n. Thus the MLE predicts that the program is perfect even when it is far from being so. Only when almost all failures have been removed can N and phi be trusted near the end of debugging.
Ismaila, Afisi S; Canty, Angelo; Thabane, Lehana
2007-01-01
Background This study compares the Bayesian and frequentist (non-Bayesian) approaches in the modelling of the association between the risk of preterm birth and maternal proximity to hazardous waste and pollution from the Sydney Tar Pond site in Nova Scotia, Canada. Methods The data includes 1604 observed cases of preterm birth out of a total population of 17559 at risk of preterm birth from 144 enumeration districts in the Cape Breton Regional Municipality. Other covariates include the distance from the Tar Pond; the rate of unemployment to population; the proportion of persons who are separated, divorced or widowed; the proportion of persons who have no high school diploma; the proportion of persons living alone; the proportion of single parent families and average income. Bayesian hierarchical Poisson regression, quasi-likelihood Poisson regression and weighted linear regression models were fitted to the data. Results The results of the analyses were compared together with their limitations. Conclusion The results of the weighted linear regression and the quasi-likelihood Poisson regression agrees with the result from the Bayesian hierarchical modelling which incorporates the spatial effects. PMID:17845717
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…
Posada, David; Buckley, Thomas R
2004-10-01
Model selection is a topic of special relevance in molecular phylogenetics that affects many, if not all, stages of phylogenetic inference. Here we discuss some fundamental concepts and techniques of model selection in the context of phylogenetics. We start by reviewing different aspects of the selection of substitution models in phylogenetics from a theoretical, philosophical and practical point of view, and summarize this comparison in table format. We argue that the most commonly implemented model selection approach, the hierarchical likelihood ratio test, is not the optimal strategy for model selection in phylogenetics, and that approaches like the Akaike Information Criterion (AIC) and Bayesian methods offer important advantages. In particular, the latter two methods are able to simultaneously compare multiple nested or nonnested models, assess model selection uncertainty, and allow for the estimation of phylogenies and model parameters using all available models (model-averaged inference or multimodel inference). We also describe how the relative importance of the different parameters included in substitution models can be depicted. To illustrate some of these points, we have applied AIC-based model averaging to 37 mitochondrial DNA sequences from the subgenus Ohomopterus(genus Carabus) ground beetles described by Sota and Vogler (2001).
Peyvandi, Shahram; Amirshahi, Seyed Hossein; Hernández-Andrés, Javier; Nieves, Juan Luis; Romero, Javier
2012-10-01
The Bayesian inference approach to the inverse problem of spectral signal recovery has been extended to mixtures of Gaussian probability distributions of a training dataset in order to increase the efficiency of estimating the spectral signal from the response of a transformation system. Bayesian (BIC) and Akaike (AIC) information criteria were assessed in order to provide the Gaussian mixture model (GMM) with the optimum number of clusters within the spectral space. The spectra of 2600 solar illuminations measured in Granada (Spain) were recovered over the range of 360-830 nm from their corresponding tristimulus values using a linear model of basis functions, the Wiener inverse (WI) method, and the Bayesian inverse approach extended to the GMM (BGMM). A model of Gaussian mixtures for solar irradiance was deemed to be more appropriate than a single Gaussian distribution for representing the probability distribution of the solar spectral data. The results showed that the estimation performance of the BGMM method was better than either the linear model or the WI method for the spectral approximation of daylight from the three-dimensional tristimulus values.
Gracia, Enrique; López-Quílez, Antonio; Marco, Miriam; Lladosa, Silvia; Lila, Marisol
2014-01-01
This paper uses spatial data of cases of intimate partner violence against women (IPVAW) to examine neighborhood-level influences on small-area variations in IPVAW risk in a police district of the city of Valencia (Spain). To analyze area variations in IPVAW risk and its association with neighborhood-level explanatory variables we use a Bayesian spatial random-effects modeling approach, as well as disease mapping methods to represent risk probabilities in each area. Analyses show that IPVAW cases are more likely in areas of high immigrant concentration, high public disorder and crime, and high physical disorder. Results also show a spatial component indicating remaining variability attributable to spatially structured random effects. Bayesian spatial modeling offers a new perspective to identify IPVAW high and low risk areas, and provides a new avenue for the design of better-informed prevention and intervention strategies. PMID:24413701
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…
Kercel, S.W.
1999-11-07
For several reasons, Bayesian parameter estimation is superior to other methods for inductively learning a model for an anticipatory system. Since it exploits prior knowledge, the analysis begins from a more advantageous starting point than other methods. Also, since "nuisance parameters" can be removed from the Bayesian analysis, the description of the model need not be as complete as is necessary for such methods as matched filtering. In the limit of perfectly random noise and a perfect description of the model, the signal-to-noise ratio improves as the square root of the number of samples in the data. Even with the imperfections of real-world data, Bayesian methods approach this ideal limit of performance more closely than other methods. These capabilities provide a strategy for addressing a major unsolved problem in pump operation: the identification of precursors of cavitation. Cavitation causes immediate degradation of pump performance and ultimate destruction of the pump. However, the most efficient point to operate a pump is just below the threshold of cavitation. It might be hoped that a straightforward method to minimize pump cavitation damage would be to simply adjust the operating point until the inception of cavitation is detected and then to slightly readjust the operating point to let the cavitation vanish. However, due to the continuously evolving state of the fluid moving through the pump, the threshold of cavitation tends to wander. What is needed is to anticipate cavitation, and this requires the detection and identification of precursor features that occur just before cavitation starts.
Analysis of housing price by means of STAR models with neighbourhood effects: a Bayesian approach
NASA Astrophysics Data System (ADS)
Beamonte, Asuncion; Gargallo, Pilar; Salvador, Manuel
2010-06-01
In this paper, we extend the Bayesian methodology introduced by Beamonte et al. (Stat Modelling 8:285-311, 2008) for the estimation and comparison of spatio-temporal autoregressive models (STAR) with neighbourhood effects, providing a more general treatment that uses larger and denser nets for the number of spatial and temporal influential neighbours and continuous distributions for their smoothing weights. This new treatment also reduces the computational time and the RAM necessities of the estimation algorithm in Beamonte et al. (Stat Modelling 8:285-311, 2008). The procedure is illustrated by an application to the Zaragoza (Spain) real estate market, improving the goodness of fit and the outsampling behaviour of the model thanks to a more flexible estimation of the neighbourhood parameters.
NASA Astrophysics Data System (ADS)
Michelioudakis, Dimitrios; Hobbs, Richard; Caiado, Camila
2015-04-01
Determining the depths of key horizons from seismic reflection data is one of the most important aspects of exploration geophysics. Here, we present Bayesian methods based on an elicitation tool and Gaussian processes to build a detailed and robust velocity model of the Mentelle Basin, located south west of Australia, with the ultimate goal to identify possible drilling targets for the Integrated Ocean Drilling Program (IODP). The Mentelle Basin is a deep water sedimentary basin located between the Naturaliste Plateau and the southern part of the Western Australian Shelf. It is among the few regions of the world where we can investigate the effects of the Cretaceous hot-house and its collapse at high latitude. The Mentelle Basin hosts a continuous shale sequence for this period that it is over a kilometer thick, the study of which, is crucial for the correlation between the paleoclimate conditions and the tectonic history of the region. By reprocessing 2D multichannel seismic reflection profiles around the proposed drill - sites, we create a detailed subsurface velocity model which is used as a priori input to the Bayesian approach. The final goal is to build a multi-layered model to estimate the depth and the root mean square velocity of each layer, both for the isotropic and anisotropic cases in terms of a multivariate posterior distribution. Having determined the RMS velocities for each layer, we can calculate, by inference, their interval velocities and finally estimate the depth of each sequence of interest with improved accuracy. The key advantage of the Bayesian approach and the major difference compared to the traditional semblance spectrum velocity analysis procedure is the calculation of uncertainty of the output model. As a result, our statistical approach can construct a robust velocity model which encompasses the noise and the band-limited nature of the data as an error function. We use this model to control the depth migration of the seismic data and
Gas turbine engine prognostics using Bayesian hierarchical models: A variational approach
NASA Astrophysics Data System (ADS)
Zaidan, Martha A.; Mills, Andrew R.; Harrison, Robert F.; Fleming, Peter J.
2016-03-01
Prognostics is an emerging requirement of modern health monitoring that aims to increase the fidelity of failure-time predictions by the appropriate use of sensory and reliability information. In the aerospace industry it is a key technology to reduce life-cycle costs, improve reliability and asset availability for a diverse fleet of gas turbine engines. In this work, a Bayesian hierarchical model is selected to utilise fleet data from multiple assets to perform probabilistic estimation of remaining useful life (RUL) for civil aerospace gas turbine engines. The hierarchical formulation allows Bayesian updates of an individual predictive model to be made, based upon data received asynchronously from a fleet of assets with different in-service lives and for the entry of new assets into the fleet. In this paper, variational inference is applied to the hierarchical formulation to overcome the computational and convergence concerns that are raised by the numerical sampling techniques needed for inference in the original formulation. The algorithm is tested on synthetic data, where the quality of approximation is shown to be satisfactory with respect to prediction performance, computational speed, and ease of use. A case study of in-service gas turbine engine data demonstrates the value of integrating fleet data for accurately predicting degradation trajectories of assets.
Cai, C.; Rodet, T.; Mohammad-Djafari, A.; Legoupil, S.
2013-11-15
Purpose: Dual-energy computed tomography (DECT) makes it possible to get two fractions of basis materials without segmentation. One is the soft-tissue equivalent water fraction and the other is the hard-matter equivalent bone fraction. Practical DECT measurements are usually obtained with polychromatic x-ray beams. Existing reconstruction approaches based on linear forward models without counting the beam polychromaticity fail to estimate the correct decomposition fractions and result in beam-hardening artifacts (BHA). The existing BHA correction approaches either need to refer to calibration measurements or suffer from the noise amplification caused by the negative-log preprocessing and the ill-conditioned water and bone separation problem. To overcome these problems, statistical DECT reconstruction approaches based on nonlinear forward models counting the beam polychromaticity show great potential for giving accurate fraction images.Methods: This work proposes a full-spectral Bayesian reconstruction approach which allows the reconstruction of high quality fraction images from ordinary polychromatic measurements. This approach is based on a Gaussian noise model with unknown variance assigned directly to the projections without taking negative-log. Referring to Bayesian inferences, the decomposition fractions and observation variance are estimated by using the joint maximum a posteriori (MAP) estimation method. Subject to an adaptive prior model assigned to the variance, the joint estimation problem is then simplified into a single estimation problem. It transforms the joint MAP estimation problem into a minimization problem with a nonquadratic cost function. To solve it, the use of a monotone conjugate gradient algorithm with suboptimal descent steps is proposed.Results: The performance of the proposed approach is analyzed with both simulated and experimental data. The results show that the proposed Bayesian approach is robust to noise and materials. It is also
NASA Astrophysics Data System (ADS)
Britton, Adrian; Copsey, Keith D.; Maskall, Guy T.; Webb, Andrew R.; West, Karl
2000-07-01
The problem we are addressing is one of generalization: given training data characterizing a set of targets (in specific configurations), how can we design a classifier that is robust to changes in target configuration and can generalize to other targets of the same generic class? The specific problem is identifying land vehicles from an inverse synthetic aperture radar image of the target. Issues in data modeling, experimental design and exploratory data analysis are discussed. Two complementary approaches are described: one that seeks to capture structure in the high- dimensional data space by projecting the data nonlinearly to a reduced dimensional feature space prior to classification; and a second that models the data in the data space using a Bayesian mixture model approach. Preliminary results for the mixture model approach are presented.
[Pulmonary nodule: a bayesian approach].
Meert, A-P
2010-01-01
A solitary pulmonary nodule is a common clinical problem. It is usually detected incidentally. The prevalence of solitary pulmonary nodule (SPN) in the lung cancer screening study varies from 8 to 50% (with a prevalence of malignant nodule from 1 to 13%). The bayesian approach can help us to identify promptly malignant nodule in order to treat them surgically and to avoid surgery for benign nodules. Therefore, it is needed to estimate the probability of cancer (Pca) in the SPN. Likelihood ratio (LR) for overall prevalence of malignancy and for different clinical and radiological information (age, smoking exposure, symptoms, cancer history, nodule size, spiculation, calcification, location, growth...) can be obtained from the literature. The odds of cancer-malignancy (odds ca) can be calculated by multiplying all of these LRs together. The Pca = odds ca/1+odds ca. Using this bayeasian approach, the probability of cancer based on an abnormal or normal fluoro-2-deoxy-D-glucose-positron emission tomography (FDG-PET) scan has been estimated. Sensitivity, specificity, positive predictive value and negative predictive value of PET scan are respectively about 90%, 83%, 92% and 90%. Moreover, the LR for malignancy are higher with an abnormal PET scan when compared to most clinical and radiological LRs. Today, the Bayesian approach of SPN must include PET scan.
NASA Astrophysics Data System (ADS)
Cha, YoonKyung; Soon Park, Seok; Won Lee, Hye; Stow, Craig A.
2016-01-01
Modeling to accurately predict river phytoplankton distribution and abundance is important in water quality and resource management. Nevertheless, the complex nature of eutrophication processes in highly connected river systems makes the task challenging. To model dynamics of river phytoplankton, represented by chlorophyll a (Chl a) concentration, we propose a Bayesian hierarchical model that explicitly accommodates seasonality and upstream-downstream spatial gradient in the structure. The utility of our model is demonstrated with an application to the Nakdong River (South Korea), which is a eutrophic, intensively regulated river, but functions as an irreplaceable water source for more than 13 million people. Chl a is modeled with two manageable factors, river flow, and total phosphorus (TP) concentration. Our model results highlight the importance of taking seasonal and spatial context into account when describing flow regimes and phosphorus delivery in rivers. A contrasting positive Chl a-flow relationship across stations versus negative Chl a-flow slopes that arose when Chl a was modeled on a station-month basis is an illustration of Simpson's paradox, which necessitates modeling Chl a-flow relationships decomposed into seasonal and spatial components. Similar Chl a-TP slopes among stations and months suggest that, with the flow effect removed, positive TP effects on Chl a are uniform regardless of the season and station in the river. Our model prediction successfully captured the shift in the spatial and monthly patterns of Chl a.
NASA Astrophysics Data System (ADS)
Humphrey, Greer B.; Gibbs, Matthew S.; Dandy, Graeme C.; Maier, Holger R.
2016-09-01
Monthly streamflow forecasts are needed to support water resources decision making in the South East of South Australia, where baseflow represents a significant proportion of the total streamflow and soil moisture and groundwater are important predictors of runoff. To address this requirement, the utility of a hybrid monthly streamflow forecasting approach is explored, whereby simulated soil moisture from the GR4J conceptual rainfall-runoff model is used to represent initial catchment conditions in a Bayesian artificial neural network (ANN) statistical forecasting model. To assess the performance of this hybrid forecasting method, a comparison is undertaken of the relative performances of the Bayesian ANN, the GR4J conceptual model and the hybrid streamflow forecasting approach for producing 1-month ahead streamflow forecasts at three key locations in the South East of South Australia. Particular attention is paid to the quantification of uncertainty in each of the forecast models and the potential for reducing forecast uncertainty by using the hybrid approach is considered. Case study results suggest that the hybrid models developed in this study are able to take advantage of the complementary strengths of both the ANN models and the GR4J conceptual models. This was particularly the case when forecasting high flows, where the hybrid models were shown to outperform the two individual modelling approaches in terms of the accuracy of the median forecasts, as well as reliability and resolution of the forecast distributions. In addition, the forecast distributions generated by the hybrid models were up to 8 times more precise than those based on climatology; thus, providing a significant improvement on the information currently available to decision makers.
The approach of Bayesian model indicates media awareness of medical errors
NASA Astrophysics Data System (ADS)
Ravichandran, K.; Arulchelvan, S.
2016-06-01
This research study brings out the factors behind the increase in medical malpractices in the Indian subcontinent in the present day environment and impacts of television media awareness towards it. Increased media reporting of medical malpractices and errors lead to hospitals taking corrective action and improve the quality of medical services that they provide. The model of Cultivation Theory can be used to measure the influence of media in creating awareness of medical errors. The patient's perceptions of various errors rendered by the medical industry from different parts of India were taken up for this study. Bayesian method was used for data analysis and it gives absolute values to indicate satisfaction of the recommended values. To find out the impact of maintaining medical records of a family online by the family doctor in reducing medical malpractices which creates the importance of service quality in medical industry through the ICT.
Determination of parameter identifiability in nonlinear biophysical models: A Bayesian approach
Hines, Keegan E.; Middendorf, Thomas R.
2014-01-01
A major goal of biophysics is to understand the physical mechanisms of biological molecules and systems. Mechanistic models are evaluated based on their ability to explain carefully controlled experiments. By fitting models to data, biophysical parameters that cannot be measured directly can be estimated from experimentation. However, it might be the case that many different combinations of model parameters can explain the observations equally well. In these cases, the model parameters are not identifiable: the experimentation has not provided sufficient constraining power to enable unique estimation of their true values. We demonstrate that this pitfall is present even in simple biophysical models. We investigate the underlying causes of parameter non-identifiability and discuss straightforward methods for determining when parameters of simple models can be inferred accurately. However, for models of even modest complexity, more general tools are required to diagnose parameter non-identifiability. We present a method based in Bayesian inference that can be used to establish the reliability of parameter estimates, as well as yield accurate quantification of parameter confidence. PMID:24516188
A structured approach to Bayesian data fusion
NASA Astrophysics Data System (ADS)
Rubin, Y. N.; Chen, J.; Hubbard, S.; Kowalsky, M. B.; Woodbury, A.
2002-12-01
Stochastic formulations of the inverse problem proved to be a powerful tool for data fusion. Bayesian-based methods are particularly attractive due to their generality and structure. A Bayesian method requires defining a prior pdf for the model parameters and a likelihood function to relate between model parameters and observations. A systematic approach for defining these two functions is needed, which departs from the customary, almost-by-default choice of normal-based models. This talk gives an overview of recent trends in Bayesian model construction. The first part of the talk focuses on identifying a prior using the information-based approach of Woodbury and Ulrych, with an application to the Cape Cod large scale tracer transport field experiment. Here we show how the tracer data can augment direct measurements of the hydraulic conductivity. In the second part, we focus on the likelihood function, and present two different concepts. The first concept defines a non-stationary, multivariate normal likelihood function, and the second employs neural networks and identifies a non-normal likelihood function. Both concepts are employed to fuse geophysical data with conventional well logs.
A Survey of Model Evaluation Approaches with a Tutorial on Hierarchical Bayesian Methods
ERIC Educational Resources Information Center
Shiffrin, Richard M.; Lee, Michael D.; Kim, Woojae; Wagenmakers, Eric-Jan
2008-01-01
This article reviews current methods for evaluating models in the cognitive sciences, including theoretically based approaches, such as Bayes factors and minimum description length measures; simulation approaches, including model mimicry evaluations; and practical approaches, such as validation and generalization measures. This article argues…
Bayesian Networks for Social Modeling
Whitney, Paul D.; White, Amanda M.; Walsh, Stephen J.; Dalton, Angela C.; Brothers, Alan J.
2011-03-28
This paper describes a body of work developed over the past five years. The work addresses the use of Bayesian network (BN) models for representing and predicting social/organizational behaviors. The topics covered include model construction, validation, and use. These topics show the bulk of the lifetime of such model, beginning with construction, moving to validation and other aspects of model ‘critiquing’, and finally demonstrating how the modeling approach might be used to inform policy analysis. To conclude, we discuss limitations of using BN for this activity and suggest remedies to address those limitations. The primary benefits of using a well-developed computational, mathematical, and statistical modeling structure, such as BN, are 1) there are significant computational, theoretical and capability bases on which to build 2) ability to empirically critique the model, and potentially evaluate competing models for a social/behavioral phenomena.
Reducing model structural uncertainty in predictions for ungauged basins via Bayesian approach.
NASA Astrophysics Data System (ADS)
Prieto, Cristina; Le Vine, Nataliya; Vitolo, Claudia; García, Eduardo; Medina, Raúl
2016-04-01
A catchment is a complex system where a multitude of interrelated energy, water and vegetation processes occur at different temporal and spatial scales. A rainfall-runoff model is a simplified representation of the system, and serves as a hypothesis about an inner catchment working. In predictions for ungauged basins, a common practice is to use a pre-selected assumed-to-be-perfect model structure to represent all catchments under analysis. However, it is unlikely that the same model structure is appropriate for diverse catchments due to the 'uniqueness of the place'. At the same time, there is no obvious justification to select a single model structure as a suitable description of the system. The contribution of this research is a move forward in the 'one size fits all' problem for predicting flows in ungauged basins. We present a statistical methodology, which allows regionalization that considers the information given by different hydrological model structures. First, the information to be regionalised is compactly represented via Principal Component Analysis. Second, the most significant principal components are regionalised using non-linear regionalisation method based on Random Forests. Third, a regionalisation error structure is derived based on the gauged catchments to be used in the Bayesian condition of the rainfall-runoff structures and their parameters. The methodological developments are demonstrated for predicting flows in ungauged basins of Northern Spain; and the results show that the methodology allows improving the flow prediction.
Hu, Yi; Ward, Michael P.; Xia, Congcong; Li, Rui; Sun, Liqian; Lynn, Henry; Gao, Fenghua; Wang, Qizhi; Zhang, Shiqing; Xiong, Chenglong; Zhang, Zhijie; Jiang, Qingwu
2016-01-01
Schistosomiasis remains a major public health problem and causes substantial economic impact in east China, particularly along the Yangtze River Basin. Disease forecasting and surveillance can assist in the development and implementation of more effective intervention measures to control disease. In this study, we applied a Bayesian hierarchical spatio-temporal model to describe trends in schistosomiasis risk in Anhui Province, China, using annual parasitological and environmental data for the period 1997–2010. A computationally efficient approach–Integrated Nested Laplace Approximation–was used for model inference. A zero-inflated, negative binomial model best described the spatio-temporal dynamics of schistosomiasis risk. It predicted that the disease risk would generally be low and stable except for some specific, local areas during the period 2011–2014. High-risk counties were identified in the forecasting maps: three in which the risk remained high, and two in which risk would become high. The results indicated that schistosomiasis risk has been reduced to consistently low levels throughout much of this region of China; however, some counties were identified in which progress in schistosomiasis control was less than satisfactory. Whilst maintaining overall control, specific interventions in the future should focus on these refractive counties as part of a strategy to eliminate schistosomiasis from this region. PMID:27053447
Sy, Mouhamadou Moustapha; Ancelet, Sophie; Henner, Pascale; Hurtevent, Pierre; Simon-Cornu, Marie
2015-09-01
Uncertainty on the parameters that describe the transfer of radioactive materials into the (terrestrial) environment may be characterized thanks to datasets such as those compiled within International Atomic Energy Agency (IAEA) documents. Nevertheless, the information included in these documents is too poor to derive a relevant and informative uncertainty distribution regarding dry interception of radionuclides by the pasture grass and the leaves of vegetables. In this paper, 145 sets of dry interception measurements by the aboveground biomass of specific plants were collected from published scientific papers. A Bayesian meta-analysis was performed to derive the posterior probability distributions of the parameters that reflect their uncertainty given the collected data. Four competing models were compared in terms of both fitting performances and predictive abilities to reproduce plausible dry interception data. The asymptotic interception factor, applicable whatever the species and radionuclide to the highest aboveground biomass values (e.g. mature leafy vegetables), was estimated with the best model, to be 0.87 with a 95% credible interval (0.85, 0.89).
Awate, Suyash P; Radhakrishnan, Thyagarajan
2015-01-01
In microscopy imaging, colocalization between two biological entities (e.g., protein-protein or protein-cell) refers to the (stochastic) dependencies between the spatial locations of the two entities in the biological specimen. Measuring colocalization between two entities relies on fluorescence imaging of the specimen using two fluorescent chemicals, each of which indicates the presence/absence of one of the entities at any pixel location. State-of-the-art methods for estimating colocalization rely on post-processing image data using an adhoc sequence of algorithms with many free parameters that are tuned visually. This leads to loss of reproducibility of the results. This paper proposes a brand-new framework for estimating the nature and strength of colocalization directly from corrupted image data by solving a single unified optimization problem that automatically deals with noise, object labeling, and parameter tuning. The proposed framework relies on probabilistic graphical image modeling and a novel inference scheme using variational Bayesian expectation maximization for estimating all model parameters, including colocalization, from data. Results on simulated and real-world data demonstrate improved performance over the state of the art.
How does aging affect recognition-based inference? A hierarchical Bayesian modeling approach.
Horn, Sebastian S; Pachur, Thorsten; Mata, Rui
2015-01-01
The recognition heuristic (RH) is a simple strategy for probabilistic inference according to which recognized objects are judged to score higher on a criterion than unrecognized objects. In this article, a hierarchical Bayesian extension of the multinomial r-model is applied to measure use of the RH on the individual participant level and to re-evaluate differences between younger and older adults' strategy reliance across environments. Further, it is explored how individual r-model parameters relate to alternative measures of the use of recognition and other knowledge, such as adherence rates and indices from signal-detection theory (SDT). Both younger and older adults used the RH substantially more often in an environment with high than low recognition validity, reflecting adaptivity in strategy use across environments. In extension of previous analyses (based on adherence rates), hierarchical modeling revealed that in an environment with low recognition validity, (a) older adults had a stronger tendency than younger adults to rely on the RH and (b) variability in RH use between individuals was larger than in an environment with high recognition validity; variability did not differ between age groups. Further, the r-model parameters correlated moderately with an SDT measure expressing how well people can discriminate cases where the RH leads to a correct vs. incorrect inference; this suggests that the r-model and the SDT measures may offer complementary insights into the use of recognition in decision making. In conclusion, younger and older adults are largely adaptive in their application of the RH, but cognitive aging may be associated with an increased tendency to rely on this strategy.
Cha, YoonKyung; Kim, Young Mo; Choi, Jae-Woo; Sthiannopkao, Suthipong; Cho, Kyung Hwa
2016-01-01
In the Mekong River basin, groundwater from tube-wells is a major drinking water source. However, arsenic (As) contamination in groundwater resources has become a critical issue in the watershed. In this study, As species such as total As (AsTOT), As(III), and As(V), were monitored across the watershed to investigate their characteristics and inter-relationships with water quality parameters, including pH and redox potential (Eh). The data illustrated a dramatic change in the relationship between AsTOT and Eh over a specific Eh range, suggesting the importance of Eh in predicting AsTOT. Thus, a Bayesian change-point model was developed to predict AsTOT concentrations based on Eh and pH, to determine changes in the AsTOT-Eh relationship. The model captured the Eh change-point (∼-100±15mV), which was compatible with the data. Importantly, the inclusion of this change-point in the model resulted in improved model fit and prediction accuracy; AsTOT concentrations were strongly negatively related to Eh values higher than the change-point. The process underlying this relationship was subsequently posited to be the reductive dissolution of mineral oxides and As release. Overall, AsTOT showed a weak positive relationship with Eh at a lower range, similar to those commonly observed in the Mekong River basin delta. It is expected that these results would serve as a guide for establishing public health strategies in the Mekong River Basin.
Testing pre-main-sequence models: the power of a Bayesian approach
NASA Astrophysics Data System (ADS)
Gennaro, M.; Prada Moroni, P. G.; Tognelli, E.
2012-02-01
Pre-main-sequence (PMS) models provide invaluable tools for the study of star-forming regions as they allow us to assign masses and ages to young stars. Thus, it is of primary importance to test the models against observations of PMS stars with dynamically determined masses. We developed a Bayesian method for testing the present generation of PMS models, which allows for a quantitative comparison with observations, largely superseding the widely used isochrones and tracks qualitative superposition. Using the available PMS data, we tested the newest PISA PMS models, establishing good agreement with the observations. The data cover a mass range from ˜0.3 to ˜3.1 M⊙, temperatures from ˜3 × 103 to ˜1.2 × 104 K and luminosities from ˜3 × 10-2 to ˜60 L⊙. Masses are correctly predicted within 20 per cent of the observed values in most of the cases, and for some of them the difference is as small as 5 per cent. Nevertheless, some discrepancies are also observed and critically discussed. By means of simulations, using typical observational errors, we evaluated the spread of log τsim- log τrec, i.e. simulated - recovered age distribution of the single objects. We also found that stars in binary systems simulated as coeval might be recovered as non-coeval, due to observational errors. The actual fraction of fake non-coevality is a complex function of the simulated ages, masses and mass ratios. We demonstrated that it is possible to recover the systems' ages with better precision than for single stars using the composite age-probability distribution, i.e. the product of the components' age distributions. Using this valuable tool, we estimated the ages of the presently observed PMS binary systems.
Model uncertainty estimation and risk assessment is essential to environmental management and informed decision making on pollution mitigation strategies. In this study, we apply a probabilistic methodology, which combines Bayesian Monte Carlo simulation and Maximum Likelihood e...
Toribo, S.G.; Gray, B.R.; Liang, S.
2011-01-01
The N-mixture model proposed by Royle in 2004 may be used to approximate the abundance and detection probability of animal species in a given region. In 2006, Royle and Dorazio discussed the advantages of using a Bayesian approach in modelling animal abundance and occurrence using a hierarchical N-mixture model. N-mixture models assume replication on sampling sites, an assumption that may be violated when the site is not closed to changes in abundance during the survey period or when nominal replicates are defined spatially. In this paper, we studied the robustness of a Bayesian approach to fitting the N-mixture model for pseudo-replicated count data. Our simulation results showed that the Bayesian estimates for abundance and detection probability are slightly biased when the actual detection probability is small and are sensitive to the presence of extra variability within local sites.
Yu, Hwa-Lung; Wang, Chih-Hsin
2013-02-05
Understanding the daily changes in ambient air quality concentrations is important to the assessing human exposure and environmental health. However, the fine temporal scales (e.g., hourly) involved in this assessment often lead to high variability in air quality concentrations. This is because of the complex short-term physical and chemical mechanisms among the pollutants. Consequently, high heterogeneity is usually present in not only the averaged pollution levels, but also the intraday variance levels of the daily observations of ambient concentration across space and time. This characteristic decreases the estimation performance of common techniques. This study proposes a novel quantile-based Bayesian maximum entropy (QBME) method to account for the nonstationary and nonhomogeneous characteristics of ambient air pollution dynamics. The QBME method characterizes the spatiotemporal dependence among the ambient air quality levels based on their location-specific quantiles and accounts for spatiotemporal variations using a local weighted smoothing technique. The epistemic framework of the QBME method can allow researchers to further consider the uncertainty of space-time observations. This study presents the spatiotemporal modeling of daily CO and PM10 concentrations across Taiwan from 1998 to 2009 using the QBME method. Results show that the QBME method can effectively improve estimation accuracy in terms of lower mean absolute errors and standard deviations over space and time, especially for pollutants with strong nonhomogeneous variances across space. In addition, the epistemic framework can allow researchers to assimilate the site-specific secondary information where the observations are absent because of the common preferential sampling issues of environmental data. The proposed QBME method provides a practical and powerful framework for the spatiotemporal modeling of ambient pollutants.
A Bayesian Hierarchical Modeling Approach to Predicting Flow in Ungauged Basins
Recent innovative approaches to identifying and applying regression-based relationships between land use patterns (such as increasing impervious surface area and decreasing vegetative cover) and rainfall-runoff model parameters represent novel and promising improvements to predic...
The Bayesian Revolution Approaches Psychological Development
ERIC Educational Resources Information Center
Shultz, Thomas R.
2007-01-01
This commentary reviews five articles that apply Bayesian ideas to psychological development, some with psychology experiments, some with computational modeling, and some with both experiments and modeling. The reviewed work extends the current Bayesian revolution into tasks often studied in children, such as causal learning and word learning, and…
An Integrated Bayesian Model for DIF Analysis
ERIC Educational Resources Information Center
Soares, Tufi M.; Goncalves, Flavio B.; Gamerman, Dani
2009-01-01
In this article, an integrated Bayesian model for differential item functioning (DIF) analysis is proposed. The model is integrated in the sense of modeling the responses along with the DIF analysis. This approach allows DIF detection and explanation in a simultaneous setup. Previous empirical studies and/or subjective beliefs about the item…
Bayesian modeling of unknown diseases for biosurveillance.
Shen, Yanna; Cooper, Gregory F
2009-11-14
This paper investigates Bayesian modeling of unknown causes of events in the context of disease-outbreak detection. We introduce a Bayesian approach that models and detects both (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 key contribution of this paper is that it introduces a Bayesian approach for jointly modeling both known and unknown causes of events. Such modeling has broad applicability in medical informatics, where the space of known causes of outcomes of interest is seldom complete.
Optimal online learning: a Bayesian approach
NASA Astrophysics Data System (ADS)
Solla, Sara A.; Winther, Ole
1999-09-01
A recently proposed Bayesian approach to online learning is applied to learning a rule defined as a noisy single layer perceptron. In the Bayesian online approach, the exact posterior distribution is approximated by a simple parametric posterior that is updated online as new examples are incorporated to the dataset. In the case of binary weights, the approximate posterior is chosen to be a biased binary distribution. The resulting online algorithm is shown to outperform several other online approaches to this problem.
Chaudhary, Abhishek; Hantush, Mohamed M
2017-01-01
Model uncertainty estimation and risk assessment is essential to environmental management and informed decision making on pollution mitigation strategies. In this study, we apply a probabilistic methodology, which combines Bayesian Monte Carlo simulation and Maximum Likelihood estimation (BMCML) to calibrate a lake oxygen recovery model. We first derive an analytical solution of the differential equation governing lake-averaged oxygen dynamics as a function of time-variable wind speed. Statistical inferences on model parameters and predictive uncertainty are then drawn by Bayesian conditioning of the analytical solution on observed daily wind speed and oxygen concentration data obtained from an earlier study during two recovery periods on a eutrophic lake in upper state New York. The model is calibrated using oxygen recovery data for one year and statistical inferences were validated using recovery data for another year. Compared with essentially two-step, regression and optimization approach, the BMCML results are more comprehensive and performed relatively better in predicting the observed temporal dissolved oxygen levels (DO) in the lake. BMCML also produced comparable calibration and validation results with those obtained using popular Markov Chain Monte Carlo technique (MCMC) and is computationally simpler and easier to implement than the MCMC. Next, using the calibrated model, we derive an optimal relationship between liquid film-transfer coefficient for oxygen and wind speed and associated 95% confidence band, which are shown to be consistent with reported measured values at five different lakes. Finally, we illustrate the robustness of the BMCML to solve risk-based water quality management problems, showing that neglecting cross-correlations between parameters could lead to improper required BOD load reduction to achieve the compliance criteria of 5 mg/L.
Bayesian structural equation modeling in sport and exercise psychology.
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.
NASA Astrophysics Data System (ADS)
Kocabas, Verda; Dragicevic, Suzana
2013-10-01
Land-use change models grounded in complexity theory such as agent-based models (ABMs) are increasingly being used to examine evolving urban systems. The objective of this study is to develop a spatial model that simulates land-use change under the influence of human land-use choice behavior. This is achieved by integrating the key physical and social drivers of land-use change using Bayesian networks (BNs) coupled with agent-based modeling. The BNAS model, integrated Bayesian network-based agent system, presented in this study uses geographic information systems, ABMs, BNs, and influence diagram principles to model population change on an irregular spatial structure. The model is parameterized with historical data and then used to simulate 20 years of future population and land-use change for the City of Surrey, British Columbia, Canada. The simulation results identify feasible new urban areas for development around the main transportation corridors. The obtained new development areas and the projected population trajectories with the“what-if” scenario capabilities can provide insights into urban planners for better and more informed land-use policy or decision-making processes.
Current Challenges in Bayesian Model Choice
NASA Astrophysics Data System (ADS)
Clyde, M. A.; Berger, J. O.; Bullard, F.; Ford, E. B.; Jefferys, W. H.; Luo, R.; Paulo, R.; Loredo, T.
2007-11-01
Model selection (and the related issue of model uncertainty) arises in many astronomical problems, and, in particular, has been one of the focal areas of the Exoplanet working group under the SAMSI (Statistics and Applied Mathematical Sciences Institute) Astrostatistcs Exoplanet program. We provide an overview of the Bayesian approach to model selection and highlight the challenges involved in implementing Bayesian model choice in four stylized problems. We review some of the current methods used by statisticians and astronomers and present recent developments in the area. We discuss the applicability, computational challenges, and performance of suggested methods and conclude with recommendations and open questions.
A Bayesian approach to earthquake source studies
NASA Astrophysics Data System (ADS)
Minson, Sarah
Bayesian sampling has several advantages over conventional optimization approaches to solving inverse problems. It produces the distribution of all possible models sampled proportionally to how much each model is consistent with the data and the specified prior information, and thus images the entire solution space, revealing the uncertainties and trade-offs in the model. Bayesian sampling is applicable to both linear and non-linear modeling, and the values of the model parameters being sampled can be constrained based on the physics of the process being studied and do not have to be regularized. However, these methods are computationally challenging for high-dimensional problems. Until now the computational expense of Bayesian sampling has been too great for it to be practicable for most geophysical problems. I present a new parallel sampling algorithm called CATMIP for Cascading Adaptive Tempered Metropolis In Parallel. This technique, based on Transitional Markov chain Monte Carlo, makes it possible to sample distributions in many hundreds of dimensions, if the forward model is fast, or to sample computationally expensive forward models in smaller numbers of dimensions. The design of the algorithm is independent of the model being sampled, so CATMIP can be applied to many areas of research. I use CATMIP to produce a finite fault source model for the 2007 Mw 7.7 Tocopilla, Chile earthquake. Surface displacements from the earthquake were recorded by six interferograms and twelve local high-rate GPS stations. Because of the wealth of near-fault data, the source process is well-constrained. I find that the near-field high-rate GPS data have significant resolving power above and beyond the slip distribution determined from static displacements. The location and magnitude of the maximum displacement are resolved. The rupture almost certainly propagated at sub-shear velocities. The full posterior distribution can be used not only to calculate source parameters but also
NASA Astrophysics Data System (ADS)
Xia, Yongqiu; Li, Yuefei; Zhang, Xinyu; Yan, Xiaoyuan
2017-01-01
Nitrate (NO3-) pollution is a serious problem worldwide, particularly in countries with intensive agricultural and population activities. Previous studies have used δ15N-NO3- and δ18O-NO3- to determine the NO3- sources in rivers. However, this approach is subject to substantial uncertainties and limitations because of the numerous NO3- sources, the wide isotopic ranges, and the existing isotopic fractionations. In this study, we outline a combined procedure for improving the determination of NO3- sources in a paddy agriculture-urban gradient watershed in eastern China. First, the main sources of NO3- in the Qinhuai River were examined by the dual-isotope biplot approach, in which we narrowed the isotope ranges using site-specific isotopic results. Next, the bacterial groups and chemical properties of the river water were analyzed to verify these sources. Finally, we introduced a Bayesian model to apportion the spatiotemporal variations of the NO3- sources. Denitrification was first incorporated into the Bayesian model because denitrification plays an important role in the nitrogen pathway. The results showed that fertilizer contributed large amounts of NO3- to the surface water in traditional agricultural regions, whereas manure effluents were the dominant NO3- source in intensified agricultural regions, especially during the wet seasons. Sewage effluents were important in all three land uses and exhibited great differences between the dry season and the wet season. This combined analysis quantitatively delineates the proportion of NO3- sources from paddy agriculture to urban river water for both dry and wet seasons and incorporates isotopic fractionation and uncertainties in the source compositions.
Rainfall-Runoff Forecast and Model Parameter Estimation: a Dynamic Bayesian Networks Approach
NASA Astrophysics Data System (ADS)
Canon Barriga, J. E.; Morillo Leon, F. C.
2013-12-01
The suggested climate-driven non-stationarities and intrinsic uncertainties of hydrological processes such as precipitation (P) and runoff (R), represent a fruitful context to develop new methods that may be able to detect parametric variations in time series and incorporate them into forecasts. In this research, we developed a method to forecast runoff from precipitation time series based on Dynamic Bayesian Networks (DBN). The purpose of the research was to determine an appropriate structure of the DBN and the optimal lengths of hydrological time series required to establish statistical parameters (i.e., first two moments) of P and optimal fits of forecasted R at daily and weekly intervals. A DBN can be briefly interpreted as a set of nodes (representing conditional probabilistic variables) connected by arrows that establish a causal, time-oriented, relationship among them. A DBN is defined by two components: a static network (structure) and a transition probability matrix between consecutive stages. Similarly to neural networks, DBN must be trained in order to learn about the subjacent process and make useful predictions. To determine the ability of the DBN to forecast R from P we initially generated long synthetic P series and run a deterministic model (HEC-HMS) to generate R. The DBN were then trained with different lengths of these synthetic series to forecast R (using smoothing and filtering methods). Two structures were considered: 1) DBN with P(t), P(t-1) and R(t-1) and 2) DBN with P(t), P(t-1), R(t-1) and ΔR=[R(t-1)-R(t-2)]. Both smoothing and filtering methods were appropriate to make predictions on a daily and weekly basis (filtration performing better). Setting the complexity (number of states of the random variables) in a DBN proves to be a critical issue, since an increase in the number of states, which implies larger training sets, does not always mean an improvement in the prediction. We found that acceptable results could be obtained from DBN
Berhane, Kiros; Molitor, Nuoo-Ting
2008-10-01
Flexible multilevel models are proposed to allow for cluster-specific smooth estimation of growth curves in a mixed-effects modeling format that includes subject-specific random effects on the growth parameters. Attention is then focused on models that examine between-cluster comparisons of the effects of an ecologic covariate of interest (e.g. air pollution) on nonlinear functionals of growth curves (e.g. maximum rate of growth). A Gibbs sampling approach is used to get posterior mean estimates of nonlinear functionals along with their uncertainty estimates. A second-stage ecologic random-effects model is used to examine the association between a covariate of interest (e.g. air pollution) and the nonlinear functionals. A unified estimation procedure is presented along with its computational and theoretical details. The models are motivated by, and illustrated with, lung function and air pollution data from the Southern California Children's Health Study.
A Bayesian Approach to Learning Scoring Systems.
Ertekin, Şeyda; Rudin, Cynthia
2015-12-01
We present a Bayesian method for building scoring systems, which are linear models with coefficients that have very few significant digits. Usually the construction of scoring systems involve manual effort-humans invent the full scoring system without using data, or they choose how logistic regression coefficients should be scaled and rounded to produce a scoring system. These kinds of heuristics lead to suboptimal solutions. Our approach is different in that humans need only specify the prior over what the coefficients should look like, and the scoring system is learned from data. For this approach, we provide a Metropolis-Hastings sampler that tends to pull the coefficient values toward their "natural scale." Empirically, the proposed method achieves a high degree of interpretability of the models while maintaining competitive generalization performances.
Bayesian Calibration of Microsimulation Models.
Rutter, Carolyn M; Miglioretti, Diana L; Savarino, James E
2009-12-01
Microsimulation models that describe disease processes synthesize information from multiple sources and can be used to estimate the effects of screening and treatment on cancer incidence and mortality at a population level. These models are characterized by simulation of individual event histories for an idealized population of interest. Microsimulation models are complex and invariably include parameters that are not well informed by existing data. Therefore, a key component of model development is the choice of parameter values. Microsimulation model parameter values are selected to reproduce expected or known results though the process of model calibration. Calibration may be done by perturbing model parameters one at a time or by using a search algorithm. As an alternative, we propose a Bayesian method to calibrate microsimulation models that uses Markov chain Monte Carlo. We show that this approach converges to the target distribution and use a simulation study to demonstrate its finite-sample performance. Although computationally intensive, this approach has several advantages over previously proposed methods, including the use of statistical criteria to select parameter values, simultaneous calibration of multiple parameters to multiple data sources, incorporation of information via prior distributions, description of parameter identifiability, and the ability to obtain interval estimates of model parameters. We develop a microsimulation model for colorectal cancer and use our proposed method to calibrate model parameters. The microsimulation model provides a good fit to the calibration data. We find evidence that some parameters are identified primarily through prior distributions. Our results underscore the need to incorporate multiple sources of variability (i.e., due to calibration data, unknown parameters, and estimated parameters and predicted values) when calibrating and applying microsimulation models.
Probabilistic Tomography: A Pragmatic Bayesian Approach
NASA Astrophysics Data System (ADS)
Trampert, J.
2014-12-01
'The future lies in uncertainty' (Spiegelhalter, Science, 345, 264, 2014), nothing could be more true for Earth Sciences. We are able to produce ever more sophisticated models but they can only inform us about the Earth in a meaningful way if we can assign uncertainties to the models. Bayesian inference is a natural choice for this task as it handles uncertainty in a natural way by explicitly modeling assumptions. Another desirable property is that Bayes' theorem contains Occam's razor implicitly. I will present our efforts over the that last 10 years to infer Earth properties using an approach we called probabilistic tomography. The word pragmatic has several meanings in this context. In more classical Bayesian inference problems, we usually prescribe subjective or informative priors. I will illustrate this by showing examples which employ the neighborhood algorithm (Sambridge, 1999) or a Metropolis rule (Mosegaard and Tarantola, 1995). Recently we started to use neural networks to parametrize the posterior. In our implementation, we do not sample the posterior directly, but make predictions on some properties of the posterior. The interpretation of the uncertainty is therefore slightly different, but the method informs us on the information gain with respect to the prior. I will show examples on source and structural inversions using so-called mixture density networks.
Xing, Junliang; Ai, Haizhou; Liu, Liwei; Lao, Shihong
2011-06-01
Multiple object tracking (MOT) is a very challenging task yet of fundamental importance for many practical applications. In this paper, we focus on the problem of tracking multiple players in sports video which is even more difficult due to the abrupt movements of players and their complex interactions. To handle the difficulties in this problem, we present a new MOT algorithm which contributes both in the observation modeling level and in the tracking strategy level. For the observation modeling, we develop a progressive observation modeling process that is able to provide strong tracking observations and greatly facilitate the tracking task. For the tracking strategy, we propose a dual-mode two-way Bayesian inference approach which dynamically switches between an offline general model and an online dedicated model to deal with single isolated object tracking and multiple occluded object tracking integrally by forward filtering and backward smoothing. Extensive experiments on different kinds of sports videos, including football, basketball, as well as hockey, demonstrate the effectiveness and efficiency of the proposed method.
A Bayesian Approach to Joint Modeling of Protein-DNA Binding, Gene Expression and Sequence Data
Xie, Yang; Pan, Wei; Jeong, Kyeong S.; Xiao, Guanghua; Khodursky, Arkady B.
2012-01-01
The genome-wide DNA-protein binding data, DNA sequence data and gene expression data represent complementary means to deciphering global and local transcriptional regulatory circuits. Combining these different types of data can not only improve the statistical power, but also provide a more comprehensive picture of gene regulation. In this paper, we propose a novel statistical model to augment proteinDNA binding data with gene expression and DNA sequence data when available. We specify a hierarchical Bayes model and use Markov chain Monte Carlo simulations to draw inferences. Both simulation studies and an analysis of an experimental dataset show that the proposed joint modeling method can significantly improve the specificity and sensitivity of identifying target genes as compared to conventional approaches relying on a single data source. PMID:20049751
NASA Astrophysics Data System (ADS)
Lee, Chieh-Han; Yu, Hwa-Lung; Chien, Lung-Chang
2014-05-01
Dengue fever has been identified as one of the most widespread vector-borne diseases in tropical and sub-tropical. In the last decade, dengue is an emerging infectious disease epidemic in Taiwan especially in the southern area where have annually high incidences. For the purpose of disease prevention and control, an early warning system is urgently needed. Previous studies have showed significant relationships between climate variables, in particular, rainfall and temperature, and the temporal epidemic patterns of dengue cases. However, the transmission of the dengue fever is a complex interactive process that mostly understated the composite space-time effects of dengue fever. This study proposes developing a one-week ahead warning system of dengue fever epidemics in the southern Taiwan that considered nonlinear associations between weekly dengue cases and meteorological factors across space and time. The early warning system based on an integration of distributed lag nonlinear model (DLNM) and stochastic Bayesian Maximum Entropy (BME) analysis. The study identified the most significant meteorological measures including weekly minimum temperature and maximum 24-hour rainfall with continuous 15-week lagged time to dengue cases variation under condition of uncertainty. Subsequently, the combination of nonlinear lagged effects of climate variables and space-time dependence function is implemented via a Bayesian framework to predict dengue fever occurrences in the southern Taiwan during 2012. The result shows the early warning system is useful for providing potential outbreak spatio-temporal prediction of dengue fever distribution. In conclusion, the proposed approach can provide a practical disease control tool for environmental regulators seeking more effective strategies for dengue fever prevention.
Hopes and Cautions in Implementing Bayesian Structural Equation Modeling
ERIC Educational Resources Information Center
MacCallum, Robert C.; Edwards, Michael C.; Cai, Li
2012-01-01
Muthen and Asparouhov (2012) have proposed and demonstrated an approach to model specification and estimation in structural equation modeling (SEM) using Bayesian methods. Their contribution builds on previous work in this area by (a) focusing on the translation of conventional SEM models into a Bayesian framework wherein parameters fixed at zero…
Massoudieh, Arash; Visser, Ate; Sharifi, Soroosh; Broers, Hans Peter
2013-10-15
The mixing of groundwaters with different ages in aquifers, groundwater age is more appropriately represented by a distribution rather than a scalar number. To infer a groundwater age distribution from environmental tracers, a mathematical form is often assumed for the shape of the distribution and the parameters of the mathematical distribution are estimated using deterministic or stochastic inverse methods. We found that the prescription of the mathematical form limits the exploration of the age distribution to the shapes that can be described by the selected distribution. In this paper, the use of freeform histograms as groundwater age distributions is evaluated. A Bayesian Markov Chain Monte Carlo approach is used to estimate the fraction of groundwater in each histogram bin. This method was able to capture the shape of a hypothetical gamma distribution from the concentrations of four age tracers. The number of bins that can be considered in this approach is limited based on the number of tracers available. The histogram method was also tested on tracer data sets from Holten (The Netherlands; ^{3}H, ^{3}He, ^{85}Kr, ^{39}Ar) and the La Selva Biological Station (Costa-Rica; SF_{ 6}, CFCs, ^{3}H, ^{4}He and ^{14}C), and compared to a number of mathematical forms. According to standard Bayesian measures of model goodness, the best mathematical distribution performs better than the histogram distributions in terms of the ability to capture the observed tracer data relative to their complexity. Among the histogram distributions, the four bin histogram performs better in most of the cases. The Monte Carlo simulations showed strong correlations in the posterior estimates of bin contributions, indicating that these bins cannot be well constrained using the available age tracers. The fact that mathematical forms overall perform better than the freeform histogram does not undermine the benefit of the
Massoudieh, Arash; Visser, Ate; Sharifi, Soroosh; ...
2013-10-15
The mixing of groundwaters with different ages in aquifers, groundwater age is more appropriately represented by a distribution rather than a scalar number. To infer a groundwater age distribution from environmental tracers, a mathematical form is often assumed for the shape of the distribution and the parameters of the mathematical distribution are estimated using deterministic or stochastic inverse methods. We found that the prescription of the mathematical form limits the exploration of the age distribution to the shapes that can be described by the selected distribution. In this paper, the use of freeform histograms as groundwater age distributions is evaluated.more » A Bayesian Markov Chain Monte Carlo approach is used to estimate the fraction of groundwater in each histogram bin. This method was able to capture the shape of a hypothetical gamma distribution from the concentrations of four age tracers. The number of bins that can be considered in this approach is limited based on the number of tracers available. The histogram method was also tested on tracer data sets from Holten (The Netherlands; 3H, 3He, 85Kr, 39Ar) and the La Selva Biological Station (Costa-Rica; SF 6, CFCs, 3H, 4He and 14C), and compared to a number of mathematical forms. According to standard Bayesian measures of model goodness, the best mathematical distribution performs better than the histogram distributions in terms of the ability to capture the observed tracer data relative to their complexity. Among the histogram distributions, the four bin histogram performs better in most of the cases. The Monte Carlo simulations showed strong correlations in the posterior estimates of bin contributions, indicating that these bins cannot be well constrained using the available age tracers. The fact that mathematical forms overall perform better than the freeform histogram does not undermine the benefit of the freeform approach, especially for the cases where a larger amount of observed data is
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…
A Bayesian approach to estimate evoked potentials.
Sparacino, Giovanni; Milani, Stefano; Arslan, Edoardo; Cobelli, Claudio
2002-06-01
Several approaches, based on different assumptions and with various degree of theoretical sophistication and implementation complexity, have been developed for improving the measurement of evoked potentials (EP) performed by conventional averaging (CA). In many of these methods, one of the major challenges is the exploitation of a priori knowledge. In this paper, we present a new method where the 2nd-order statistical information on the background EEG and on the unknown EP, necessary for the optimal filtering of each sweep in a Bayesian estimation framework, is, respectively, estimated from pre-stimulus data and obtained through a multiple integration of a white noise process model. The latter model is flexible (i.e. it can be employed for a large class of EP) and simple enough to be easily identifiable from the post-stimulus data thanks to a smoothing criterion. The mean EP is determined as the weighted average of the filtered sweeps, where each weight is inversely proportional to the expected value of the norm of the correspondent filter error, a quantity determinable thanks to the employment of the Bayesian approach. The performance of the new approach is shown on both simulated and real auditory EP. A signal-to-noise ratio enhancement is obtained that can allow the (possibly automatic) identification of peak latencies and amplitudes with less sweeps than those required by CA. For cochlear EP, the method also allows the audiology investigator to gather new and clinically important information. The possibility of handling single-sweep analysis with further development of the method is also addressed.
A SEMIPARAMETRIC BAYESIAN MODEL FOR CIRCULAR-LINEAR REGRESSION
We present a Bayesian approach to regress a circular variable on a linear predictor. The regression coefficients are assumed to have a nonparametric distribution with a Dirichlet process prior. The semiparametric Bayesian approach gives added flexibility to the model and is usefu...
NASA Astrophysics Data System (ADS)
Cucchi, Karina; Flipo, Nicolas; Rivière, Agnès; Rubin, Yoram
2016-04-01
Hydrothermal properties of the stream-aquifer interface are key information for modeling water and heat transfers in hydrological basins. Our study introduces an algorithm to estimate hydrological and thermal parameters of the hyporheic zone (HZ), as well as their associated uncertainties. Properties of the HZ are inferred from a combination of head differential time series and vertically-distributed temperature time series measured continually in a HZ vertical profile. Head differential and two temperature time series are used as boundary conditions for the vertical profile; the other temperature time series are used as conditioning measurements. Following the Bayesian framework, model parameters are treated as random variables and we seek to characterize their probability density function (PDF) conditional on the temperature time series. Our algorithm follows the Method of Anchored Distributions (MAD) implemented in the MAD# software. In order to cut down the number of simulations needed, we develop a hybrid discrete-continuous inversion approach. We first identify the most sensitive parameters in a sensitivity analysis, these parameters are characterized with continuous PDFs. Less sensitive parameters are represented with a discrete PDFs using a finite number of discrete outcomes. We use a non-parametric likelihood function and time series dimension reduction techniques in order to calculate posterior PDFs of HZ parameters. We demonstrate the approach on a synthetic study using an analytical solution and then apply it to field measurements gathered in the Avenelles basin, France. We present one application of this approach, the uncertainty-quantified time series of localized stream-aquifer exchanges.
Bayesian stable isotope mixing models
In this paper we review recent advances in Stable Isotope Mixing Models (SIMMs) and place them into an over-arching Bayesian statistical framework which allows for several useful extensions. SIMMs are used to quantify the proportional contributions of various sources to a mixtur...
Particle identification in ALICE: a Bayesian approach
NASA Astrophysics Data System (ADS)
Adam, J.; Adamová, D.; Aggarwal, M. M.; Aglieri Rinella, G.; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahmad, S.; Ahn, S. U.; Aiola, S.; Akindinov, A.; Alam, S. N.; Albuquerque, D. S. D.; Aleksandrov, D.; Alessandro, B.; Alexandre, D.; Alfaro Molina, R.; Alici, A.; Alkin, A.; Almaraz, J. R. M.; Alme, J.; Alt, T.; Altinpinar, S.; Altsybeev, I.; Alves Garcia Prado, C.; Andrei, C.; Andronic, A.; Anguelov, V.; Antičić, T.; Antinori, F.; Antonioli, P.; Aphecetche, L.; Appelshäuser, H.; Arcelli, S.; Arnaldi, R.; Arnold, O. W.; Arsene, I. C.; Arslandok, M.; Audurier, B.; Augustinus, A.; Averbeck, R.; Azmi, M. D.; Badalà, A.; Baek, Y. W.; Bagnasco, S.; Bailhache, R.; Bala, R.; Balasubramanian, S.; Baldisseri, A.; Baral, R. C.; Barbano, A. M.; Barbera, R.; Barile, F.; Barnaföldi, G. G.; Barnby, L. S.; Barret, V.; Bartalini, P.; Barth, K.; Bartke, J.; Bartsch, E.; Basile, M.; Bastid, N.; Basu, S.; Bathen, B.; Batigne, G.; Batista Camejo, A.; Batyunya, B.; Batzing, P. C.; Bearden, I. G.; Beck, H.; Bedda, C.; Behera, N. K.; Belikov, I.; Bellini, F.; Bello Martinez, H.; Bellwied, R.; Belmont, R.; Belmont-Moreno, E.; Belyaev, V.; Benacek, P.; Bencedi, G.; Beole, S.; Berceanu, I.; Bercuci, A.; Berdnikov, Y.; Berenyi, D.; Bertens, R. A.; Berzano, D.; Betev, L.; Bhasin, A.; Bhat, I. R.; Bhati, A. K.; Bhattacharjee, B.; Bhom, J.; Bianchi, L.; Bianchi, N.; Bianchin, C.; Bielčík, J.; Bielčíková, J.; Bilandzic, A.; Biro, G.; Biswas, R.; Biswas, S.; Bjelogrlic, S.; Blair, J. T.; Blau, D.; Blume, C.; Bock, F.; Bogdanov, A.; Bøggild, H.; Boldizsár, L.; Bombara, M.; Book, J.; Borel, H.; Borissov, A.; Borri, M.; Bossú, F.; Botta, E.; Bourjau, C.; Braun-Munzinger, P.; Bregant, M.; Breitner, T.; Broker, T. A.; Browning, T. A.; Broz, M.; Brucken, E. J.; Bruna, E.; Bruno, G. E.; Budnikov, D.; Buesching, H.; Bufalino, S.; Buncic, P.; Busch, O.; Buthelezi, Z.; Butt, J. B.; Buxton, J. T.; Cabala, J.; Caffarri, D.; Cai, X.; Caines, H.; Calero Diaz, L.; Caliva, A.; Calvo Villar, E.; Camerini, P.; Carena, F.; Carena, W.; Carnesecchi, F.; Castillo Castellanos, J.; Castro, A. J.; Casula, E. A. R.; Ceballos Sanchez, C.; Cepila, J.; Cerello, P.; Cerkala, J.; Chang, B.; Chapeland, S.; Chartier, M.; Charvet, J. L.; Chattopadhyay, S.; Chattopadhyay, S.; Chauvin, A.; Chelnokov, V.; Cherney, M.; Cheshkov, C.; Cheynis, B.; Chibante Barroso, V.; Chinellato, D. D.; Cho, S.; Chochula, P.; Choi, K.; Chojnacki, M.; Choudhury, S.; Christakoglou, P.; Christensen, C. H.; Christiansen, P.; Chujo, T.; Chung, S. U.; Cicalo, C.; Cifarelli, L.; Cindolo, F.; Cleymans, J.; Colamaria, F.; Colella, D.; Collu, A.; Colocci, M.; Conesa Balbastre, G.; Conesa del Valle, Z.; Connors, M. E.; Contreras, J. G.; Cormier, T. M.; Corrales Morales, Y.; Cortés Maldonado, I.; Cortese, P.; Cosentino, M. R.; Costa, F.; Crochet, P.; Cruz Albino, R.; Cuautle, E.; Cunqueiro, L.; Dahms, T.; Dainese, A.; Danisch, M. C.; Danu, A.; Das, D.; Das, I.; Das, S.; Dash, A.; Dash, S.; De, S.; De Caro, A.; de Cataldo, G.; de Conti, C.; de Cuveland, J.; De Falco, A.; De Gruttola, D.; De Marco, N.; De Pasquale, S.; Deisting, A.; Deloff, A.; Dénes, E.; Deplano, C.; Dhankher, P.; Di Bari, D.; Di Mauro, A.; Di Nezza, P.; Diaz Corchero, M. A.; Dietel, T.; Dillenseger, P.; Divià, R.; Djuvsland, Ø.; Dobrin, A.; Domenicis Gimenez, D.; Dönigus, B.; Dordic, O.; Drozhzhova, T.; Dubey, A. K.; Dubla, A.; Ducroux, L.; Dupieux, P.; Ehlers, R. J.; Elia, D.; Endress, E.; Engel, H.; Epple, E.; Erazmus, B.; Erdemir, I.; Erhardt, F.; Espagnon, B.; Estienne, M.; Esumi, S.; Eum, J.; Evans, D.; Evdokimov, S.; Eyyubova, G.; Fabbietti, L.; Fabris, D.; Faivre, J.; Fantoni, A.; Fasel, M.; Feldkamp, L.; Feliciello, A.; Feofilov, G.; Ferencei, J.; Fernández Téllez, A.; Ferreiro, E. G.; Ferretti, A.; Festanti, A.; Feuillard, V. J. G.; Figiel, J.; Figueredo, M. A. S.; Filchagin, S.; Finogeev, D.; Fionda, F. M.; Fiore, E. M.; Fleck, M. G.; Floris, M.; Foertsch, S.; Foka, P.; Fokin, S.; Fragiacomo, E.; Francescon, A.; Frankenfeld, U.; Fronze, G. G.; Fuchs, U.; Furget, C.; Furs, A.; Fusco Girard, M.; Gaardhøje, J. J.; Gagliardi, M.; Gago, A. M.; Gallio, M.; Gangadharan, D. R.; Ganoti, P.; Gao, C.; Garabatos, C.; Garcia-Solis, E.; Gargiulo, C.; Gasik, P.; Gauger, E. F.; Germain, M.; Gheata, A.; Gheata, M.; Ghosh, P.; Ghosh, S. K.; Gianotti, P.; Giubellino, P.; Giubilato, P.; Gladysz-Dziadus, E.; Glässel, P.; Goméz Coral, D. M.; Gomez Ramirez, A.; Gonzalez, A. S.; Gonzalez, V.; González-Zamora, P.; Gorbunov, S.; Görlich, L.; Gotovac, S.; Grabski, V.; Grachov, O. A.; Graczykowski, L. K.; Graham, K. L.; Grelli, A.; Grigoras, A.; Grigoras, C.; Grigoriev, V.; Grigoryan, A.; Grigoryan, S.; Grinyov, B.; Grion, N.; Gronefeld, J. M.; Grosse-Oetringhaus, J. F.; Grosso, R.; Guber, F.; Guernane, R.; Guerzoni, B.; Gulbrandsen, K.; Gunji, T.; Gupta, A.; Gupta, R.; Haake, R.; Haaland, Ø.; Hadjidakis, C.; Haiduc, M.; Hamagaki, H.; Hamar, G.; Hamon, J. C.; Harris, J. W.; Harton, A.; Hatzifotiadou, D.; Hayashi, S.; Heckel, S. T.; Hellbär, E.; Helstrup, H.; Herghelegiu, A.; Herrera Corral, G.; Hess, B. A.; Hetland, K. F.; Hillemanns, H.; Hippolyte, B.; Horak, D.; Hosokawa, R.; Hristov, P.; Humanic, T. J.; Hussain, N.; Hussain, T.; Hutter, D.; Hwang, D. S.; Ilkaev, R.; Inaba, M.; Incani, E.; Ippolitov, M.; Irfan, M.; Ivanov, M.; Ivanov, V.; Izucheev, V.; Jacazio, N.; Jacobs, P. M.; Jadhav, M. B.; Jadlovska, S.; Jadlovsky, J.; Jahnke, C.; Jakubowska, M. J.; Jang, H. J.; Janik, M. A.; Jayarathna, P. H. S. Y.; Jena, C.; Jena, S.; Jimenez Bustamante, R. T.; Jones, P. G.; Jusko, A.; Kalinak, P.; Kalweit, A.; Kamin, J.; Kang, J. H.; Kaplin, V.; Kar, S.; Karasu Uysal, A.; Karavichev, O.; Karavicheva, T.; Karayan, L.; Karpechev, E.; Kebschull, U.; Keidel, R.; Keijdener, D. L. D.; Keil, M.; Mohisin Khan, M.; Khan, P.; Khan, S. A.; Khanzadeev, A.; Kharlov, Y.; Kileng, B.; Kim, D. W.; Kim, D. J.; Kim, D.; Kim, H.; Kim, J. S.; Kim, M.; Kim, S.; Kim, T.; Kirsch, S.; Kisel, I.; Kiselev, S.; Kisiel, A.; Kiss, G.; Klay, J. L.; Klein, C.; Klein, J.; Klein-Bösing, C.; Klewin, S.; Kluge, A.; Knichel, M. L.; Knospe, A. G.; Kobdaj, C.; Kofarago, M.; Kollegger, T.; Kolojvari, A.; Kondratiev, V.; Kondratyeva, N.; Kondratyuk, E.; Konevskikh, A.; Kopcik, M.; Kostarakis, P.; Kour, M.; Kouzinopoulos, C.; Kovalenko, O.; Kovalenko, V.; Kowalski, M.; Koyithatta Meethaleveedu, G.; Králik, I.; Kravčáková, A.; Krivda, M.; Krizek, F.; Kryshen, E.; Krzewicki, M.; Kubera, A. M.; Kučera, V.; Kuhn, C.; Kuijer, P. G.; Kumar, A.; Kumar, J.; Kumar, L.; Kumar, S.; Kurashvili, P.; Kurepin, A.; Kurepin, A. B.; Kuryakin, A.; Kweon, M. J.; Kwon, Y.; La Pointe, S. L.; La Rocca, P.; Ladron de Guevara, P.; Lagana Fernandes, C.; Lakomov, I.; Langoy, R.; Lara, C.; Lardeux, A.; Lattuca, A.; Laudi, E.; Lea, R.; Leardini, L.; Lee, G. R.; Lee, S.; Lehas, F.; Lemmon, R. C.; Lenti, V.; Leogrande, E.; León Monzón, I.; León Vargas, H.; Leoncino, M.; Lévai, P.; Li, S.; Li, X.; Lien, J.; Lietava, R.; Lindal, S.; Lindenstruth, V.; Lippmann, C.; Lisa, M. A.; Ljunggren, H. M.; Lodato, D. F.; Loenne, P. I.; Loginov, V.; Loizides, C.; Lopez, X.; López Torres, E.; Lowe, A.; Luettig, P.; Lunardon, M.; Luparello, G.; Lutz, T. H.; Maevskaya, A.; Mager, M.; Mahajan, S.; Mahmood, S. M.; Maire, A.; Majka, R. D.; Malaev, M.; Maldonado Cervantes, I.; Malinina, L.; Mal'Kevich, D.; Malzacher, P.; Mamonov, A.; Manko, V.; Manso, F.; Manzari, V.; Marchisone, M.; Mareš, J.; Margagliotti, G. V.; Margotti, A.; Margutti, J.; Marín, A.; Markert, C.; Marquard, M.; Martin, N. A.; Martin Blanco, J.; Martinengo, P.; Martínez, M. I.; Martínez García, G.; Martinez Pedreira, M.; Mas, A.; Masciocchi, S.; Masera, M.; Masoni, A.; Mastroserio, A.; Matyja, A.; Mayer, C.; Mazer, J.; Mazzoni, M. A.; Mcdonald, D.; Meddi, F.; Melikyan, Y.; Menchaca-Rocha, A.; Meninno, E.; Mercado Pérez, J.; Meres, M.; Miake, Y.; Mieskolainen, M. M.; Mikhaylov, K.; Milano, L.; Milosevic, J.; Mischke, A.; Mishra, A. N.; Miśkowiec, D.; Mitra, J.; Mitu, C. M.; Mohammadi, N.; Mohanty, B.; Molnar, L.; Montaño Zetina, L.; Montes, E.; Moreira De Godoy, D. A.; Moreno, L. A. P.; Moretto, S.; Morreale, A.; Morsch, A.; Muccifora, V.; Mudnic, E.; Mühlheim, D.; Muhuri, S.; Mukherjee, M.; Mulligan, J. D.; Munhoz, M. G.; Munzer, R. H.; Murakami, H.; Murray, S.; Musa, L.; Musinsky, J.; Naik, B.; Nair, R.; Nandi, B. K.; Nania, R.; Nappi, E.; Naru, M. U.; Natal da Luz, H.; Nattrass, C.; Navarro, S. R.; Nayak, K.; Nayak, R.; Nayak, T. K.; Nazarenko, S.; Nedosekin, A.; Nellen, L.; Ng, F.; Nicassio, M.; Niculescu, M.; Niedziela, J.; Nielsen, B. S.; Nikolaev, S.; Nikulin, S.; Nikulin, V.; Noferini, F.; Nomokonov, P.; Nooren, G.; Noris, J. C. C.; Norman, J.; Nyanin, A.; Nystrand, J.; Oeschler, H.; Oh, S.; Oh, S. K.; Ohlson, A.; Okatan, A.; Okubo, T.; Olah, L.; Oleniacz, J.; Oliveira Da Silva, A. C.; Oliver, M. H.; Onderwaater, J.; Oppedisano, C.; Orava, R.; Oravec, M.; Ortiz Velasquez, A.; Oskarsson, A.; Otwinowski, J.; Oyama, K.; Ozdemir, M.; Pachmayer, Y.; Pagano, D.; Pagano, P.; Paić, G.; Pal, S. K.; Pan, J.; Pandey, A. K.; Papikyan, V.; Pappalardo, G. S.; Pareek, P.; Park, W. J.; Parmar, S.; Passfeld, A.; Paticchio, V.; Patra, R. N.; Paul, B.; Pei, H.; Peitzmann, T.; Pereira Da Costa, H.; Peresunko, D.; Pérez Lara, C. E.; Perez Lezama, E.; Peskov, V.; Pestov, Y.; Petráček, V.; Petrov, V.; Petrovici, M.; Petta, C.; Piano, S.; Pikna, M.; Pillot, P.; Pimentel, L. O. D. L.; Pinazza, O.; Pinsky, L.; Piyarathna, D. B.; Płoskoń, M.; Planinic, M.; Pluta, J.; Pochybova, S.; Podesta-Lerma, P. L. M.; Poghosyan, M. G.; Polichtchouk, B.; Poljak, N.; Poonsawat, W.; Pop, A.; Porteboeuf-Houssais, S.; Porter, J.; Pospisil, J.; Prasad, S. K.; Preghenella, R.; Prino, F.; Pruneau, C. A.; Pshenichnov, I.; Puccio, M.; Puddu, G.; Pujahari, P.; Punin, V.; Putschke, J.; Qvigstad, H.; Rachevski, A.; Raha, S.; Rajput, S.; Rak, J.; Rakotozafindrabe, A.; Ramello, L.; Rami, F.; Raniwala, R.; Raniwala, S.; Räsänen, S. S.; Rascanu, B. T.; Rathee, D.; Read, K. F.; Redlich, K.; Reed, R. J.; Rehman, A.; Reichelt, P.; Reidt, F.; Ren, X.; Renfordt, R.; Reolon, A. R.; Reshetin, A.; Reygers, K.; Riabov, V.; Ricci, R. A.; Richert, T.; Richter, M.; Riedler, P.; Riegler, W.; Riggi, F.; Ristea, C.; Rocco, E.; Rodríguez Cahuantzi, M.; Rodriguez Manso, A.; Røed, K.; Rogochaya, E.; Rohr, D.; Röhrich, D.; Ronchetti, F.; Ronflette, L.; Rosnet, P.; Rossi, A.; Roukoutakis, F.; Roy, A.; Roy, C.; Roy, P.; Rubio Montero, A. J.; Rui, R.; Russo, R.; Ryabinkin, E.; Ryabov, Y.; Rybicki, A.; Saarinen, S.; Sadhu, S.; Sadovsky, S.; Šafařík, K.; Sahlmuller, B.; Sahoo, P.; Sahoo, R.; Sahoo, S.; Sahu, P. K.; Saini, J.; Sakai, S.; Saleh, M. A.; Salzwedel, J.; Sambyal, S.; Samsonov, V.; Šándor, L.; Sandoval, A.; Sano, M.; Sarkar, D.; Sarkar, N.; Sarma, P.; Scapparone, E.; Scarlassara, F.; Schiaua, C.; Schicker, R.; Schmidt, C.; Schmidt, H. R.; Schuchmann, S.; Schukraft, J.; Schulc, M.; Schutz, Y.; Schwarz, K.; Schweda, K.; Scioli, G.; Scomparin, E.; Scott, R.; Šefčík, M.; Seger, J. E.; Sekiguchi, Y.; Sekihata, D.; Selyuzhenkov, I.; Senosi, K.; Senyukov, S.; Serradilla, E.; Sevcenco, A.; Shabanov, A.; Shabetai, A.; Shadura, O.; Shahoyan, R.; Shahzad, M. I.; Shangaraev, A.; Sharma, A.; Sharma, M.; Sharma, M.; Sharma, N.; Sheikh, A. I.; Shigaki, K.; Shou, Q.; Shtejer, K.; Sibiriak, Y.; Siddhanta, S.; Sielewicz, K. M.; Siemiarczuk, T.; Silvermyr, D.; Silvestre, C.; Simatovic, G.; Simonetti, G.; Singaraju, R.; Singh, R.; Singha, S.; Singhal, V.; Sinha, B. C.; Sinha, T.; Sitar, B.; Sitta, M.; Skaali, T. B.; Slupecki, M.; Smirnov, N.; Snellings, R. J. M.; Snellman, T. W.; Song, J.; Song, M.; Song, Z.; Soramel, F.; Sorensen, S.; Souza, R. D. de; Sozzi, F.; Spacek, M.; Spiriti, E.; Sputowska, I.; Spyropoulou-Stassinaki, M.; Stachel, J.; Stan, I.; Stankus, P.; Stenlund, E.; Steyn, G.; Stiller, J. H.; Stocco, D.; Strmen, P.; Suaide, A. A. P.; Sugitate, T.; Suire, C.; Suleymanov, M.; Suljic, M.; Sultanov, R.; Šumbera, M.; Sumowidagdo, S.; Szabo, A.; Szanto de Toledo, A.; Szarka, I.; Szczepankiewicz, A.; Szymanski, M.; Tabassam, U.; Takahashi, J.; Tambave, G. J.; Tanaka, N.; Tarhini, M.; Tariq, M.; Tarzila, M. G.; Tauro, A.; Tejeda Muñoz, G.; Telesca, A.; Terasaki, K.; Terrevoli, C.; Teyssier, B.; Thäder, J.; Thakur, D.; Thomas, D.; Tieulent, R.; Timmins, A. R.; Toia, A.; Trogolo, S.; Trombetta, G.; Trubnikov, V.; Trzaska, W. H.; Tsuji, T.; Tumkin, A.; Turrisi, R.; Tveter, T. S.; Ullaland, K.; Uras, A.; Usai, G. L.; Utrobicic, A.; Vala, M.; Valencia Palomo, L.; Vallero, S.; Van Der Maarel, J.; Van Hoorne, J. W.; van Leeuwen, M.; Vanat, T.; Vande Vyvre, P.; Varga, D.; Vargas, A.; Vargyas, M.; Varma, R.; Vasileiou, M.; Vasiliev, A.; Vauthier, A.; Vechernin, V.; Veen, A. M.; Veldhoen, M.; Velure, A.; Vercellin, E.; Vergara Limón, S.; Vernet, R.; Verweij, M.; Vickovic, L.; Viesti, G.; Viinikainen, J.; Vilakazi, Z.; Villalobos Baillie, O.; Villatoro Tello, A.; Vinogradov, A.; Vinogradov, L.; Vinogradov, Y.; Virgili, T.; Vislavicius, V.; Viyogi, Y. P.; Vodopyanov, A.; Völkl, M. A.; Voloshin, K.; Voloshin, S. A.; Volpe, G.; von Haller, B.; Vorobyev, I.; Vranic, D.; Vrláková, J.; Vulpescu, B.; Wagner, B.; Wagner, J.; Wang, H.; Wang, M.; Watanabe, D.; Watanabe, Y.; Weber, M.; Weber, S. G.; Weiser, D. F.; Wessels, J. P.; Westerhoff, U.; Whitehead, A. M.; Wiechula, J.; Wikne, J.; Wilk, G.; Wilkinson, J.; Williams, M. C. S.; Windelband, B.; Winn, M.; Yang, H.; Yang, P.; Yano, S.; Yasin, Z.; Yin, Z.; Yokoyama, H.; Yoo, I.-K.; Yoon, J. H.; Yurchenko, V.; Yushmanov, I.; Zaborowska, A.; Zaccolo, V.; Zaman, A.; Zampolli, C.; Zanoli, H. J. C.; Zaporozhets, S.; Zardoshti, N.; Zarochentsev, A.; Závada, P.; Zaviyalov, N.; Zbroszczyk, H.; Zgura, I. S.; Zhalov, M.; Zhang, H.; Zhang, X.; Zhang, Y.; Zhang, C.; Zhang, Z.; Zhao, C.; Zhigareva, N.; Zhou, D.; Zhou, Y.; Zhou, Z.; Zhu, H.; Zhu, J.; Zichichi, A.; Zimmermann, A.; Zimmermann, M. B.; Zinovjev, G.; Zyzak, M.
2016-05-01
We present a Bayesian approach to particle identification (PID) within the ALICE experiment. The aim is to more effectively combine the particle identification capabilities of its various detectors. After a brief explanation of the adopted methodology and formalism, the performance of the Bayesian PID approach for charged pions, kaons and protons in the central barrel of ALICE is studied. PID is performed via measurements of specific energy loss ( d E/d x) and time of flight. PID efficiencies and misidentification probabilities are extracted and compared with Monte Carlo simulations using high-purity samples of identified particles in the decay channels K0S → π-π+, φ→ K-K+, and Λ→ p π- in p-Pb collisions at √{s_{NN}}=5.02 TeV. In order to thoroughly assess the validity of the Bayesian approach, this methodology was used to obtain corrected pT spectra of pions, kaons, protons, and D0 mesons in pp collisions at √{s}=7 TeV. In all cases, the results using Bayesian PID were found to be consistent with previous measurements performed by ALICE using a standard PID approach. For the measurement of D0 → K-π+, it was found that a Bayesian PID approach gave a higher signal-to-background ratio and a similar or larger statistical significance when compared with standard PID selections, despite a reduced identification efficiency. Finally, we present an exploratory study of the measurement of Λc+ → p K-π+ in pp collisions at √{s}=7 TeV, using the Bayesian approach for the identification of its decay products.
BAYESIAN METHODS FOR REGIONAL-SCALE EUTROPHICATION MODELS. (R830887)
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...
Incorporating Prior Theory in Covariance Structure Analysis: A Bayesian Approach.
ERIC Educational Resources Information Center
Fornell, Claes; Rust, Roland T.
1989-01-01
A Bayesian approach to the testing of competing covariance structures is developed. Approximate posterior probabilities are easily obtained from the chi square values and other known constants. The approach is illustrated using an example that demonstrates how the prior probabilities can alter results concerning the preferred model specification.…
NASA Astrophysics Data System (ADS)
Law, Jane; Quick, Matthew
2013-01-01
This paper adopts a Bayesian spatial modeling approach to investigate the distribution of young offender residences in York Region, Southern Ontario, Canada, at the census dissemination area level. Few geographic researches have analyzed offender (as opposed to offense) data at a large map scale (i.e., using a relatively small areal unit of analysis) to minimize aggregation effects. Providing context is the social disorganization theory, which hypothesizes that areas with economic deprivation, high population turnover, and high ethnic heterogeneity exhibit social disorganization and are expected to facilitate higher instances of young offenders. Non-spatial and spatial Poisson models indicate that spatial methods are superior to non-spatial models with respect to model fit and that index of ethnic heterogeneity, residential mobility (1 year moving rate), and percentage of residents receiving government transfer payments are, respectively, the most significant explanatory variables related to young offender location. These findings provide overwhelming support for social disorganization theory as it applies to offender location in York Region, Ontario. Targeting areas where prevalence of young offenders could or could not be explained by social disorganization through decomposing the estimated risk map are helpful for dealing with juvenile offenders in the region. Results prompt discussion into geographically targeted police services and young offender placement pertaining to risk of recidivism. We discuss possible reasons for differences and similarities between the previous findings (that analyzed offense data and/or were conducted at a smaller map scale) and our findings, limitations of our study, and practical outcomes of this research from a law enforcement perspective.
Bayesian network approach to spatial data mining: a case study
NASA Astrophysics Data System (ADS)
Huang, Jiejun; Wan, Youchuan
2006-10-01
Spatial data mining is a process of discovering interesting, novel, and potentially useful information or knowledge hidden in spatial data sets. It involves different techniques and different methods from various areas of research. A Bayesian network is a graphical model that encodes causal probabilistic relationships among variables of interest, which has a powerful ability for representing and reasoning and provides an effective way to spatial data mining. In this paper we give an introduction to Bayesian networks, and discuss using Bayesian networks for spatial data mining. We propose a framework of spatial data mining based on Bayesian networks. Then we show a case study and use the experimental results to validate the practical viability of the proposed approach to spatial data mining. Finally, the paper gives a summary and some remarks.
Fire risk in San Diego County, California: A weighted Bayesian model approach
Kolden, Crystal A.; Weigel, Timothy J.
2007-01-01
Fire risk models are widely utilized to mitigate wildfire hazards, but models are often based on expert opinions of less understood fire-ignition and spread processes. In this study, we used an empirically derived weights-of-evidence model to assess what factors produce fire ignitions east of San Diego, California. We created and validated a dynamic model of fire-ignition risk based on land characteristics and existing fire-ignition history data, and predicted ignition risk for a future urbanization scenario. We then combined our empirical ignition-risk model with a fuzzy fire behavior-risk model developed by wildfire experts to create a hybrid model of overall fire risk. We found that roads influence fire ignitions and that future growth will increase risk in new rural development areas. We conclude that empirically derived risk models and hybrid models offer an alternative method to assess current and future fire risk based on management actions.
A Semi-Parametric Bayesian Mixture Modeling Approach for the Analysis of Judge Mediated Data
ERIC Educational Resources Information Center
Muckle, Timothy Joseph
2010-01-01
Existing methods for the analysis of ordinal-level data arising from judge ratings, such as the Multi-Facet Rasch model (MFRM, or the so-called Facets model) have been widely used in assessment in order to render fair examinee ability estimates in situations where the judges vary in their behavior or severity. However, this model makes certain…
ERIC Educational Resources Information Center
Song, Xin-Yuan; Lee, Sik-Yum
2008-01-01
Structural equation models are widely appreciated in behavioral, social, and psychological research to model relations between latent constructs and manifest variables, and to control for measurement errors. Most applications of structural equation models are based on fully observed data that are independently distributed. However, hierarchical…
Model Reduction for Dynamic Sensor Steering: A Bayesian Approach to Inverse Problems
2008-06-01
Neumann conditions. In particular, a Poiseuille flow is imposed on the inflow boundary, a no- flow (zero velocity) condition is imposed on the top and...can be incorporated into the solution very elegantly. In [34, 35] an approach is proposed for the description of atmospheric flows based on proper...Steering Al- gorithm setting in Chapter 4, which enables a more realistic simulation of physical processes. The posed challenge is to maintain the
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…
Bayesian Student Modeling and the Problem of Parameter Specification.
ERIC Educational Resources Information Center
Millan, Eva; Agosta, John Mark; Perez de la Cruz, Jose Luis
2001-01-01
Discusses intelligent tutoring systems and the application of Bayesian networks to student modeling. Considers reasons for not using Bayesian networks, including the computational complexity of the algorithms and the difficulty of knowledge acquisition, and proposes an approach to simplify knowledge acquisition that applies causal independence to…
Objective Bayesian model selection for Cox regression.
Held, Leonhard; Gravestock, Isaac; Sabanés Bové, Daniel
2016-12-20
There is now a large literature on objective Bayesian model selection in the linear model based on the g-prior. The methodology has been recently extended to generalized linear models using test-based Bayes factors. In this paper, we show that test-based Bayes factors can also be applied to the Cox proportional hazards model. If the goal is to select a single model, then both the maximum a posteriori and the median probability model can be calculated. For clinical prediction of survival, we shrink the model-specific log hazard ratio estimates with subsequent calculation of the Breslow estimate of the cumulative baseline hazard function. A Bayesian model average can also be employed. We illustrate the proposed methodology with the analysis of survival data on primary biliary cirrhosis patients and the development of a clinical prediction model for future cardiovascular events based on data from the Second Manifestations of ARTerial disease (SMART) cohort study. Cross-validation is applied to compare the predictive performance with alternative model selection approaches based on Harrell's c-Index, the calibration slope and the integrated Brier score. Finally, a novel application of Bayesian variable selection to optimal conditional prediction via landmarking is described. Copyright © 2016 John Wiley & Sons, Ltd.
A Bayesian Approach for Image Segmentation with Shape Priors
Chang, Hang; Yang, Qing; Parvin, Bahram
2008-06-20
Color and texture have been widely used in image segmentation; however, their performance is often hindered by scene ambiguities, overlapping objects, or missingparts. In this paper, we propose an interactive image segmentation approach with shape prior models within a Bayesian framework. Interactive features, through mouse strokes, reduce ambiguities, and the incorporation of shape priors enhances quality of the segmentation where color and/or texture are not solely adequate. The novelties of our approach are in (i) formulating the segmentation problem in a well-de?ned Bayesian framework with multiple shape priors, (ii) ef?ciently estimating parameters of the Bayesian model, and (iii) multi-object segmentation through user-speci?ed priors. We demonstrate the effectiveness of our method on a set of natural and synthetic images.
Hierarchical Bayesian model updating for structural identification
NASA Astrophysics Data System (ADS)
Behmanesh, Iman; Moaveni, Babak; Lombaert, Geert; Papadimitriou, Costas
2015-12-01
A new probabilistic finite element (FE) model updating technique based on Hierarchical Bayesian modeling is proposed for identification of civil structural systems under changing ambient/environmental conditions. The performance of the proposed technique is investigated for (1) uncertainty quantification of model updating parameters, and (2) probabilistic damage identification of the structural systems. Accurate estimation of the uncertainty in modeling parameters such as mass or stiffness is a challenging task. Several Bayesian model updating frameworks have been proposed in the literature that can successfully provide the "parameter estimation uncertainty" of model parameters with the assumption that there is no underlying inherent variability in the updating parameters. However, this assumption may not be valid for civil structures where structural mass and stiffness have inherent variability due to different sources of uncertainty such as changing ambient temperature, temperature gradient, wind speed, and traffic loads. Hierarchical Bayesian model updating is capable of predicting the overall uncertainty/variability of updating parameters by assuming time-variability of the underlying linear system. A general solution based on Gibbs Sampler is proposed to estimate the joint probability distributions of the updating parameters. The performance of the proposed Hierarchical approach is evaluated numerically for uncertainty quantification and damage identification of a 3-story shear building model. Effects of modeling errors and incomplete modal data are considered in the numerical study.
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…
A Bayesian Approach to Sensor Characterization
NASA Technical Reports Server (NTRS)
Timucin, Dogan A.
2003-01-01
The physical model of a generic electro-optic sensor is derived and incorporated into a Bayesian framework for the estimation of key instrument parameters from calibration data. The sensor characterization thus achieved enables optimal subsequent removal of instrument effects from field data, leading to the highest possible accuracy in the retrieved physical quantities.
A guide to Bayesian model selection for ecologists
Hooten, Mevin B.; Hobbs, N.T.
2015-01-01
The steady upward trend in the use of model selection and Bayesian methods in ecological research has made it clear that both approaches to inference are important for modern analysis of models and data. However, in teaching Bayesian methods and in working with our research colleagues, we have noticed a general dissatisfaction with the available literature on Bayesian model selection and multimodel inference. Students and researchers new to Bayesian methods quickly find that the published advice on model selection is often preferential in its treatment of options for analysis, frequently advocating one particular method above others. The recent appearance of many articles and textbooks on Bayesian modeling has provided welcome background on relevant approaches to model selection in the Bayesian framework, but most of these are either very narrowly focused in scope or inaccessible to ecologists. Moreover, the methodological details of Bayesian model selection approaches are spread thinly throughout the literature, appearing in journals from many different fields. Our aim with this guide is to condense the large body of literature on Bayesian approaches to model selection and multimodel inference and present it specifically for quantitative ecologists as neutrally as possible. We also bring to light a few important and fundamental concepts relating directly to model selection that seem to have gone unnoticed in the ecological literature. Throughout, we provide only a minimal discussion of philosophy, preferring instead to examine the breadth of approaches as well as their practical advantages and disadvantages. This guide serves as a reference for ecologists using Bayesian methods, so that they can better understand their options and can make an informed choice that is best aligned with their goals for inference.
Hierarchical Bayesian Approach to Locating Seismic Events
Johannesson, G; Myers, S C; Hanley, W G
2005-11-09
We propose a hierarchical Bayesian model for conducting inference on the location of multiple seismic events (earthquakes) given data on the arrival of various seismic phases to sensor locations. The model explicitly accounts for the uncertainty associated with a theoretical seismic-wave travel-time model used along with the uncertainty of the arrival data. Posterior inferences is carried out using Markov chain Monte Carlo (MCMC).
Kaolin Quality Prediction from Samples: A Bayesian Network Approach
Rivas, T.; Taboada, J.; Ordonez, C.; Matias, J. M.
2009-08-13
We describe the results of an expert system applied to the evaluation of samples of kaolin for industrial use in paper or ceramic manufacture. Different machine learning techniques - classification trees, support vector machines and Bayesian networks - were applied with the aim of evaluating and comparing their interpretability and prediction capacities. The predictive capacity of these models for the samples analyzed was highly satisfactory, both for ceramic quality and paper quality. However, Bayesian networks generally proved to be the most useful technique for our study, as this approach combines good predictive capacity with excellent interpretability of the kaolin quality structure, as it graphically represents relationships between variables and facilitates what-if analyses.
Probabilistic Damage Characterization Using the Computationally-Efficient Bayesian Approach
NASA Technical Reports Server (NTRS)
Warner, James E.; Hochhalter, Jacob D.
2016-01-01
This work presents a computationally-ecient approach for damage determination that quanti es uncertainty in the provided diagnosis. Given strain sensor data that are polluted with measurement errors, Bayesian inference is used to estimate the location, size, and orientation of damage. This approach uses Bayes' Theorem to combine any prior knowledge an analyst may have about the nature of the damage with information provided implicitly by the strain sensor data to form a posterior probability distribution over possible damage states. The unknown damage parameters are then estimated based on samples drawn numerically from this distribution using a Markov Chain Monte Carlo (MCMC) sampling algorithm. Several modi cations are made to the traditional Bayesian inference approach to provide signi cant computational speedup. First, an ecient surrogate model is constructed using sparse grid interpolation to replace a costly nite element model that must otherwise be evaluated for each sample drawn with MCMC. Next, the standard Bayesian posterior distribution is modi ed using a weighted likelihood formulation, which is shown to improve the convergence of the sampling process. Finally, a robust MCMC algorithm, Delayed Rejection Adaptive Metropolis (DRAM), is adopted to sample the probability distribution more eciently. Numerical examples demonstrate that the proposed framework e ectively provides damage estimates with uncertainty quanti cation and can yield orders of magnitude speedup over standard Bayesian approaches.
Bayesian Model Selection for Group Studies
Stephan, Klaas Enno; Penny, Will D.; Daunizeau, Jean; Moran, Rosalyn J.; Friston, Karl J.
2009-01-01
Bayesian model selection (BMS) is a powerful method for determining the most likely among a set of competing hypotheses about the mechanisms that generated observed data. BMS has recently found widespread application in neuroimaging, particularly in the context of dynamic causal modelling (DCM). However, so far, combining BMS results from several subjects has relied on simple (fixed effects) metrics, e.g. the group Bayes factor (GBF), that do not account for group heterogeneity or outliers. In this paper, we compare the GBF with two random effects methods for BMS at the between-subject or group level. These methods provide inference on model-space using a classical and Bayesian perspective respectively. First, a classical (frequentist) approach uses the log model evidence as a subject-specific summary statistic. This enables one to use analysis of variance to test for differences in log-evidences over models, relative to inter-subject differences. We then consider the same problem in Bayesian terms and describe a novel hierarchical model, which is optimised to furnish a probability density on the models themselves. This new variational Bayes method rests on treating the model as a random variable and estimating the parameters of a Dirichlet distribution which describes the probabilities for all models considered. These probabilities then define a multinomial distribution over model space, allowing one to compute how likely it is that a specific model generated the data of a randomly chosen subject as well as the exceedance probability of one model being more likely than any other model. Using empirical and synthetic data, we show that optimising a conditional density of the model probabilities, given the log-evidences for each model over subjects, is more informative and appropriate than both the GBF and frequentist tests of the log-evidences. In particular, we found that the hierarchical Bayesian approach is considerably more robust than either of the other
A Bayesian approach to reliability and confidence
NASA Technical Reports Server (NTRS)
Barnes, Ron
1989-01-01
The historical evolution of NASA's interest in quantitative measures of reliability assessment is outlined. The introduction of some quantitative methodologies into the Vehicle Reliability Branch of the Safety, Reliability and Quality Assurance (SR and QA) Division at Johnson Space Center (JSC) was noted along with the development of the Extended Orbiter Duration--Weakest Link study which will utilize quantitative tools for a Bayesian statistical analysis. Extending the earlier work of NASA sponsor, Richard Heydorn, researchers were able to produce a consistent Bayesian estimate for the reliability of a component and hence by a simple extension for a system of components in some cases where the rate of failure is not constant but varies over time. Mechanical systems in general have this property since the reliability usually decreases markedly as the parts degrade over time. While they have been able to reduce the Bayesian estimator to a simple closed form for a large class of such systems, the form for the most general case needs to be attacked by the computer. Once a table is generated for this form, researchers will have a numerical form for the general solution. With this, the corresponding probability statements about the reliability of a system can be made in the most general setting. Note that the utilization of uniform Bayesian priors represents a worst case scenario in the sense that as researchers incorporate more expert opinion into the model, they will be able to improve the strength of the probability calculations.
Kim, Seongho; Hall, Stephen D.; Li, Lang
2009-01-01
In this paper, various Bayesian Monte Carlo Markov Chain (MCMC) methods and the proposed algorithm, Gibbs maximum a posteriori (GMAP) algorithm, are compared for implementing the nonlinear mixed-effects model in pharmacokinetics (PK) studies. An intravenous two-compartmental PK model is adopted to fit the PK data from the midazolam (MDZ) studies, which recruited 24 individuals with 9 different time points per subject. The three-stage hierarchical nonlinear mixed model is constructed. Data analysis and model performance comparisons show that GMAP converges the fastest, and provides reliable results. At the mean time, data augmentation (DA) methods are used for the Random-walk Metropolis method. Data analysis shows that the speed of the convergence of Random-walk Metropolis can be improved by DA, but all of them are not as fast as GMAP. The performance of GMAP and various MCMC algorithms are compared through Midazolam data analysis and simulation. PMID:20183435
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…
Bayesian Nonparametric Models for Multiway Data Analysis.
Xu, Zenglin; Yan, Feng; Qi, Yuan
2015-02-01
Tensor decomposition is a powerful computational tool for multiway data analysis. Many popular tensor decomposition approaches-such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)-amount to multi-linear factorization. They are insufficient to model (i) complex interactions between data entities, (ii) various data types (e.g., missing data and binary data), and (iii) noisy observations and outliers. To address these issues, we propose tensor-variate latent nonparametric Bayesian models for multiway data analysis. We name these models InfTucker. These new models essentially conduct Tucker decomposition in an infinite feature space. Unlike classical tensor decomposition models, our new approaches handle both continuous and binary data in a probabilistic framework. Unlike previous Bayesian models on matrices and tensors, our models are based on latent Gaussian or t processes with nonlinear covariance functions. Moreover, on network data, our models reduce to nonparametric stochastic blockmodels and can be used to discover latent groups and predict missing interactions. To learn the models efficiently from data, we develop a variational inference technique and explore properties of the Kronecker product for computational efficiency. Compared with a classical variational implementation, this technique reduces both time and space complexities by several orders of magnitude. On real multiway and network data, our new models achieved significantly higher prediction accuracy than state-of-art tensor decomposition methods and blockmodels.
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
Radioactive Contraband Detection: A Bayesian Approach
Candy, J; Breitfeller, E; Guidry, B; Manatt, D; Sale, K; Chambers, D; Axelrod, M; Meyer, A
2009-03-16
Radionuclide emissions from nuclear contraband challenge both detection and measurement technologies to capture and record each event. The development of a sequential Bayesian processor incorporating both the physics of gamma-ray emissions and the measurement of photon energies offers a physics-based approach to attack this challenging problem. It is shown that a 'physics-based' structure can be used to develop an effective detection technique, but also motivates the implementation of this approach using or particle filters to enhance and extract the required information.
Bayesian Models of Individual Differences
Powell, Georgie; Meredith, Zoe; McMillin, Rebecca; Freeman, Tom C. A.
2016-01-01
According to Bayesian models, perception and cognition depend on the optimal combination of noisy incoming evidence with prior knowledge of the world. Individual differences in perception should therefore be jointly determined by a person’s sensitivity to incoming evidence and his or her prior expectations. It has been proposed that individuals with autism have flatter prior distributions than do nonautistic individuals, which suggests that prior variance is linked to the degree of autistic traits in the general population. We tested this idea by studying how perceived speed changes during pursuit eye movement and at low contrast. We found that individual differences in these two motion phenomena were predicted by differences in thresholds and autistic traits when combined in a quantitative Bayesian model. Our findings therefore support the flatter-prior hypothesis and suggest that individual differences in prior expectations are more systematic than previously thought. In order to be revealed, however, individual differences in sensitivity must also be taken into account. PMID:27770059
A Bayesian sequential processor approach to spectroscopic portal system decisions
Sale, K; Candy, J; Breitfeller, E; Guidry, B; Manatt, D; Gosnell, T; Chambers, D
2007-07-31
The development of faster more reliable techniques to detect radioactive contraband in a portal type scenario is an extremely important problem especially in this era of constant terrorist threats. Towards this goal the development of a model-based, Bayesian sequential data processor for the detection problem is discussed. In the sequential processor each datum (detector energy deposit and pulse arrival time) is used to update the posterior probability distribution over the space of model parameters. The nature of the sequential processor approach is that a detection is produced as soon as it is statistically justified by the data rather than waiting for a fixed counting interval before any analysis is performed. In this paper the Bayesian model-based approach, physics and signal processing models and decision functions are discussed along with the first results of our research.
Bayesian variable selection for latent class models.
Ghosh, Joyee; Herring, Amy H; Siega-Riz, Anna Maria
2011-09-01
In this article, we develop a latent class model with class probabilities that depend on subject-specific covariates. One of our major goals is to identify important predictors of latent classes. We consider methodology that allows estimation of latent classes while allowing for variable selection uncertainty. We propose a Bayesian variable selection approach and implement a stochastic search Gibbs sampler for posterior computation to obtain model-averaged estimates of quantities of interest such as marginal inclusion probabilities of predictors. Our methods are illustrated through simulation studies and application to data on weight gain during pregnancy, where it is of interest to identify important predictors of latent weight gain classes.
Bayesian Approach to Effective Model of NiGa2S4 Triangular Lattice with Boltzmann Factor
NASA Astrophysics Data System (ADS)
Takenaka, Hikaru; Nagata, Kenji; Mizokawa, Takashi; Okada, Masato
2016-12-01
We propose a method for inducting the Boltzmann factor to extract effective classical spin Hamiltonians from mean-field-type electronic structural calculations by means of the Bayesian inference. This method enables us to compare electronic structural calculations with experiments according to the classical model at a finite temperature. Application of this method to the unrestricted Hartree-Fock calculations for NiGa2S4 led to the estimation that the superexchange interaction between the nearest neighbor sites is ferromagnetic at low temperature, which is consistent with magnetic experiment results. This supports the theory that competition between the antiferromagnetic third neighbor interaction and ferromagnetic nearest neighbor interaction may lead to the quantum spin liquid in NiGa2S4.
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…
Experience With Bayesian Image Based Surface Modeling
NASA Technical Reports Server (NTRS)
Stutz, John C.
2005-01-01
Bayesian surface modeling from images requires modeling both the surface and the image generation process, in order to optimize the models by comparing actual and generated images. Thus it differs greatly, both conceptually and in computational difficulty, from conventional stereo surface recovery techniques. But it offers the possibility of using any number of images, taken under quite different conditions, and by different instruments that provide independent and often complementary information, to generate a single surface model that fuses all available information. I describe an implemented system, with a brief introduction to the underlying mathematical models and the compromises made for computational efficiency. I describe successes and failures achieved on actual imagery, where we went wrong and what we did right, and how our approach could be improved. Lastly I discuss how the same approach can be extended to distinct types of instruments, to achieve true sensor fusion.
Guo, Qiang; Xu, Pengpeng; Pei, Xin; Wong, S C; Yao, Danya
2017-02-01
Pedestrian safety is increasingly recognized as a major public health concern. Extensive safety studies have been conducted to examine the influence of multiple variables on the occurrence of pedestrian-vehicle crashes. However, the explicit relationship between pedestrian safety and road network characteristics remains unknown. This study particularly focused on the role of different road network patterns on the occurrence of crashes involving pedestrians. A global integration index via space syntax was introduced to quantify the topological structures of road networks. The Bayesian Poisson-lognormal (PLN) models with conditional autoregressive (CAR) prior were then developed via three different proximity structures: contiguity, geometry-centroid distance, and road network connectivity. The models were also compared with the PLN counterpart without spatial correlation effects. The analysis was based on a comprehensive crash dataset from 131 selected traffic analysis zones in Hong Kong. The results indicated that higher global integration was associated with more pedestrian-vehicle crashes; the irregular pattern network was proved to be safest in terms of pedestrian crash occurrences, whereas the grid pattern was the least safe; the CAR model with a neighborhood structure based on road network connectivity was found to outperform in model goodness-of-fit, implying the importance of accurately accounting for spatial correlation when modeling spatially aggregated crash data.
A Bayesian approach to simultaneously quantify assignments and linguistic uncertainty
Chavez, Gregory M; Booker, Jane M; Ross, Timothy J
2010-10-07
Subject matter expert assessments can include both assignment and linguistic uncertainty. This paper examines assessments containing linguistic uncertainty associated with a qualitative description of a specific state of interest and the assignment uncertainty associated with assigning a qualitative value to that state. A Bayesian approach is examined to simultaneously quantify both assignment and linguistic uncertainty in the posterior probability. The approach is applied to a simplified damage assessment model involving both assignment and linguistic uncertainty. The utility of the approach and the conditions under which the approach is feasible are examined and identified.
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.
Brimo, Khaled; Garnier, Patricia; Sun, Siao; Bertrand-Krajewski, Jean-Luc; Cébron, Aurélie; Ouvrard, Stéphanie
2016-08-01
A novel kinetics model that describes the dynamics of polycyclic aromatic hydrocarbons (PAHs) in contaminated soils is presented. The model includes two typical biodegradation pathways: the co-metabolic pathway using pseudo first order kinetics and the specific biodegradation pathway modeled using Monod kinetics. The sorption of PAHs to the solid soil occurs through bi-phasic fist order kinetics, and two types of non-extractible bounded residues are considered: the biogenic and the physically sequestrated into soil matrix. The PAH model was developed in Matlab, parameterized and tested successfully on batch experimental data using a Bayesian approach (DREAM). Preliminary results led to significant model simplifications. They also highlighted that the specific biodegradation pathway was the most efficient at explaining experimental data, as would be expected for an old industrial contaminated soil. Global analysis of sensitivity showed that the amount of PAHs ultimately degraded was mostly governed by physicochemical interactions rather than by biological activity.
Guenole, Nigel
2016-01-01
We describe a Monte Carlo study examining the impact of assuming item isomorphism (i.e., equivalent construct meaning across levels of analysis) on conclusions about homology (i.e., equivalent structural relations across levels of analysis) under varying degrees of non-isomorphism in the context of ordinal indicator multilevel structural equation models (MSEMs). We focus on the condition where one or more loadings are higher on the between level than on the within level to show that while much past research on homology has ignored the issue of psychometric isomorphism, psychometric isomorphism is in fact critical to valid conclusions about homology. More specifically, when a measurement model with non-isomorphic items occupies an exogenous position in a multilevel structural model and the non-isomorphism of these items is not modeled, the within level exogenous latent variance is under-estimated leading to over-estimation of the within level structural coefficient, while the between level exogenous latent variance is overestimated leading to underestimation of the between structural coefficient. When a measurement model with non-isomorphic items occupies an endogenous position in a multilevel structural model and the non-isomorphism of these items is not modeled, the endogenous within level latent variance is under-estimated leading to under-estimation of the within level structural coefficient while the endogenous between level latent variance is over-estimated leading to over-estimation of the between level structural coefficient. The innovative aspect of this article is demonstrating that even minor violations of psychometric isomorphism render claims of homology untenable. We also show that posterior predictive p-values for ordinal indicator Bayesian MSEMs are insensitive to violations of isomorphism even when they lead to severely biased within and between level structural parameters. We highlight conditions where poor estimation of even correctly specified
Guenole, Nigel
2016-01-01
We describe a Monte Carlo study examining the impact of assuming item isomorphism (i.e., equivalent construct meaning across levels of analysis) on conclusions about homology (i.e., equivalent structural relations across levels of analysis) under varying degrees of non-isomorphism in the context of ordinal indicator multilevel structural equation models (MSEMs). We focus on the condition where one or more loadings are higher on the between level than on the within level to show that while much past research on homology has ignored the issue of psychometric isomorphism, psychometric isomorphism is in fact critical to valid conclusions about homology. More specifically, when a measurement model with non-isomorphic items occupies an exogenous position in a multilevel structural model and the non-isomorphism of these items is not modeled, the within level exogenous latent variance is under-estimated leading to over-estimation of the within level structural coefficient, while the between level exogenous latent variance is overestimated leading to underestimation of the between structural coefficient. When a measurement model with non-isomorphic items occupies an endogenous position in a multilevel structural model and the non-isomorphism of these items is not modeled, the endogenous within level latent variance is under-estimated leading to under-estimation of the within level structural coefficient while the endogenous between level latent variance is over-estimated leading to over-estimation of the between level structural coefficient. The innovative aspect of this article is demonstrating that even minor violations of psychometric isomorphism render claims of homology untenable. We also show that posterior predictive p-values for ordinal indicator Bayesian MSEMs are insensitive to violations of isomorphism even when they lead to severely biased within and between level structural parameters. We highlight conditions where poor estimation of even correctly specified
Covariate Balance in Bayesian Propensity Score Approaches for Observational Studies
ERIC Educational Resources Information Center
Chen, Jianshen; Kaplan, David
2015-01-01
Bayesian alternatives to frequentist propensity score approaches have recently been proposed. However, few studies have investigated their covariate balancing properties. This article compares a recently developed two-step Bayesian propensity score approach to the frequentist approach with respect to covariate balance. The effects of different…
Bayesian model selection and isocurvature perturbations
NASA Astrophysics Data System (ADS)
Beltrán, María; García-Bellido, Juan; Lesgourgues, Julien; Liddle, Andrew R.; Slosar, Anže
2005-03-01
Present cosmological data are well explained assuming purely adiabatic perturbations, but an admixture of isocurvature perturbations is also permitted. We use a Bayesian framework to compare the performance of cosmological models including isocurvature modes with the purely adiabatic case; this framework automatically and consistently penalizes models which use more parameters to fit the data. We compute the Bayesian evidence for fits to a data set comprised of WMAP and other microwave anisotropy data, the galaxy power spectrum from 2dFGRS and SDSS, and Type Ia supernovae luminosity distances. We find that Bayesian model selection favors the purely adiabatic models, but so far only at low significance.
Overlapping community detection in weighted networks via a Bayesian approach
NASA Astrophysics Data System (ADS)
Chen, Yi; Wang, Xiaolong; Xiang, Xin; Tang, Buzhou; Chen, Qingcai; Fan, Shixi; Bu, Junzhao
2017-02-01
Complex networks as a powerful way to represent complex systems have been widely studied during the past several years. One of the most important tasks of complex network analysis is to detect communities embedded in networks. In the real world, weighted networks are very common and may contain overlapping communities where a node is allowed to belong to multiple communities. In this paper, we propose a novel Bayesian approach, called the Bayesian mixture network (BMN) model, to detect overlapping communities in weighted networks. The advantages of our method are (i) providing soft-partition solutions in weighted networks; (ii) providing soft memberships, which quantify 'how strongly' a node belongs to a community. Experiments on a large number of real and synthetic networks show that our model has the ability in detecting overlapping communities in weighted networks and is competitive with other state-of-the-art models at shedding light on community partition.
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…
NASA Astrophysics Data System (ADS)
Xiao, H.; Wu, J.-L.; Wang, J.-X.; Sun, R.; Roy, C. J.
2016-11-01
Despite their well-known limitations, Reynolds-Averaged Navier-Stokes (RANS) models are still the workhorse tools for turbulent flow simulations in today's engineering analysis, design and optimization. While the predictive capability of RANS models depends on many factors, for many practical flows the turbulence models are by far the largest source of uncertainty. As RANS models are used in the design and safety evaluation of many mission-critical systems such as airplanes and nuclear power plants, quantifying their model-form uncertainties has significant implications in enabling risk-informed decision-making. In this work we develop a data-driven, physics-informed Bayesian framework for quantifying model-form uncertainties in RANS simulations. Uncertainties are introduced directly to the Reynolds stresses and are represented with compact parameterization accounting for empirical prior knowledge and physical constraints (e.g., realizability, smoothness, and symmetry). An iterative ensemble Kalman method is used to assimilate the prior knowledge and observation data in a Bayesian framework, and to propagate them to posterior distributions of velocities and other Quantities of Interest (QoIs). We use two representative cases, the flow over periodic hills and the flow in a square duct, to evaluate the performance of the proposed framework. Both cases are challenging for standard RANS turbulence models. Simulation results suggest that, even with very sparse observations, the obtained posterior mean velocities and other QoIs have significantly better agreement with the benchmark data compared to the baseline results. At most locations the posterior distribution adequately captures the true model error within the developed model form uncertainty bounds. The framework is a major improvement over existing black-box, physics-neutral methods for model-form uncertainty quantification, where prior knowledge and details of the models are not exploited. This approach has
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…
Adam-Poupart, Ariane; Brand, Allan; Fournier, Michel; Jerrett, Michael
2014-01-01
Background: Ambient air ozone (O3) is a pulmonary irritant that has been associated with respiratory health effects including increased lung inflammation and permeability, airway hyperreactivity, respiratory symptoms, and decreased lung function. Estimation of O3 exposure is a complex task because the pollutant exhibits complex spatiotemporal patterns. To refine the quality of exposure estimation, various spatiotemporal methods have been developed worldwide. Objectives: We sought to compare the accuracy of three spatiotemporal models to predict summer ground-level O3 in Quebec, Canada. Methods: We developed a land-use mixed-effects regression (LUR) model based on readily available data (air quality and meteorological monitoring data, road networks information, latitude), a Bayesian maximum entropy (BME) model incorporating both O3 monitoring station data and the land-use mixed model outputs (BME-LUR), and a kriging method model based only on available O3 monitoring station data (BME kriging). We performed leave-one-station-out cross-validation and visually assessed the predictive capability of each model by examining the mean temporal and spatial distributions of the average estimated errors. Results: The BME-LUR was the best predictive model (R2 = 0.653) with the lowest root mean-square error (RMSE ;7.06 ppb), followed by the LUR model (R2 = 0.466, RMSE = 8.747) and the BME kriging model (R2 = 0.414, RMSE = 9.164). Conclusions: Our findings suggest that errors of estimation in the interpolation of O3 concentrations with BME can be greatly reduced by incorporating outputs from a LUR model developed with readily available data. Citation: Adam-Poupart A, Brand A, Fournier M, Jerrett M, Smargiassi A. 2014. Spatiotemporal modeling of ozone levels in Quebec (Canada): a comparison of kriging, land-use regression (LUR), and combined Bayesian maximum entropy–LUR approaches. Environ Health Perspect 122:970–976; http://dx.doi.org/10.1289/ehp.1306566 PMID:24879650
Dichroic polarization at mid-infrared wavelengths: a Bayesian approach
NASA Astrophysics Data System (ADS)
Lopez-Rodriguez, E.
2016-01-01
A fast and general Bayesian inference framework to infer the physical properties of dichroic polarization using mid-infrared imaging- and spectro-polarimetric observations is presented. The Bayesian approach is based on a hierarchical regression and No-U-Turn Sampler method. This approach simultaneously infers the normalized Stokes parameters to find the full family of solutions that best describe the observations. In comparison with previous methods, the developed Bayesian approach allows the user to introduce a customized absorptive polarization component based on the dust composition, and the appropriate extinction curve of the object. This approach allows the user to obtain more precise estimations of the magnetic-field strength and geometry for tomographic studies, and information about the dominant polarization components of the object. Based on this model, imaging-polarimetric observations using two or three filters located in the central 9.5-10.5 μm, and the edges 8-9 μm and/or 11-13 μm, of the wavelength range are recommended to optimally disentangle the polarization mechanisms.
A Bayesian Approach to Multifractal Extremes
NASA Astrophysics Data System (ADS)
Tchiguirinskaia, Ioulia; Schertzer, Daniel; Lovejoy, Shaun
2013-04-01
Drivers such as climate change and rapid urbanisation will result in increasing flood problems in urban environments through this century. Problems encountered in existing flood defence strategies are often related to the data non-stationary, long range dependencies and the clustering of extremes often resulting in fat tailed (i.e., a power-law tail) probability distributions. We discuss how to better predict the floods by using a physically based approach established on systems that respect a scale symmetry over a wide range of space-time scales to determine the relationship between flood magnitude and return period for a wide range of aggregation periods. The classical quantile distributions unfortunately rely on two hypotheses that are questionable: stationarity and independency of the components of the time series. We pointed out that beyond the classical sampling of the extremes and its limitations, there is the possibility to eliminate long-range dependency by uncovering a white-noise process whose fractional integration generates the observed long-range dependent process. The results were obtained during the CEATI Project "Multifractals and physically based estimates of extreme floods". The ambition of this project was to investigate very large data sets of reasonable quality (e.g., daily stream flow data recorded for at least 20 years for several thousands of gages distributed all over Canada and the USA). The multifractal parameters such as the mean intermittency parameter and the multifractality index were estimated on 8332 time series. The results confirm the dependence of multifractal parameter estimates on the length of available data. Then developing a metric for parameter estimation error became a principal step in uncertainty evaluation with respect to the multifractal estimates. A technique for estimating confidence intervals with the help of a Bayesian approach was developed. A detailed comparison of multifractal quantile plots and paleoflood data
2014-01-01
Background Transmission models can aid understanding of disease dynamics and are useful in testing the efficiency of control measures. The aim of this study was to formulate an appropriate stochastic Susceptible-Infectious-Resistant/Carrier (SIR) model for Salmonella Typhimurium in pigs and thus estimate the transmission parameters between states. Results The transmission parameters were estimated using data from a longitudinal study of three Danish farrow-to-finish pig herds known to be infected. A Bayesian model framework was proposed, which comprised Binomial components for the transition from susceptible to infectious and from infectious to carrier; and a Poisson component for carrier to infectious. Cohort random effects were incorporated into these models to allow for unobserved cohort-specific variables as well as unobserved sources of transmission, thus enabling a more realistic estimation of the transmission parameters. In the case of the transition from susceptible to infectious, the cohort random effects were also time varying. The number of infectious pigs not detected by the parallel testing was treated as unknown, and the probability of non-detection was estimated using information about the sensitivity and specificity of the bacteriological and serological tests. The estimate of the transmission rate from susceptible to infectious was 0.33 [0.06, 1.52], from infectious to carrier was 0.18 [0.14, 0.23] and from carrier to infectious was 0.01 [0.0001, 0.04]. The estimate for the basic reproduction ration (R 0 ) was 1.91 [0.78, 5.24]. The probability of non-detection was estimated to be 0.18 [0.12, 0.25]. Conclusions The proposed framework for stochastic SIR models was successfully implemented to estimate transmission rate parameters for Salmonella Typhimurium in swine field data. R 0 was 1.91, implying that there was dissemination of the infection within pigs of the same cohort. There was significant temporal-cohort variability, especially at the
Bayesian Inference for Nonnegative Matrix Factorisation Models
Cemgil, Ali Taylan
2009-01-01
We describe nonnegative matrix factorisation (NMF) with a Kullback-Leibler (KL) error measure in a statistical framework, with a hierarchical generative model consisting of an observation and a prior component. Omitting the prior leads to the standard KL-NMF algorithms as special cases, where maximum likelihood parameter estimation is carried out via the Expectation-Maximisation (EM) algorithm. Starting from this view, we develop full Bayesian inference via variational Bayes or Monte Carlo. Our construction retains conjugacy and enables us to develop more powerful models while retaining attractive features of standard NMF such as monotonic convergence and easy implementation. We illustrate our approach on model order selection and image reconstruction. PMID:19536273
A Bayesian Ensemble Approach for Epidemiological Projections
Lindström, Tom; Tildesley, Michael; Webb, Colleen
2015-01-01
Mathematical models are powerful tools for epidemiology and can be used to compare control actions. However, different models and model parameterizations may provide different prediction of outcomes. In other fields of research, ensemble modeling has been used to combine multiple projections. We explore the possibility of applying such methods to epidemiology by adapting Bayesian techniques developed for climate forecasting. We exemplify the implementation with single model ensembles based on different parameterizations of the Warwick model run for the 2001 United Kingdom foot and mouth disease outbreak and compare the efficacy of different control actions. This allows us to investigate the effect that discrepancy among projections based on different modeling assumptions has on the ensemble prediction. A sensitivity analysis showed that the choice of prior can have a pronounced effect on the posterior estimates of quantities of interest, in particular for ensembles with large discrepancy among projections. However, by using a hierarchical extension of the method we show that prior sensitivity can be circumvented. We further extend the method to include a priori beliefs about different modeling assumptions and demonstrate that the effect of this can have different consequences depending on the discrepancy among projections. We propose that the method is a promising analytical tool for ensemble modeling of disease outbreaks. PMID:25927892
[Bayesian statistic: an approach fitted to clinic].
Meyer, N; Vinzio, S; Goichot, B
2009-03-01
Bayesian statistic has known a growing success though quite limited. This is surprising since Bayes' theorem on which this paradigm relies is frequently used by the clinicians. There is a direct link between the routine diagnostic test and the Bayesian statistic. This link is the Bayes' theorem which allows one to compute positive and negative predictive values of a test. The principle of this theorem is extended to simple statistical situations as an introduction to Bayesian statistic. The conceptual simplicity of Bayesian statistic should make for a greater acceptance in the biomedical world.
Bobb, Jennifer F.; Dominici, Francesca; Peng, Roger D.
2011-01-01
Summary Estimating the risks heat waves pose to human health is a critical part of assessing the future impact of climate change. In this paper we propose a flexible class of time series models to estimate the relative risk of mortality associated with heat waves and conduct Bayesian model averaging (BMA) to account for the multiplicity of potential models. Applying these methods to data from 105 U.S. cities for the period 1987–2005, we identify those cities having a high posterior probability of increased mortality risk during heat waves, examine the heterogeneity of the posterior distributions of mortality risk across cities, assess sensitivity of the results to the selection of prior distributions, and compare our BMA results to a model selection approach. Our results show that no single model best predicts risk across the majority of cities, and that for some cities heat wave risk estimation is sensitive to model choice. While model averaging leads to posterior distributions with increased variance as compared to statistical inference conditional on a model obtained through model selection, we find that the posterior mean of heat wave mortality risk is robust to accounting for model uncertainty over a broad class of models. PMID:21447046
Technical note: Bayesian calibration of dynamic ruminant nutrition models.
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.
Bayesian failure probability model sensitivity study. Final report
Not Available
1986-05-30
The Office of the Manager, National Communications System (OMNCS) has developed a system-level approach for estimating the effects of High-Altitude Electromagnetic Pulse (HEMP) on the connectivity of telecommunications networks. This approach incorporates a Bayesian statistical model which estimates the HEMP-induced failure probabilities of telecommunications switches and transmission facilities. The purpose of this analysis is to address the sensitivity of the Bayesian model. This is done by systematically varying two model input parameters--the number of observations, and the equipment failure rates. Throughout the study, a non-informative prior distribution is used. The sensitivity of the Bayesian model to the noninformative prior distribution is investigated from a theoretical mathematical perspective.
Coggins, Lewis G.; Bacheler, Nathan M.; Gwinn, Daniel C.
2014-01-01
Occupancy models using incidence data collected repeatedly at sites across the range of a population are increasingly employed to infer patterns and processes influencing population distribution and dynamics. While such work is common in terrestrial systems, fewer examples exist in marine applications. This disparity likely exists because the replicate samples required by these models to account for imperfect detection are often impractical to obtain when surveying aquatic organisms, particularly fishes. We employ simultaneous sampling using fish traps and novel underwater camera observations to generate the requisite replicate samples for occupancy models of red snapper, a reef fish species. Since the replicate samples are collected simultaneously by multiple sampling devices, many typical problems encountered when obtaining replicate observations are avoided. Our results suggest that augmenting traditional fish trap sampling with camera observations not only doubled the probability of detecting red snapper in reef habitats off the Southeast coast of the United States, but supplied the necessary observations to infer factors influencing population distribution and abundance while accounting for imperfect detection. We found that detection probabilities tended to be higher for camera traps than traditional fish traps. Furthermore, camera trap detections were influenced by the current direction and turbidity of the water, indicating that collecting data on these variables is important for future monitoring. These models indicate that the distribution and abundance of this species is more heavily influenced by latitude and depth than by micro-scale reef characteristics lending credence to previous characterizations of red snapper as a reef habitat generalist. This study demonstrates the utility of simultaneous sampling devices, including camera traps, in aquatic environments to inform occupancy models and account for imperfect detection when describing factors
Bayesian generalized linear mixed modeling of Tuberculosis using informative priors
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 generalized linear mixed modeling of Tuberculosis using informative priors.
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 Analysis of Order-Statistics Models for Ranking Data.
ERIC Educational Resources Information Center
Yu, Philip L. H.
2000-01-01
Studied the order-statistics models, extending the usual normal order-statistics model into one in which the underlying random variables followed a multivariate normal distribution. Used a Bayesian approach and the Gibbs sampling technique. Applied the proposed method to analyze presidential election data from the American Psychological…
ERIC Educational Resources Information Center
Finch, Holmes; Edwards, Julianne M.
2016-01-01
Standard approaches for estimating item response theory (IRT) model parameters generally work under the assumption that the latent trait being measured by a set of items follows the normal distribution. Estimation of IRT parameters in the presence of nonnormal latent traits has been shown to generate biased person and item parameter estimates. A…
A Bayesian approach to multivariate measurement system assessment
Hamada, Michael Scott
2016-07-01
This article considers system assessment for multivariate measurements and presents a Bayesian approach to analyzing gauge R&R study data. The evaluation of variances for univariate measurement becomes the evaluation of covariance matrices for multivariate measurements. The Bayesian approach ensures positive definite estimates of the covariance matrices and easily provides their uncertainty. Furthermore, various measurement system assessment criteria are easily evaluated. The approach is illustrated with data from a real gauge R&R study as well as simulated data.
NASA Astrophysics Data System (ADS)
Kim, Jang-Gyeong; Kwon, Hyun-Han; Kim, Dongkyun
2017-01-01
Poisson cluster stochastic rainfall generators (e.g., modified Bartlett-Lewis rectangular pulse, MBLRP) have been widely applied to generate synthetic sub-daily rainfall sequences. The MBLRP model reproduces the underlying distribution of the rainfall generating process. The existing optimization techniques are typically based on individual parameter estimates that treat each parameter as independent. However, parameter estimates sometimes compensate for the estimates of other parameters, which can cause high variability in the results if the covariance structure is not formally considered. Moreover, uncertainty associated with model parameters in the MBLRP rainfall generator is not usually addressed properly. Here, we develop a hierarchical Bayesian model (HBM)-based MBLRP model to jointly estimate parameters across weather stations and explicitly consider the covariance and uncertainty through a Bayesian framework. The model is tested using weather stations in South Korea. The HBM-based MBLRP model improves the identification of parameters with better reproduction of rainfall statistics at various temporal scales. Additionally, the spatial variability of the parameters across weather stations is substantially reduced compared to that of other methods.
Bayesian analysis of the backreaction models
Kurek, Aleksandra; Bolejko, Krzysztof; Szydlowski, Marek
2010-03-15
We present a Bayesian analysis of four different types of backreaction models, which are based on the Buchert equations. In this approach, one considers a solution to the Einstein equations for a general matter distribution and then an average of various observable quantities is taken. Such an approach became of considerable interest when it was shown that it could lead to agreement with observations without resorting to dark energy. In this paper we compare the {Lambda}CDM model and the backreaction models with type Ia supernovae, baryon acoustic oscillations, and cosmic microwave background data, and find that the former is favored. However, the tested models were based on some particular assumptions about the relation between the average spatial curvature and the backreaction, as well as the relation between the curvature and curvature index. In this paper we modified the latter assumption, leaving the former unchanged. We find that, by varying the relation between the curvature and curvature index, we can obtain a better fit. Therefore, some further work is still needed--in particular, the relation between the backreaction and the curvature should be revisited in order to fully determine the feasibility of the backreaction models to mimic dark energy.
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…
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…
Bayesian modeling of flexible cognitive control
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
Bayesian model selection for LISA pathfinder
NASA Astrophysics Data System (ADS)
Karnesis, Nikolaos; Nofrarias, Miquel; Sopuerta, Carlos F.; Gibert, Ferran; Armano, Michele; Audley, Heather; Congedo, Giuseppe; Diepholz, Ingo; Ferraioli, Luigi; Hewitson, Martin; Hueller, Mauro; Korsakova, Natalia; McNamara, Paul W.; Plagnol, Eric; Vitale, Stefano
2014-03-01
The main goal of the LISA Pathfinder (LPF) mission is to fully characterize the acceleration noise models and to test key technologies for future space-based gravitational-wave observatories similar to the eLISA concept. The data analysis team has developed complex three-dimensional models of the LISA Technology Package (LTP) experiment onboard the LPF. These models are used for simulations, but, more importantly, they will be used for parameter estimation purposes during flight operations. One of the tasks of the data analysis team is to identify the physical effects that contribute significantly to the properties of the instrument noise. A way of approaching this problem is to recover the essential parameters of a LTP model fitting the data. Thus, we want to define the simplest model that efficiently explains the observations. To do so, adopting a Bayesian framework, one has to estimate the so-called Bayes factor between two competing models. In our analysis, we use three main different methods to estimate it: the reversible jump Markov chain Monte Carlo method, the Schwarz criterion, and the Laplace approximation. They are applied to simulated LPF experiments in which the most probable LTP model that explains the observations is recovered. The same type of analysis presented in this paper is expected to be followed during flight operations. Moreover, the correlation of the output of the aforementioned methods with the design of the experiment is explored.
A variational Bayesian approach for inverse problems with skew-t error distributions
NASA Astrophysics Data System (ADS)
Guha, Nilabja; Wu, Xiaoqing; Efendiev, Yalchin; Jin, Bangti; Mallick, Bani K.
2015-11-01
In this work, we develop a novel robust Bayesian approach to inverse problems with data errors following a skew-t distribution. A hierarchical Bayesian model is developed in the inverse problem setup. The Bayesian approach contains a natural mechanism for regularization in the form of a prior distribution, and a LASSO type prior distribution is used to strongly induce sparseness. We propose a variational type algorithm by minimizing the Kullback-Leibler divergence between the true posterior distribution and a separable approximation. The proposed method is illustrated on several two-dimensional linear and nonlinear inverse problems, e.g. Cauchy problem and permeability estimation problem.
Bayesian hierarchical model for large-scale covariance matrix estimation.
Zhu, Dongxiao; Hero, Alfred O
2007-12-01
Many bioinformatics problems implicitly depend on estimating large-scale covariance matrix. The traditional approaches tend to give rise to high variance and low accuracy due to "overfitting." We cast the large-scale covariance matrix estimation problem into the Bayesian hierarchical model framework, and introduce dependency between covariance parameters. We demonstrate the advantages of our approaches over the traditional approaches using simulations and OMICS data analysis.
An approach to quantifying the efficiency of a Bayesian filter
Technology Transfer Automated Retrieval System (TEKTRAN)
Data assimilation is defined as the Bayesian conditioning of uncertain model simulations on observations for the purpose of reducing uncertainty about model states. Practical data assimilation applications require that simplifying assumptions be made about the prior and posterior state distributions...
Pham, Lisa M; Carvalho, Luis; Schaus, Scott; Kolaczyk, Eric D
Cellular response to a perturbation is the result of a dynamic system of biological variables linked in a complex network. A major challenge in drug and disease studies is identifying the key factors of a biological network that are essential in determining the cell's fate. Here our goal is the identification of perturbed pathways from high-throughput gene expression data. We develop a three-level hierarchical model, where (i) the first level captures the relationship between gene expression and biological pathways using confirmatory factor analysis, (ii) the second level models the behavior within an underlying network of pathways induced by an unknown perturbation using a conditional autoregressive model, and (iii) the third level is a spike-and-slab prior on the perturbations. We then identify perturbations through posterior-based variable selection. We illustrate our approach using gene transcription drug perturbation profiles from the DREAM7 drug sensitivity predication challenge data set. Our proposed method identified regulatory pathways that are known to play a causative role and that were not readily resolved using gene set enrichment analysis or exploratory factor models. Simulation results are presented assessing the performance of this model relative to a network-free variant and its robustness to inaccuracies in biological databases.
A Bayesian geostatistical transfer function approach to tracer test analysis
NASA Astrophysics Data System (ADS)
Fienen, Michael N.; Luo, Jian; Kitanidis, Peter K.
2006-07-01
Reactive transport modeling is often used in support of bioremediation and chemical treatment planning and design. There remains a pressing need for practical and efficient models that do not require (or assume attainable) the high level of characterization needed by complex numerical models. We focus on a linear systems or transfer function approach to the problem of reactive tracer transport in a heterogeneous saprolite aquifer. Transfer functions are obtained through the Bayesian geostatistical inverse method applied to tracer injection histories and breakthrough curves. We employ nonparametric transfer functions, which require minimal assumptions about shape and structure. The resulting flexibility empowers the data to determine the nature of the transfer function with minimal prior assumptions. Nonnegativity is enforced through a reflected Brownian motion stochastic model. The inverse method enables us to quantify uncertainty and to generate conditional realizations of the transfer function. Complex information about a hydrogeologic system is distilled into a relatively simple but rigorously obtained function that describes the transport behavior of the system between two wells. The resulting transfer functions are valuable in reactive transport models based on traveltime and streamline methods. The information contained in the data, particularly in the case of strong heterogeneity, is not overextended but is fully used. This is the first application of Bayesian geostatistical inversion to transfer functions in hydrogeology but the methodology can be extended to any linear system.
Bayesian Monte Carlo and Maximum Likelihood Approach for ...
Model uncertainty estimation and risk assessment is essential to environmental management and informed decision making on pollution mitigation strategies. In this study, we apply a probabilistic methodology, which combines Bayesian Monte Carlo simulation and Maximum Likelihood estimation (BMCML) to calibrate a lake oxygen recovery model. We first derive an analytical solution of the differential equation governing lake-averaged oxygen dynamics as a function of time-variable wind speed. Statistical inferences on model parameters and predictive uncertainty are then drawn by Bayesian conditioning of the analytical solution on observed daily wind speed and oxygen concentration data obtained from an earlier study during two recovery periods on a eutrophic lake in upper state New York. The model is calibrated using oxygen recovery data for one year and statistical inferences were validated using recovery data for another year. Compared with essentially two-step, regression and optimization approach, the BMCML results are more comprehensive and performed relatively better in predicting the observed temporal dissolved oxygen levels (DO) in the lake. BMCML also produced comparable calibration and validation results with those obtained using popular Markov Chain Monte Carlo technique (MCMC) and is computationally simpler and easier to implement than the MCMC. Next, using the calibrated model, we derive an optimal relationship between liquid film-transfer coefficien
Bonangelino, Pablo; Irony, Telba; Liang, Shengde; Li, Xuefeng; Mukhi, Vandana; Ruan, Shiling; Xu, Yunling; Yang, Xiting; Wang, Chenguang
2011-09-01
Challenging statistical issues often arise in the design and analysis of clinical trials to assess safety and effectiveness of medical devices in the regulatory setting. The use of Bayesian methods in the design and analysis of medical device clinical trials has been increasing significantly in the past decade, not only due to the availability of prior information, but mainly due to the appealing nature of Bayesian clinical trial designs. The Center for Devices and Radiological Health at the Food and Drug Administration (FDA) has gained extensive experience with the use of Bayesian statistical methods and has identified some important issues that need further exploration. In this article, we discuss several topics relating to the use of Bayesian statistical methods in medical device trials, based on our experience and real applications. We illustrate the benefits and challenges of Bayesian approaches when incorporating prior information to evaluate the effectiveness and safety of a medical device. We further present an example of a Bayesian adaptive clinical trial and compare it to a traditional frequentist design. Finally, we discuss the use of Bayesian hierarchical models for multiregional trials and highlight the advantages of the Bayesian approach when specifying clinically relevant study hypotheses.
Estimating hazardous concentrations by an informative Bayesian approach.
Ciffroy, Philippe; Keller, Merlin; Pasanisi, Alberto
2013-03-01
The species sensitivity distribution (SSD) approach is recommended for assessing chemical risk. In practice, however, it can be used only for the few substances for which large-scale ecotoxicological results are available. Indeed, the statistical frequentist approaches used for building SSDs and for deriving hazardous concentrations (HC5) inherently require extensive data to guarantee goodness-of-fit. An alternative Bayesian approach to estimating HC5 from small data sets was developed. In contrast to the noninformative Bayesian approaches that have been tested to date, the authors' method used informative priors related to the expected species sensitivity variance. This method was tested on actual ecotoxicological data for 21 well-informed substances. A cross-validation compared the HC5 values calculated using frequentist approaches with the results of our Bayesian approach, using both complete and truncated data samples. The authors' informative Bayesian approach was compared with noninformative Bayesian methods published in the past, including those incorporating loss functions. The authors found that even for the truncated sample the HC5 values derived from the informative Bayesian approach were generally close to those obtained using the frequentist approach, which requires more data. In addition, the probability of overestimating an HC5 is rather limited. More robust HC5 estimates can be practically obtained from additional data without impairing regulatory protection levels, which will encourage collecting new ecotoxicological data. In conclusion, the Bayesian informative approach was shown to be relatively robust and could be a good surrogate approach for deriving HC5 values from small data sets.
Application of the Bayesian dynamic survival model in medicine.
He, Jianghua; McGee, Daniel L; Niu, Xufeng
2010-02-10
The Bayesian dynamic survival model (BDSM), a time-varying coefficient survival model from the Bayesian prospective, was proposed in early 1990s but has not been widely used or discussed. In this paper, we describe the model structure of the BDSM and introduce two estimation approaches for BDSMs: the Markov Chain Monte Carlo (MCMC) approach and the linear Bayesian (LB) method. The MCMC approach estimates model parameters through sampling and is computationally intensive. With the newly developed geoadditive survival models and software BayesX, the BDSM is available for general applications. The LB approach is easier in terms of computations but it requires the prespecification of some unknown smoothing parameters. In a simulation study, we use the LB approach to show the effects of smoothing parameters on the performance of the BDSM and propose an ad hoc method for identifying appropriate values for those parameters. We also demonstrate the performance of the MCMC approach compared with the LB approach and a penalized partial likelihood method available in software R packages. A gastric cancer trial is utilized to illustrate the application of the BDSM.
Hierarchical Bayesian models of subtask learning.
Anglim, Jeromy; Wynton, Sarah K A
2015-07-01
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 task, which logged participant actions, enabling measurement of strategy use and subtask performance. Model comparison was performed using deviance information criterion (DIC), posterior predictive checks, plots of model fits, and model recovery simulations. Results showed that although learning tended to be monotonically decreasing and decelerating, and approaching an asymptote for all subtasks, there was substantial inconsistency in learning curves both at the group- and individual-levels. This inconsistency was most apparent when constraining both the rate and the ratio of learning to asymptote to be equal across subtasks, thereby giving learning curves only 1 parameter for scaling. The inclusion of 6 strategy covariates provided improved prediction of subtask performance capturing different subtask learning processes and subtask trade-offs. In addition, strategy use partially explained the inconsistency in subtask learning. Overall, the model provided a more nuanced representation of how complex tasks can be decomposed in terms of simpler learning mechanisms.
Survey of Bayesian Models for Modelling of Stochastic Temporal Processes
Ng, B
2006-10-12
This survey gives an overview of popular generative models used in the modeling of stochastic temporal systems. In particular, this survey is organized into two parts. The first part discusses the discrete-time representations of dynamic Bayesian networks and dynamic relational probabilistic models, while the second part discusses the continuous-time representation of continuous-time Bayesian networks.
Bayesian log-periodic model for financial crashes
NASA Astrophysics Data System (ADS)
Rodríguez-Caballero, Carlos Vladimir; Knapik, Oskar
2014-10-01
This paper introduces a Bayesian approach in econophysics literature about financial bubbles in order to estimate the most probable time for a financial crash to occur. To this end, we propose using noninformative prior distributions to obtain posterior distributions. Since these distributions cannot be performed analytically, we develop a Markov Chain Monte Carlo algorithm to draw from posterior distributions. We consider three Bayesian models that involve normal and Student's t-distributions in the disturbances and an AR(1)-GARCH(1,1) structure only within the first case. In the empirical part of the study, we analyze a well-known example of financial bubble - the S&P 500 1987 crash - to show the usefulness of the three methods under consideration and crashes of Merval-94, Bovespa-97, IPCMX-94, Hang Seng-97 using the simplest method. The novelty of this research is that the Bayesian models provide 95% credible intervals for the estimated crash time.
ERIC Educational Resources Information Center
Lee, Sik-Yum; Song, Xin-Yuan; Tang, Nian-Sheng
2007-01-01
The analysis of interaction among latent variables has received much attention. This article introduces a Bayesian approach to analyze a general structural equation model that accommodates the general nonlinear terms of latent variables and covariates. This approach produces a Bayesian estimate that has the same statistical optimal properties as a…
Liang, Shidong; Jia, Haifeng; Xu, Changqing; Xu, Te; Melching, Charles
2016-08-01
Facing increasingly serious water pollution, the Chinese government is changing the environmental management strategy from solely pollutant concentration control to a Total Maximum Daily Load (TMDL) program, and water quality models are increasingly being applied to determine the allowable pollutant load in the TMDL. Despite the frequent use of models, few studies have focused on how parameter uncertainty in water quality models affect the allowable pollutant loads in the TMDL program, particularly for complicated and high-dimension water quality models. Uncertainty analysis for such models is limited by time-consuming simulation and high-dimensionality and nonlinearity in parameter spaces. In this study, an allowable pollutant load calculation platform was established using the Environmental Fluid Dynamics Code (EFDC), which is a widely applied hydrodynamic-water quality model. A Bayesian approach, i.e. the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm, which is a high-efficiency, multi-chain Markov Chain Monte Carlo (MCMC) method, was applied to assess the effects of parameter uncertainty on the water quality model simulations and its influence on the allowable pollutant load calculation in the TMDL program. Miyun Reservoir, which is the most important surface drinking water source for Beijing, suffers from eutrophication and was selected as a case study. The relations between pollutant loads and water quality indicators are obtained through a graphical method in the simulation platform. Ranges of allowable pollutant loads were obtained according to the results of parameter uncertainty analysis, i.e. Total Organic Carbon (TOC): 581.5-1030.6t·yr(-1); Total Phosphorus (TP): 23.3-31.0t·yr(-1); and Total Nitrogen (TN): 480-1918.0t·yr(-1). The wide ranges of allowable pollutant loads reveal the importance of parameter uncertainty analysis in a TMDL program for allowable pollutant load calculation and margin of safety (MOS) determination. The sources
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…
Quantification Of Margins And Uncertainties: A Bayesian Approach (full Paper)
Wallstrom, Timothy C
2008-01-01
Quantification of Margins and Uncertainties (QMU) is 'a formalism for dealing with the reliability of complex technical systems, and the confidence which can be placed in estimates of that reliability.' (Eardleyet al, 2005). In this paper, we show how QMU may be interpreted in the framework of Bayesian statistical inference, using a probabilistic network. The Bayesian approach clarifies the probabilistic underpinnings of the formalism, and shows how the formalism can be used for deciSion-making.
NASA Astrophysics Data System (ADS)
Baresel, Björn; Bucher, Hugo; Brosse, Morgane; Bagherpour, Borhan; Schaltegger, Urs
2016-04-01
Chemical abrasion isotope dilution thermal ionization mass spectrometry (CA-ID-TIMS) U-Pb dating of single-zircon crystals is preferably applied to tephra beds intercalated in sedimentary sequences. By assuming that the zircon crystallization age closely approximate that of the volcanic eruption and ash deposition, U-Pb zircon geochronology is the preferred approach for dating mass extinction events (such as the Permian-Triassic boundary mass extinction) in the sedimentary record. As tephra from large volcanic eruptions is often transported over long distances, it additionally provide an invaluable tool for stratigraphic correlation across distant geologic sections. Therefore, the combination of high-precision zircon geochronology with apatite chemistry of the same tephra bed (so called apatite tephrochronology) provides a robust fingerprint of one particular volcanic eruption. In addition we provide coherent Bayesian model ages for the Permian-Triassic boundary (PTB) mass extinction, then compare it with PTB model ages at Meishan after Burgess et al. (2014). We will present new high-precision U-Pb zircon dates for a series of volcanic ash beds in deep- and shallow-marine Permian-Triassic sections in the Nanpanjiang Basin, South China. In addition, apatite crystals out of the same ash beds were analysed focusing on their halogen (F, Cl) and trace-element (e.g. Fe, Mg, REE) chemistry. We also show that Bayesian age models produce reproducible results from different geologic sections. On the basis of these data, including litho- and biostratigraphic correlations, we can precisely and accurately constrain the Permian-Triassic boundary in an equatorial marine setting, and correlate tephra beds over different sections and facies in the Nanpanjiang Basin independently from litho-, bio- or chemostratigraphic criteria. The results evidence that data produced in laboratories associated to the global EARTHTIME consortium can provide age information at the 0.05% level of 206
A Bayesian Hierarchical Approach to Regional Frequency Analysis of Extremes
NASA Astrophysics Data System (ADS)
Renard, B.
2010-12-01
Rainfall and runoff frequency analysis is a major issue for the hydrological community. The distribution of hydrological extremes varies in space and possibly in time. Describing and understanding this spatiotemporal variability are primary challenges to improve hazard quantification and risk assessment. This presentation proposes a general approach based on a Bayesian hierarchical model, following previous work by Cooley et al. [2007], Micevski [2007], Aryal et al. [2009] or Lima and Lall [2009; 2010]. Such a hierarchical model is made up of two levels: (1) a data level modeling the distribution of observations, and (2) a process level describing the fluctuation of the distribution parameters in space and possibly in time. At the first level of the model, at-site data (e.g., annual maxima series) are modeled with a chosen distribution (e.g., a GEV distribution). Since data from several sites are considered, the joint distribution of a vector of (spatial) observations needs to be derived. This is challenging because data are in general not spatially independent, especially for nearby sites. An elliptical copula is therefore used to formally account for spatial dependence between at-site data. This choice might be questionable in the context of extreme value distributions. However, it is motivated by its applicability in spatial highly dimensional problems, where the joint pdf of a vector of n observations is required to derive the likelihood function (with n possibly amounting to hundreds of sites). At the second level of the model, parameters of the chosen at-site distribution are then modeled by a Gaussian spatial process, whose mean may depend on covariates (e.g. elevation, distance to sea, weather pattern, time). In particular, this spatial process allows estimating parameters at ungauged sites, and deriving the predictive distribution of rainfall/runoff at every pixel/catchment of the studied domain. An application to extreme rainfall series from the French
de la Cruz-Mesía, Rolando; Quintana, Fernando A
2007-04-01
This paper discusses Bayesian statistical methods for the classification of observations into two or more groups based on hierarchical models for nonlinear longitudinal profiles. Parameter estimation for a discriminant model that classifies individuals into distinct predefined groups or populations uses appropriate posterior simulation schemes. The methods are illustrated with data from a study involving 173 pregnant women. The main objective in this study is to predict normal versus abnormal pregnancy outcomes from beta human chorionic gonadotropin data available at early stages of pregnancy.
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…
Toyinbo, Peter A; Vanderploeg, Rodney D; Belanger, Heather G; Spehar, Andrea M; Lapcevic, William A; Scott, Steven G
2017-01-15
We sought to further define the epidemiology of the complex, multiple injuries collectively known as polytrauma/blast-related injury (PT/BRI). Using a systems science approach, we performed Bayesian network modeling to find the most accurate representation of the complex system of PT/BRI and identify key variables for understanding the subsequent effects of blast exposure in a sample of Florida National Guard members (1,443 deployed to Operation Enduring Freedom/Operation Iraqi Freedom and 1,655 not deployed) who completed an online survey during the period from 2009 to 2010. We found that postdeployment symptoms reported as present at the time of the survey were largely independent of deployment per se. Blast exposure, not mild traumatic brain injury (TBI), acted as the primary military deployment-related driver of PT/BRI symptoms. Blast exposure was indirectly linked to mild TBI via other deployment-related traumas and was a significant risk for a high level of posttraumatic stress disorder (PTSD) arousal symptoms. PTSD arousal symptoms and tinnitus were directly dependent upon blast exposure, with both acting as bridge symptoms to other postdeployment mental health and physical symptoms, respectively. Neurobehavioral or postconcussion-like symptoms had no significant dependence relationship with mild TBI, but they were synergistic with blast exposure in influencing PTSD arousal symptoms. A replication of this analysis using a larger PT/BRI database is warranted.
Normativity, interpretation, and Bayesian models
Oaksford, Mike
2014-01-01
It has been suggested that evaluative normativity should be expunged from the psychology of reasoning. A broadly Davidsonian response to these arguments is presented. It is suggested that two distinctions, between different types of rationality, are more permeable than this argument requires and that the fundamental objection is to selecting theories that make the most rational sense of the data. It is argued that this is inevitable consequence of radical interpretation where understanding others requires assuming they share our own norms of reasoning. This requires evaluative normativity and it is shown that when asked to evaluate others’ arguments participants conform to rational Bayesian norms. It is suggested that logic and probability are not in competition and that the variety of norms is more limited than the arguments against evaluative normativity suppose. Moreover, the universality of belief ascription suggests that many of our norms are universal and hence evaluative. It is concluded that the union of evaluative normativity and descriptive psychology implicit in Davidson and apparent in the psychology of reasoning is a good thing. PMID:24860519
The need to assess large numbers of chemicals for their potential toxicities has resulted in increased emphasis on medium- and high-throughput in vitro screening approaches. For such approaches to be useful, efficient and reliable data analysis and hit detection methods are also ...
A Full Bayesian Approach for Boolean Genetic Network Inference
Han, Shengtong; Wong, Raymond K. W.; Lee, Thomas C. M.; Shen, Linghao; Li, Shuo-Yen R.; Fan, Xiaodan
2014-01-01
Boolean networks are a simple but efficient model for describing gene regulatory systems. A number of algorithms have been proposed to infer Boolean networks. However, these methods do not take full consideration of the effects of noise and model uncertainty. In this paper, we propose a full Bayesian approach to infer Boolean genetic networks. Markov chain Monte Carlo algorithms are used to obtain the posterior samples of both the network structure and the related parameters. In addition to regular link addition and removal moves, which can guarantee the irreducibility of the Markov chain for traversing the whole network space, carefully constructed mixture proposals are used to improve the Markov chain Monte Carlo convergence. Both simulations and a real application on cell-cycle data show that our method is more powerful than existing methods for the inference of both the topology and logic relations of the Boolean network from observed data. PMID:25551820
Bayesian neural network for rainfall-runoff modeling
NASA Astrophysics Data System (ADS)
Khan, Mohammad Sajjad; Coulibaly, Paulin
2006-07-01
In this paper, a Bayesian learning approach is introduced to train a multilayer feed-forward network for daily river flow and reservoir inflow simulation in a cold region river basin in Canada. In Bayesian approach, uncertainty about the relationship between inputs and outputs is initially taken care of by an assumed prior distribution of parameters (weights and biases). This prior distribution is updated to posterior distribution using a likelihood function following Bayes' theorem while data are observed. This posterior distribution is called the objective function of a network in the Bayesian learning approach. The objective function is maximized using a suitable optimization technique. Once the network is trained, the predictive distribution of the network outputs is obtained by integrating over the posterior distribution of weights. In this study, Gaussian prior distribution and a Gaussian noise model are used in defining posterior distribution. The network has been optimized using a scaled conjugate gradient technique. Posterior distribution of weights is approximated to Gaussian during prediction. Prediction performance of the Bayesian neural network (BNN) is compared with the results obtained from a standard artificial neural network (ANN) model and a widely used conceptual rainfall-runoff model, namely, HBV-96. The BNN model outperformed the conceptual model and slightly outperformed the standard ANN model in simulating mean, peak, and low river flows and reservoir inflows. The significant contribution of the Bayesian method over the conventional ANN approach, among others, is the uncertainty estimation of the outputs in the form of confidence intervals which are particularly needed in practical water resources applications. Prediction confidence limits (or intervals) indicate the extent to which one can rely on predictions for decision making. It is shown that the BNN can provide reliable streamflow and reservoir inflow forecasts without a loss in model
Bayesian restoration of ion channel records using hidden Markov models.
Rosales, R; Stark, J A; Fitzgerald, W J; Hladky, S B
2001-03-01
Hidden Markov models have been used to restore recorded signals of single ion channels buried in background noise. Parameter estimation and signal restoration are usually carried out through likelihood maximization by using variants of the Baum-Welch forward-backward procedures. This paper presents an alternative approach for dealing with this inferential task. The inferences are made by using a combination of the framework provided by Bayesian statistics and numerical methods based on Markov chain Monte Carlo stochastic simulation. The reliability of this approach is tested by using synthetic signals of known characteristics. The expectations of the model parameters estimated here are close to those calculated using the Baum-Welch algorithm, but the present methods also yield estimates of their errors. Comparisons of the results of the Bayesian Markov Chain Monte Carlo approach with those obtained by filtering and thresholding demonstrate clearly the superiority of the new methods.
Sparse Event Modeling with Hierarchical Bayesian Kernel Methods
2016-01-05
events (and subsequently, their likelihood of occurrence) based on historical evidence of the counts of previous event occurrences. The novel Bayesian...Aug-2014 22-May-2015 Approved for Public Release; Distribution Unlimited Final Report: Sparse Event Modeling with Hierarchical Bayesian Kernel Methods...Sparse Event Modeling with Hierarchical Bayesian Kernel Methods Report Title The research objective of this proposal was to develop a predictive Bayesian
Bayesian approach to non-inferiority trials for normal means.
Gamalo, M Amper; Wu, Rui; Tiwari, Ram C
2016-02-01
Regulatory framework recommends that novel statistical methodology for analyzing trial results parallels the frequentist strategy, e.g. the new method must protect type-I error and arrive at a similar conclusion. Keeping these in mind, we construct a Bayesian approach for non-inferiority trials with normal response. A non-informative prior is assumed for the mean response of the experimental treatment and Jeffrey's prior for its corresponding variance when it is unknown. The posteriors of the mean response and variance of the treatment in historical trials are then assumed as priors for its corresponding parameters in the current trial, where that treatment serves as the active control. From these priors, a Bayesian decision criterion is derived to determine whether the experimental treatment is non-inferior to the active control. This criterion is evaluated and compared with the frequentist method using simulation studies. Results show that both Bayesian and frequentist approaches perform alike, but the Bayesian approach has a higher power when the variances are unknown. Both methods also arrive at the same conclusion of non-inferiority when applied on two real datasets. A major advantage of the proposed Bayesian approach lies in its ability to provide posterior probabilities for varying effect sizes of the experimental treatment over the active control.
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 graphical models for genomewide association studies.
Verzilli, Claudio J; Stallard, Nigel; Whittaker, John C
2006-07-01
As the extent of human genetic variation becomes more fully characterized, the research community is faced with the challenging task of using this information to dissect the heritable components of complex traits. Genomewide association studies offer great promise in this respect, but their analysis poses formidable difficulties. In this article, we describe a computationally efficient approach to mining genotype-phenotype associations that scales to the size of the data sets currently being collected in such studies. We use discrete graphical models as a data-mining tool, searching for single- or multilocus patterns of association around a causative site. The approach is fully Bayesian, allowing us to incorporate prior knowledge on the spatial dependencies around each marker due to linkage disequilibrium, which reduces considerably the number of possible graphical structures. A Markov chain-Monte Carlo scheme is developed that yields samples from the posterior distribution of graphs conditional on the data from which probabilistic statements about the strength of any genotype-phenotype association can be made. Using data simulated under scenarios that vary in marker density, genotype relative risk of a causative allele, and mode of inheritance, we show that the proposed approach has better localization properties and leads to lower false-positive rates than do single-locus analyses. Finally, we present an application of our method to a quasi-synthetic data set in which data from the CYP2D6 region are embedded within simulated data on 100K single-nucleotide polymorphisms. Analysis is quick (<5 min), and we are able to localize the causative site to a very short interval.
Technology Transfer Automated Retrieval System (TEKTRAN)
The objective was to study alternative models for genetic analyses of carcass traits assessed by ultrasonography in Guzerá cattle. Data from 947 measurements (655 animals) of Rib-eye area (REA), rump fat thickness (RFT) and backfat thickness (BFT) were used. Finite polygenic models (FPM), infinitesi...
Linderman, Scott W.; Johnson, Matthew J.; Wilson, Matthew A.; Chen, Zhe
2016-01-01
Background Rodent hippocampal population codes represent important spatial information about the environment during navigation. Computational methods have been developed to uncover the neural representation of spatial topology embedded in rodent hippocampal ensemble spike activity. New method We extend our previous work and propose a novel nonparametric Bayesian approach to infer rat hippocampal population codes during spatial navigation. To tackle the model selection problem, we leverage a nonparametric Bayesian model. Specifically, we apply a hierarchical Dirichlet process-hidden Markov model (HDP-HMM) using two Bayesian inference methods, one based on Markov chain Monte Carlo (MCMC) and the other based on variational Bayes (VB). Results The effectiveness of our Bayesian approaches is demonstrated on recordings from a freely-behaving rat navigating in an open field environment. Comparison with existing methods The HDP-HMM outperforms the finite-state HMM in both simulated and experimental data. For HPD-HMM, the MCMC-based inference with Hamiltonian Monte Carlo (HMC) hyperparameter sampling is flexible and efficient, and outperforms VB and MCMC approaches with hyperparameters set by empirical Bayes. Conclusion The nonparametric Bayesian HDP-HMM method can efficiently perform model selection and identify model parameters, which can used for modeling latent-state neuronal population dynamics. PMID:26854398
Cho, Kang Su; Jung, Hae Do; Ham, Won Sik; Chung, Doo Yong; Kang, Yong Jin; Jang, Won Sik; Kwon, Jong Kyou; Choi, Young Deuk; Lee, Joo Yong
2015-01-01
Objectives To investigate whether skin-to-stone distance (SSD), which remains controversial in patients with ureter stones, can be a predicting factor for one session success following extracorporeal shock wave lithotripsy (ESWL) in patients with upper ureter stones. Patients and Methods We retrospectively reviewed the medical records of 1,519 patients who underwent their first ESWL between January 2005 and December 2013. Among these patients, 492 had upper ureter stones that measured 4–20 mm and were eligible for our analyses. Maximal stone length, mean stone density (HU), and SSD were determined on pretreatment non-contrast computed tomography (NCCT). For subgroup analyses, patients were divided into four groups. Group 1 consisted of patients with SSD<25th percentile, group 2 consisted of patients with SSD in the 25th to 50th percentile, group 3 patients had SSD in the 50th to 75th percentile, and group 4 patients had SSD≥75th percentile. Results In analyses of group 2 patients versus others, there were no statistical differences in mean age, stone length and density. However, the one session success rate in group 2 was higher than other groups (77.9% vs. 67.0%; P = 0.032). The multivariate logistic regression model revealed that shorter stone length, lower stone density, and the group 2 SSD were positive predictors for successful outcomes in ESWL. Using the Bayesian model-averaging approach, longer stone length, lower stone density, and group 2 SSD can be also positive predictors for successful outcomes following ESWL. Conclusions Our data indicate that a group 2 SSD of approximately 10 cm is a positive predictor for success following ESWL. PMID:26659086
Bayesian analysis of structural equation models with dichotomous variables.
Lee, Sik-Yum; Song, Xin-Yuan
2003-10-15
Structural equation modelling has been used extensively in the behavioural and social sciences for studying interrelationships among manifest and latent variables. Recently, its uses have been well recognized in medical research. This paper introduces a Bayesian approach to analysing general structural equation models with dichotomous variables. In the posterior analysis, the observed dichotomous data are augmented with the hypothetical missing values, which involve the latent variables in the model and the unobserved continuous measurements underlying the dichotomous data. An algorithm based on the Gibbs sampler is developed for drawing the parameters values and the hypothetical missing values from the joint posterior distributions. Useful statistics, such as the Bayesian estimates and their standard error estimates, and the highest posterior density intervals, can be obtained from the simulated observations. A posterior predictive p-value is used to test the goodness-of-fit of the posited model. The methodology is applied to a study of hypertensive patient non-adherence to medication.
Spatial Bayesian hierarchical modelling of extreme sea states
NASA Astrophysics Data System (ADS)
Clancy, Colm; O'Sullivan, John; Sweeney, Conor; Dias, Frédéric; Parnell, Andrew C.
2016-11-01
A Bayesian hierarchical framework is used to model extreme sea states, incorporating a latent spatial process to more effectively capture the spatial variation of the extremes. The model is applied to a 34-year hindcast of significant wave height off the west coast of Ireland. The generalised Pareto distribution is fitted to declustered peaks over a threshold given by the 99.8th percentile of the data. Return levels of significant wave height are computed and compared against those from a model based on the commonly-used maximum likelihood inference method. The Bayesian spatial model produces smoother maps of return levels. Furthermore, this approach greatly reduces the uncertainty in the estimates, thus providing information on extremes which is more useful for practical applications.
Bayesian non parametric modelling of Higgs pair production
NASA Astrophysics Data System (ADS)
Scarpa, Bruno; Dorigo, Tommaso
2017-03-01
Statistical classification models are commonly used to separate a signal from a background. In this talk we face the problem of isolating the signal of Higgs pair production using the decay channel in which each boson decays into a pair of b-quarks. Typically in this context non parametric methods are used, such as Random Forests or different types of boosting tools. We remain in the same non-parametric framework, but we propose to face the problem following a Bayesian approach. A Dirichlet process is used as prior for the random effects in a logit model which is fitted by leveraging the Polya-Gamma data augmentation. Refinements of the model include the insertion in the simple model of P-splines to relate explanatory variables with the response and the use of Bayesian trees (BART) to describe the atoms in the Dirichlet process.
Bayesian model selection analysis of WMAP3
Parkinson, David; Mukherjee, Pia; Liddle, Andrew R.
2006-06-15
We present a Bayesian model selection analysis of WMAP3 data using our code CosmoNest. We focus on the density perturbation spectral index n{sub S} and the tensor-to-scalar ratio r, which define the plane of slow-roll inflationary models. We find that while the Bayesian evidence supports the conclusion that n{sub S}{ne}1, the data are not yet powerful enough to do so at a strong or decisive level. If tensors are assumed absent, the current odds are approximately 8 to 1 in favor of n{sub S}{ne}1 under our assumptions, when WMAP3 data is used together with external data sets. WMAP3 data on its own is unable to distinguish between the two models. Further, inclusion of r as a parameter weakens the conclusion against the Harrison-Zel'dovich case (n{sub S}=1, r=0), albeit in a prior-dependent way. In appendices we describe the CosmoNest code in detail, noting its ability to supply posterior samples as well as to accurately compute the Bayesian evidence. We make a first public release of CosmoNest, now available at www.cosmonest.org.
Bayesian probability approach to ADHD appraisal.
Robeva, Raina; Penberthy, Jennifer Kim
2009-01-01
Accurate diagnosis of attentional disorders such as attention-deficit hyperactivity disorder (ADHD) is imperative because there are multiple negative psychosocial sequelae related to undiagnosed and untreated ADHD. Early and accurate detection can lead to effective intervention and prevention of negative sequelae. Unfortunately, diagnosing ADHD presents a challenge to traditional assessment paradigms because there is no single test that definitively establishes its presence. Even though ADHD is a physiologically based disorder with a multifactorial etiology, the diagnosis has been traditionally based on a subjective history of symptoms. In this chapter we outline a stochastic method that utilizes a Bayesian interface for quantifying and assessing ADHD. It can be used to combine of a variety of psychometric tests and physiological markers into a single standardized instrument that, on each step, refines a probability for ADHD for each individual based on information provided by the individual assessments. The method is illustrated with data from a small study of six college female students with ADHD and six matched controls in which the method achieves correct classification for all participants, where none of the individual assessments was capable of achieving perfect classification. Further, we provide a framework for applying this Bayesian method for performing meta-analysis of data obtained from disparate studies and using disparate tests for ADHD based on calibration of the data into a unified probability scale. We use this method to combine data from five studies that examine the diagnostic abilities of different behavioral rating scales and EEG assessments of ADHD, enrolling a total of 56 ADHD and 55 control subjects of different age groups and gender.
A Bayesian subgroup analysis using collections of ANOVA models.
Liu, Jinzhong; Sivaganesan, Siva; Laud, Purushottam W; Müller, Peter
2017-03-20
We develop a Bayesian approach to subgroup analysis using ANOVA models with multiple covariates, extending an earlier work. We assume a two-arm clinical trial with normally distributed response variable. We also assume that the covariates for subgroup finding are categorical and are a priori specified, and parsimonious easy-to-interpret subgroups are preferable. We represent the subgroups of interest by a collection of models and use a model selection approach to finding subgroups with heterogeneous effects. We develop suitable priors for the model space and use an objective Bayesian approach that yields multiplicity adjusted posterior probabilities for the models. We use a structured algorithm based on the posterior probabilities of the models to determine which subgroup effects to report. Frequentist operating characteristics of the approach are evaluated using simulation. While our approach is applicable in more general cases, we mainly focus on the 2 × 2 case of two covariates each at two levels for ease of presentation. The approach is illustrated using a real data example.
Bayesian and maximum likelihood estimation of hierarchical response time models
Farrell, Simon; Ludwig, Casimir
2008-01-01
Hierarchical (or multilevel) statistical models have become increasingly popular in psychology in the last few years. We consider the application of multilevel modeling to the ex-Gaussian, a popular model of response times. Single-level estimation is compared with hierarchical estimation of parameters of the ex-Gaussian distribution. Additionally, for each approach maximum likelihood (ML) estimation is compared with Bayesian estimation. A set of simulations and analyses of parameter recovery show that although all methods perform adequately well, hierarchical methods are better able to recover the parameters of the ex-Gaussian by reducing the variability in recovered parameters. At each level, little overall difference was observed between the ML and Bayesian methods. PMID:19001592
AutoClass: A Bayesian Approach to Classification
NASA Technical Reports Server (NTRS)
Stutz, John; Cheeseman, Peter; Hanson, Robin; Taylor, Will; Lum, Henry, Jr. (Technical Monitor)
1994-01-01
We describe a Bayesian approach to the untutored discovery of classes in a set of cases, sometimes called finite mixture separation or clustering. The main difference between clustering and our approach is that we search for the "best" set of class descriptions rather than grouping the cases themselves. We describe our classes in terms of a probability distribution or density function, and the locally maximal posterior probability valued function parameters. We rate our classifications with an approximate joint probability of the data and functional form, marginalizing over the parameters. Approximation is necessitated by the computational complexity of the joint probability. Thus, we marginalize w.r.t. local maxima in the parameter space. We discuss the rationale behind our approach to classification. We give the mathematical development for the basic mixture model and describe the approximations needed for computational tractability. We instantiate the basic model with the discrete Dirichlet distribution and multivariant Gaussian density likelihoods. Then we show some results for both constructed and actual data.
Bayesian analysis of physiologically based toxicokinetic and toxicodynamic models.
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.
Bayesian penalized log-likelihood ratio approach for dose response clinical trial studies.
Tang, Yuanyuan; Cai, Chunyan; Sun, Liangrui; He, Jianghua
2017-02-13
In literature, there are a few unified approaches to test proof of concept and estimate a target dose, including the multiple comparison procedure using modeling approach, and the permutation approach proposed by Klingenberg. We discuss and compare the operating characteristics of these unified approaches and further develop an alternative approach in a Bayesian framework based on the posterior distribution of a penalized log-likelihood ratio test statistic. Our Bayesian approach is much more flexible to handle linear or nonlinear dose-response relationships and is more efficient than the permutation approach. The operating characteristics of our Bayesian approach are comparable to and sometimes better than both approaches in a wide range of dose-response relationships. It yields credible intervals as well as predictive distribution for the response rate at a specific dose level for the target dose estimation. Our Bayesian approach can be easily extended to continuous, categorical, and time-to-event responses. We illustrate the performance of our proposed method with extensive simulations and Phase II clinical trial data examples.
A Bayesian approach to tracking patients having changing pharmacokinetic parameters
NASA Technical Reports Server (NTRS)
Bayard, David S.; Jelliffe, Roger W.
2004-01-01
This paper considers the updating of Bayesian posterior densities for pharmacokinetic models associated with patients having changing parameter values. For estimation purposes it is proposed to use the Interacting Multiple Model (IMM) estimation algorithm, which is currently a popular algorithm in the aerospace community for tracking maneuvering targets. The IMM algorithm is described, and compared to the multiple model (MM) and Maximum A-Posteriori (MAP) Bayesian estimation methods, which are presently used for posterior updating when pharmacokinetic parameters do not change. Both the MM and MAP Bayesian estimation methods are used in their sequential forms, to facilitate tracking of changing parameters. Results indicate that the IMM algorithm is well suited for tracking time-varying pharmacokinetic parameters in acutely ill and unstable patients, incurring only about half of the integrated error compared to the sequential MM and MAP methods on the same example.
A Bayesian Approach to Multicenter Trials and Metaanalysis.
ERIC Educational Resources Information Center
Berry, Donald A.
The use of a Bayesian approach in evaluating data from clinical trials with many treatment centers and from many studies is discussed. The main distinction between a metaanalysis and an analysis of a multicenter trial is that different studies may have very different designs, while the centers in a multicenter trial usually follow the same…
A Bayesian approach to extracting meaning from system behavior
Dress, W.B.
1998-08-01
The modeling relation and its reformulation to include the semiotic hierarchy is essential for the understanding, control, and successful re-creation of natural systems. This presentation will argue for a careful application of Rosen`s modeling relationship to the problems of intelligence and autonomy in natural and artificial systems. To this end, the authors discuss the essential need for a correct theory of induction, learning, and probability; and suggest that modern Bayesian probability theory, developed by Cox, Jaynes, and others, can adequately meet such demands, especially on the operational level of extracting meaning from observations. The methods of Bayesian and maximum Entropy parameter estimation have been applied to measurements of system observables to directly infer the underlying differential equations generating system behavior. This approach by-passes the usual method of parameter estimation based on assuming a functional form for the observable and then estimating the parameters that would lead to the particular observed behavior. The computational savings is great since only location parameters enter into the maximum-entropy calculations; this innovation finesses the need for nonlinear parameters altogether. Such an approach more directly extracts the semantics inherent in a given system by going to the root of system meaning as expressed by abstract form or shape, rather than in syntactic particulars, such as signal amplitude and phase. Examples will be shown how the form of a system can be followed while ignoring unnecessary details. In this sense, the authors are observing the meaning of the words rather than being concerned with their particular expression or language. For the present discussion, empirical models are embodied by the differential equations underlying, producing, or describing the behavior of a process as measured or tracked by a particular variable set--the observables. The a priori models are probability structures that
Wan, Rongrong; Cai, Shanshan; Li, Hengpeng; Yang, Guishan; Li, Zhaofu; Nie, Xiaofei
2014-01-15
Lake eutrophication has become a very serious environmental problem in China. If water pollution is to be controlled and ultimately eliminated, it is essential to understand how human activities affect surface water quality. A recently developed technique using the Bayesian hierarchical linear regression model revealed the effects of land use and land cover (LULC) on stream water quality at a watershed scale. Six LULC categories combined with watershed characteristics, including size, slope, and permeability were the variables that were studied. The pollutants of concern were nutrient concentrations of total nitrogen (TN) and total phosphorus (TP), common pollutants found in eutrophication. The monthly monitoring data at 41 sites in the Xitiaoxi Watershed, China during 2009-2010 were used for model demonstration. The results showed that the relationships between LULC and stream water quality are so complicated that the effects are varied over large areas. The models suggested that urban and agricultural land are important sources of TN and TP concentrations, while rural residential land is one of the major sources of TN. Certain agricultural practices (excessive fertilizer application) result in greater concentrations of nutrients in paddy fields, artificial grasslands, and artificial woodlands. This study suggests that Bayesian hierarchical modeling is a powerful tool for examining the complicated relationships between land use and water quality on different scales, and for developing land use and water management policies.
Bressolle, F; Bologna, C; Edno, L; Bernard, J C; Gomeni, R; Sany, J; Combe, B
1996-01-01
This paper describes a methodology to calculate methotrexate (MTX) pharmacokinetic parameters after intramuscular administration using two samples and the population parameters. Total and free MTX were measured over a 36-h period in 56 rheumatoid arthritis patients; 14 patients were studied after a two-dose scheme at 15-day intervals. The Hill equation was used to relate the free MTX to the total MTX changes in plasma concentrations, and a two-compartment open model was used to fit the total MTX plasma concentrations. A non-linear mixed effect procedure was used to estimate the population parameters and to explore the interindividual variability in relation to the following covariables: age, weight, height, haemoglobin, erythrocyte sedimentation rate, platelet count, creatinine clearance, rheumatoid factor, C-reactive protein, swelling joint count, and Ritchie's articular index. Population parameters were evaluated for 40 patients using a three-step approach. The population average parameters and the interindividual variabilities expressed as coefficients of variation (CV%) were: CL, 6.94 l center dot h-1 (20.5%); V, 34.8 l (32.2%); k12, 0.0838 h-1 (47.7%); k21, 0.0769 h-1 (61.6%); ka, 4.31 h-1 (58%); Emax, 1.12 mu mol center dot l-1 (19.7%); gamma, 0.932 (12.3%); and EC50, 2.14 mu mol center dot l-1 (27.3%). Thirty additional data sets (16 new patients and 14 patients of the previous population but treated on a separate occasion) were used to evaluate the predictive performance of the population parameters. Twelve blood samples were collected from each individual in order to calculate individual parameters using standard fitting procedures. These values were compared to the ones estimated using a Bayesian approach with population parameters as a priori information together with two samples, selected from the individual observations. The results show that the bias was not statistically different from zero and the precision of these parameters was excellent.
Application of a predictive Bayesian model to environmental accounting.
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.
Du, Qingyun; Zhang, Mingxiao; Li, Yayan; Luan, Hui; Liang, Shi; Ren, Fu
2016-04-20
Incorporating the information of hypertension, this paper applies Bayesian multi-disease analysis to model the spatial patterns of Ischemic Heart Disease (IHD) risks. Patterns of harmful alcohol intake (HAI) and overweight/obesity are also modelled as they are common risk factors contributing to both IHD and hypertension. The hospitalization data of IHD and hypertension in 2012 were analyzed with three Bayesian multi-disease models at the sub-district level of Shenzhen. Results revealed that the IHD high-risk cluster shifted slightly north-eastward compared with the IHD Standardized Hospitalization Ratio (SHR). Spatial variations of overweight/obesity and HAI were found to contribute most to the IHD patterns. Identified patterns of IHD risk would benefit IHD integrated prevention. Spatial patterns of overweight/obesity and HAI could supplement the current disease surveillance system by providing information about small-area level risk factors, and thus benefit integrated prevention of related chronic diseases. Middle southern Shenzhen, where high risk of IHD, overweight/obesity, and HAI are present, should be prioritized for interventions, including alcohol control, innovative healthy diet toolkit distribution, insurance system revision, and community-based chronic disease intervention. Related health resource planning is also suggested to focus on these areas first.
NASA Astrophysics Data System (ADS)
Xiao, Heng; Wu, Jinlong; Wang, Jianxun; Sun, Rui; Roy, Christopher J.
2015-11-01
For many practical flows, the turbulence models are the most important source of uncertainty in Reynolds-Averaged Navier-Stokes (RANS) predictions. In this work, we develop an open-box, physics-informed Bayesian framework for quantifying the model-form uncertainties in RANS simulations. Uncertainties are introduced directly to the Reynolds stresses and are represented with compact parameterization accounting for empirical prior knowledge and physical constraints (e.g., realizability, smoothness, and symmetry). An iterative ensemble Kalman method is used to incorporate the prior information with available observation data in a Bayesian framework to posterior distributions of the Reynolds stresses and other quantities of interest. Two representative cases, the flow over periodic hills and the flow in a square duct, are used to evaluate the performance of the proposed framework. Simulation results suggest that the obtained posterior mean has significantly better agreement with the benchmark data compared to the baseline simulation, even with very sparse observations. At most locations, the posterior distribution adequately represents the model-form uncertainties.
NASA Astrophysics Data System (ADS)
Frey, M. P.; Stamm, C.; Schneider, M. K.; Reichert, P.
2011-12-01
A distributed hydrological model was used to simulate the distribution of fast runoff formation as a proxy for critical source areas for herbicide pollution in a small agricultural catchment in Switzerland. We tested to what degree predictions based on prior knowledge without local measurements could be improved upon relying on observed discharge. This learning process consisted of five steps: For the prior prediction (step 1), knowledge of the model parameters was coarse and predictions were fairly uncertain. In the second step, discharge data were used to update the prior parameter distribution. Effects of uncertainty in input data and model structure were accounted for by an autoregressive error model. This step decreased the width of the marginal distributions of parameters describing the lower boundary (percolation rates) but hardly affected soil hydraulic parameters. Residual analysis (step 3) revealed model structure deficits. We modified the model, and in the subsequent Bayesian updating (step 4) the widths of the posterior marginal distributions were reduced for most parameters compared to those of the prior. This incremental procedure led to a strong reduction in the uncertainty of the spatial prediction. Thus, despite only using spatially integrated data (discharge), the spatially distributed effect of the improved model structure can be expected to improve the spatially distributed predictions also. The fifth step consisted of a test with independent spatial data on herbicide losses and revealed ambiguous results. The comparison depended critically on the ratio of event to preevent water that was discharged. This ratio cannot be estimated from hydrological data only. The results demonstrate that the value of local data is strongly dependent on a correct model structure. An iterative procedure of Bayesian updating, model testing, and model modification is suggested.
A bayesian approach to classification criteria for spectacled eiders
Taylor, B.L.; Wade, P.R.; Stehn, R.A.; Cochrane, J.F.
1996-01-01
To facilitate decisions to classify species according to risk of extinction, we used Bayesian methods to analyze trend data for the Spectacled Eider, an arctic sea duck. Trend data from three independent surveys of the Yukon-Kuskokwim Delta were analyzed individually and in combination to yield posterior distributions for population growth rates. We used classification criteria developed by the recovery team for Spectacled Eiders that seek to equalize errors of under- or overprotecting the species. We conducted both a Bayesian decision analysis and a frequentist (classical statistical inference) decision analysis. Bayesian decision analyses are computationally easier, yield basically the same results, and yield results that are easier to explain to nonscientists. With the exception of the aerial survey analysis of the 10 most recent years, both Bayesian and frequentist methods indicated that an endangered classification is warranted. The discrepancy between surveys warrants further research. Although the trend data are abundance indices, we used a preliminary estimate of absolute abundance to demonstrate how to calculate extinction distributions using the joint probability distributions for population growth rate and variance in growth rate generated by the Bayesian analysis. Recent apparent increases in abundance highlight the need for models that apply to declining and then recovering species.
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…
A Bayesian approach to meta-analysis of plant pathology studies.
Mila, A L; Ngugi, H K
2011-01-01
Bayesian statistical methods are used for meta-analysis in many disciplines, including medicine, molecular biology, and engineering, but have not yet been applied for quantitative synthesis of plant pathology studies. In this paper, we illustrate the key concepts of Bayesian statistics and outline the differences between Bayesian and classical (frequentist) methods in the way parameters describing population attributes are considered. We then describe a Bayesian approach to meta-analysis and present a plant pathological example based on studies evaluating the efficacy of plant protection products that induce systemic acquired resistance for the management of fire blight of apple. In a simple random-effects model assuming a normal distribution of effect sizes and no prior information (i.e., a noninformative prior), the results of the Bayesian meta-analysis are similar to those obtained with classical methods. Implementing the same model with a Student's t distribution and a noninformative prior for the effect sizes, instead of a normal distribution, yields similar results for all but acibenzolar-S-methyl (Actigard) which was evaluated only in seven studies in this example. Whereas both the classical (P = 0.28) and the Bayesian analysis with a noninformative prior (95% credibility interval [CRI] for the log response ratio: -0.63 to 0.08) indicate a nonsignificant effect for Actigard, specifying a t distribution resulted in a significant, albeit variable, effect for this product (CRI: -0.73 to -0.10). These results confirm the sensitivity of the analytical outcome (i.e., the posterior distribution) to the choice of prior in Bayesian meta-analyses involving a limited number of studies. We review some pertinent literature on more advanced topics, including modeling of among-study heterogeneity, publication bias, analyses involving a limited number of studies, and methods for dealing with missing data, and show how these issues can be approached in a Bayesian framework
Bayesian inference approach to room-acoustic modal analysis
NASA Astrophysics Data System (ADS)
Henderson, Wesley; Goggans, Paul; Xiang, Ning; Botts, Jonathan
2013-08-01
Spectrum estimation is a problem common to many fields of physics, science, and engineering, and it has thus received a great deal of attention from the Bayesian data analysis community. In room acoustics, the modal or frequency response of a room is important for diagnosing and remedying acoustical defects. The physics of a sound field in a room dictates a model comprised of exponentially decaying sinusoids. Continuing in the tradition of the seminal work of Bretthorst and Jaynes, this work contributes an approach to analyzing the modal responses of rooms with a time-domain model. Room acoustic spectra are constructed of damped sinusoids, and the modelbased approach allows estimation of the number of sinusoids in the signal as well as their frequencies, amplitudes, damping constants, and phase delays. The frequency-amplitude spectrum may be most useful for characterizing a room, but in some settings the damping constants are of primary interest. This is the case for measuring the absorptive properties of materials, for example. A further challenge of the room acoustic spectrum problem is that modal density increases quadratically with frequency. At a point called the Schroeder frequency, adjacent modes overlap enough that the spectrum - particularly when estimated with the discrete Fourier transform - can be treated as a continuum. The time-domain, model-based approach can resolve overlapping modes and in some cases be used to estimate the Schroeder frequency. The proposed approach addresses the issue of filtering and preprocessing in order for the sampling to accurately identify all present room modes with their quadratically increasing density.
Fast Bayesian Inference in Dirichlet Process Mixture Models.
Wang, Lianming; Dunson, David B
2011-01-01
There has been increasing interest in applying Bayesian nonparametric methods in large samples and high dimensions. As Markov chain Monte Carlo (MCMC) algorithms are often infeasible, there is a pressing need for much faster algorithms. This article proposes a fast approach for inference in Dirichlet process mixture (DPM) models. Viewing the partitioning of subjects into clusters as a model selection problem, we propose a sequential greedy search algorithm for selecting the partition. Then, when conjugate priors are chosen, the resulting posterior conditionally on the selected partition is available in closed form. This approach allows testing of parametric models versus nonparametric alternatives based on Bayes factors. We evaluate the approach using simulation studies and compare it with four other fast nonparametric methods in the literature. We apply the proposed approach to three datasets including one from a large epidemiologic study. Matlab codes for the simulation and data analyses using the proposed approach are available online in the supplemental materials.
A Bayesian view on acoustic model-based techniques for robust speech recognition
NASA Astrophysics Data System (ADS)
Maas, Roland; Huemmer, Christian; Sehr, Armin; Kellermann, Walter
2015-12-01
This article provides a unifying Bayesian view on various approaches for acoustic model adaptation, missing feature, and uncertainty decoding that are well-known in the literature of robust automatic speech recognition. The representatives of these classes can often be deduced from a Bayesian network that extends the conventional hidden Markov models used in speech recognition. These extensions, in turn, can in many cases be motivated from an underlying observation model that relates clean and distorted feature vectors. By identifying and converting the observation models into a Bayesian network representation, we formulate the corresponding compensation rules. We thus summarize the various approaches as approximations or modifications of the same Bayesian decoding rule leading to a unified view on known derivations as well as to new formulations for certain approaches.
Model feedback in Bayesian propensity score estimation.
Zigler, Corwin M; Watts, Krista; Yeh, Robert W; Wang, Yun; Coull, Brent A; Dominici, Francesca
2013-03-01
Methods based on the propensity score comprise one set of valuable tools for comparative effectiveness research and for estimating causal effects more generally. These methods typically consist of two distinct stages: (1) a propensity score stage where a model is fit to predict the propensity to receive treatment (the propensity score), and (2) an outcome stage where responses are compared in treated and untreated units having similar values of the estimated propensity score. Traditional techniques conduct estimation in these two stages separately; estimates from the first stage are treated as fixed and known for use in the second stage. Bayesian methods have natural appeal in these settings because separate likelihoods for the two stages can be combined into a single joint likelihood, with estimation of the two stages carried out simultaneously. One key feature of joint estimation in this context is "feedback" between the outcome stage and the propensity score stage, meaning that quantities in a model for the outcome contribute information to posterior distributions of quantities in the model for the propensity score. We provide a rigorous assessment of Bayesian propensity score estimation to show that model feedback can produce poor estimates of causal effects absent strategies that augment propensity score adjustment with adjustment for individual covariates. We illustrate this phenomenon with a simulation study and with a comparative effectiveness investigation of carotid artery stenting versus carotid endarterectomy among 123,286 Medicare beneficiaries hospitlized for stroke in 2006 and 2007.
Tauber, Sean; Navarro, Daniel J; Perfors, Amy; Steyvers, Mark
2017-03-30
Recent debates in the psychological literature have raised questions about the assumptions that underpin Bayesian models of cognition and what inferences they license about human cognition. In this paper we revisit this topic, arguing that there are 2 qualitatively different ways in which a Bayesian model could be constructed. The most common approach uses a Bayesian model as a normative standard upon which to license a claim about optimality. In the alternative approach, a descriptive Bayesian model need not correspond to any claim that the underlying cognition is optimal or rational, and is used solely as a tool for instantiating a substantive psychological theory. We present 3 case studies in which these 2 perspectives lead to different computational models and license different conclusions about human cognition. We demonstrate how the descriptive Bayesian approach can be used to answer different sorts of questions than the optimal approach, especially when combined with principled tools for model evaluation and model selection. More generally we argue for the importance of making a clear distinction between the 2 perspectives. Considerable confusion results when descriptive models and optimal models are conflated, and if Bayesians are to avoid contributing to this confusion it is important to avoid making normative claims when none are intended. (PsycINFO Database Record
A BAYESIAN STATISTICAL APPROACH FOR THE EVALUATION OF CMAQ
Bayesian statistical methods are used to evaluate Community Multiscale Air Quality (CMAQ) model simulations of sulfate aerosol over a section of the eastern US for 4-week periods in summer and winter 2001. The observed data come from two U.S. Environmental Protection Agency data ...
Defining statistical perceptions with an empirical Bayesian approach
NASA Astrophysics Data System (ADS)
Tajima, Satohiro
2013-04-01
Extracting statistical structures (including textures or contrasts) from a natural stimulus is a central challenge in both biological and engineering contexts. This study interprets the process of statistical recognition in terms of hyperparameter estimations and free-energy minimization procedures with an empirical Bayesian approach. This mathematical interpretation resulted in a framework for relating physiological insights in animal sensory systems to the functional properties of recognizing stimulus statistics. We applied the present theoretical framework to two typical models of natural images that are encoded by a population of simulated retinal neurons, and demonstrated that the resulting cognitive performances could be quantified with the Fisher information measure. The current enterprise yielded predictions about the properties of human texture perception, suggesting that the perceptual resolution of image statistics depends on visual field angles, internal noise, and neuronal information processing pathways, such as the magnocellular, parvocellular, and koniocellular systems. Furthermore, the two conceptually similar natural-image models were found to yield qualitatively different predictions, striking a note of warning against confusing the two models when describing a natural image.
A Hierarchical Bayesian Model for Crowd Emotions
Urizar, Oscar J.; Baig, Mirza S.; Barakova, Emilia I.; Regazzoni, Carlo S.; Marcenaro, Lucio; Rauterberg, Matthias
2016-01-01
Estimation of emotions is an essential aspect in developing intelligent systems intended for crowded environments. However, emotion estimation in crowds remains a challenging problem due to the complexity in which human emotions are manifested and the capability of a system to perceive them in such conditions. This paper proposes a hierarchical Bayesian model to learn in unsupervised manner the behavior of individuals and of the crowd as a single entity, and explore the relation between behavior and emotions to infer emotional states. Information about the motion patterns of individuals are described using a self-organizing map, and a hierarchical Bayesian network builds probabilistic models to identify behaviors and infer the emotional state of individuals and the crowd. This model is trained and tested using data produced from simulated scenarios that resemble real-life environments. The conducted experiments tested the efficiency of our method to learn, detect and associate behaviors with emotional states yielding accuracy levels of 74% for individuals and 81% for the crowd, similar in performance with existing methods for pedestrian behavior detection but with novel concepts regarding the analysis of crowds. PMID:27458366
Poor-data and data-poor species stock assessment using a Bayesian hierarchical approach.
Jiao, Yan; Cortés, Enric; Andrews, Kate; Guo, Feng
2011-10-01
Appropriate inference for stocks or species with low-quality data (poor data) or limited data (data poor) is extremely important. Hierarchical Bayesian methods are especially applicable to small-area, small-sample-size estimation problems because they allow poor-data species to borrow strength from species with good-quality data. We used a hammerhead shark complex as an example to investigate the advantages of using hierarchical Bayesian models in assessing the status of poor-data and data-poor exploited species. The hammerhead shark complex (Sphyrna spp.) along the Atlantic and Gulf of Mexico coasts of the United States is composed of three species: the scalloped hammerhead (S. lewini), the great hammerhead (S. mokarran), and the smooth hammerhead (S. zygaena) sharks. The scalloped hammerhead comprises 70-80% of the catch and has catch and relative abundance data of good quality, whereas great and smooth hammerheads have relative abundance indices that are both limited and of low quality presumably because of low stock density and limited sampling. Four hierarchical Bayesian state-space surplus production models were developed to simulate variability in population growth rates, carrying capacity, and catchability of the species. The results from the hierarchical Bayesian models were considerably more robust than those of the nonhierarchical models. The hierarchical Bayesian approach represents an intermediate strategy between traditional models that assume different population parameters for each species and those that assume all species share identical parameters. Use of the hierarchical Bayesian approach is suggested for future hammerhead shark stock assessments and for modeling fish complexes with species-specific data, because the poor-data species can borrow strength from the species with good data, making the estimation more stable and robust.
A Two-Step Bayesian Approach for Propensity Score Analysis: Simulations and Case Study
ERIC Educational Resources Information Center
Kaplan, David; Chen, Jianshen
2012-01-01
A two-step Bayesian propensity score approach is introduced that incorporates prior information in the propensity score equation and outcome equation without the problems associated with simultaneous Bayesian propensity score approaches. The corresponding variance estimators are also provided. The two-step Bayesian propensity score is provided for…
Predicting coastal cliff erosion using a Bayesian probabilistic model
Hapke, C.; Plant, N.
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. ?? 2010.
Effect on Prediction when Modeling Covariates in Bayesian Nonparametric Models.
Cruz-Marcelo, Alejandro; Rosner, Gary L; Müller, Peter; Stewart, Clinton F
2013-04-01
In biomedical research, it is often of interest to characterize biologic processes giving rise to observations and to make predictions of future observations. Bayesian nonparametric methods provide a means for carrying out Bayesian inference making as few assumptions about restrictive parametric models as possible. There are several proposals in the literature for extending Bayesian nonparametric models to include dependence on covariates. Limited attention, however, has been directed to the following two aspects. In this article, we examine the effect on fitting and predictive performance of incorporating covariates in a class of Bayesian nonparametric models by one of two primary ways: either in the weights or in the locations of a discrete random probability measure. We show that different strategies for incorporating continuous covariates in Bayesian nonparametric models can result in big differences when used for prediction, even though they lead to otherwise similar posterior inferences. When one needs the predictive density, as in optimal design, and this density is a mixture, it is better to make the weights depend on the covariates. We demonstrate these points via a simulated data example and in an application in which one wants to determine the optimal dose of an anticancer drug used in pediatric oncology.
A Bayesian Analysis of Finite Mixtures in the LISREL Model.
ERIC Educational Resources Information Center
Zhu, Hong-Tu; Lee, Sik-Yum
2001-01-01
Proposes a Bayesian framework for estimating finite mixtures of the LISREL model. The model augments the observed data of the manifest variables with the latent variables and allocation variables and uses the Gibbs sampler to obtain the Bayesian solution. Discusses other associated statistical inferences. (SLD)
Bayesian model of Snellen visual acuity.
Nestares, Oscar; Navarro, Rafael; Antona, Beatriz
2003-07-01
A Bayesian model of Snellen visual acuity (VA) has been developed that, as far as we know, is the first one that includes the three main stages of VA: (1) optical degradations, (2) neural image representation and contrast thresholding, and (3) character recognition. The retinal image of a Snellen test chart is obtained from experimental wave-aberration data. Then a subband image decomposition with a set of visual channels tuned to different spatial frequencies and orientations is applied to the retinal image, as in standard computational models of early cortical image representation. A neural threshold is applied to the contrast responses to include the effect of the neural contrast sensitivity. The resulting image representation is the base of a Bayesian pattern-recognition method robust to the presence of optical aberrations. The model is applied to images containing sets of letter optotypes at different scales, and the number of correct answers is obtained at each scale; the final output is the decimal Snellen VA. The model has no free parameters to adjust. The main input data are the eye's optical aberrations, and standard values are used for all other parameters, including the Stiles-Crawford effect, visual channels, and neural contrast threshold, when no subject specific values are available. When aberrations are large, Snellen VA involving pattern recognition differs from grating acuity, which is based on a simpler detection (or orientation-discrimination) task and hence is basically unaffected by phase distortions introduced by the optical transfer function. A preliminary test of the model in one subject produced close agreement between actual measurements and predicted VA values. Two examples are also included: (1) application of the method to the prediction of the VAin refractive-surgery patients and (2) simulation of the VA attainable by correcting ocular aberrations.
A Bayesian network approach to linear and nonlinear acoustic echo cancellation
NASA Astrophysics Data System (ADS)
Huemmer, Christian; Maas, Roland; Hofmann, Christian; Kellermann, Walter
2015-12-01
This article provides a general Bayesian approach to the tasks of linear and nonlinear acoustic echo cancellation (AEC). We introduce a state-space model with latent state vector modeling all relevant information of the unknown system. Based on three cases for defining the state vector (to model a linear or nonlinear echo path) and its mathematical relation to the observation, it is shown that the normalized least mean square algorithm (with fixed and adaptive stepsize), the Hammerstein group model, and a numerical sampling scheme for nonlinear AEC can be derived by applying fundamental techniques for probabilistic graphical models. As a consequence, the major contribution of this Bayesian approach is a unifying graphical-model perspective which may serve as a powerful framework for future work in linear and nonlinear AEC.
NASA Astrophysics Data System (ADS)
Mendes, B. S.; Draper, D.
2008-12-01
The issue of model uncertainty and model choice is central in any groundwater modeling effort [Neuman and Wierenga, 2003]; among the several approaches to the problem we favour using Bayesian statistics because it is a method that integrates in a natural way uncertainties (arising from any source) and experimental data. In this work, we experiment with several Bayesian approaches to model choice, focusing primarily on demonstrating the usefulness of the Reversible Jump Markov Chain Monte Carlo (RJMCMC) simulation method [Green, 1995]; this is an extension of the now- common MCMC methods. Standard MCMC techniques approximate posterior distributions for quantities of interest, often by creating a random walk in parameter space; RJMCMC allows the random walk to take place between parameter spaces with different dimensionalities. This fact allows us to explore state spaces that are associated with different deterministic models for experimental data. Our work is exploratory in nature; we restrict our study to comparing two simple transport models applied to a data set gathered to estimate the breakthrough curve for a tracer compound in groundwater. One model has a mean surface based on a simple advection dispersion differential equation; the second model's mean surface is also governed by a differential equation but in two dimensions. We focus on artificial data sets (in which truth is known) to see if model identification is done correctly, but we also address the issues of over and under-paramerization, and we compare RJMCMC's performance with other traditional methods for model selection and propagation of model uncertainty, including Bayesian model averaging, BIC and DIC.References Neuman and Wierenga (2003). A Comprehensive Strategy of Hydrogeologic Modeling and Uncertainty Analysis for Nuclear Facilities and Sites. NUREG/CR-6805, Division of Systems Analysis and Regulatory Effectiveness Office of Nuclear Regulatory Research, U. S. Nuclear Regulatory Commission
2009-01-01
Background Assessing agreement in method comparison studies depends on two fundamentally important components; validity (the between method agreement) and reproducibility (the within method agreement). The Bland-Altman limits of agreement technique is one of the favoured approaches in medical literature for assessing between method validity. However, few researchers have adopted this approach for the assessment of both validity and reproducibility. This may be partly due to a lack of a flexible, easily implemented and readily available statistical machinery to analyse repeated measurement method comparison data. Methods Adopting the Bland-Altman framework, but using Bayesian methods, we present this statistical machinery. Two multivariate hierarchical Bayesian models are advocated, one which assumes that the underlying values for subjects remain static (exchangeable replicates) and one which assumes that the underlying values can change between repeated measurements (non-exchangeable replicates). Results We illustrate the salient advantages of these models using two separate datasets that have been previously analysed and presented; (i) assuming static underlying values analysed using both multivariate hierarchical Bayesian models, and (ii) assuming each subject's underlying value is continually changing quantity and analysed using the non-exchangeable replicate multivariate hierarchical Bayesian model. Conclusion These easily implemented models allow for full parameter uncertainty, simultaneous method comparison, handle unbalanced or missing data, and provide estimates and credible regions for all the parameters of interest. Computer code for the analyses in also presented, provided in the freely available and currently cost free software package WinBUGS. PMID:19161599
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
Yu, Rongjie; Abdel-Aty, Mohamed
2013-07-01
The Bayesian inference method has been frequently adopted to develop safety performance functions. One advantage of the Bayesian inference is that prior information for the independent variables can be included in the inference procedures. However, there are few studies that discussed how to formulate informative priors for the independent variables and evaluated the effects of incorporating informative priors in developing safety performance functions. This paper addresses this deficiency by introducing four approaches of developing informative priors for the independent variables based on historical data and expert experience. Merits of these informative priors have been tested along with two types of Bayesian hierarchical models (Poisson-gamma and Poisson-lognormal models). Deviance information criterion (DIC), R-square values, and coefficients of variance for the estimations were utilized as evaluation measures to select the best model(s). Comparison across the models indicated that the Poisson-gamma model is superior with a better model fit and it is much more robust with the informative priors. Moreover, the two-stage Bayesian updating informative priors provided the best goodness-of-fit and coefficient estimation accuracies. Furthermore, informative priors for the inverse dispersion parameter have also been introduced and tested. Different types of informative priors' effects on the model estimations and goodness-of-fit have been compared and concluded. Finally, based on the results, recommendations for future research topics and study applications have been made.
Walsh, Stephen J.; Whitney, Paul D.
2012-12-14
Bayesian networks have attained widespread use in data analysis and decision making. Well studied topics include: efficient inference, evidence propagation, parameter learning from data for complete and incomplete data scenarios, expert elicitation for calibrating Bayesian network probabilities, and structure learning. It is not uncommon for the researcher to assume the structure of the Bayesian network or to glean the structure from expert elicitation or domain knowledge. In this scenario, the model may be calibrated through learning the parameters from relevant data. There is a lack of work on model diagnostics for fitted Bayesian networks; this is the contribution of this paper. We key on the definition of (conditional) independence to develop a graphical diagnostic method which indicates if the conditional independence assumptions imposed when one assumes the structure of the Bayesian network are supported by the data. We develop the approach theoretically and describe a Monte Carlo method to generate uncertainty measures for the consistency of the data with conditional independence assumptions under the model structure. We describe how this theoretical information and the data are presented in a graphical diagnostic tool. We demonstrate the approach through data simulated from Bayesian networks under different conditional independence assumptions. We also apply the diagnostic to a real world data set. The results indicate that our approach is a reasonable way of visualizing and inspecting the conditional independence assumption of a Bayesian network given data.
Genealogical Working Distributions for Bayesian Model Testing with Phylogenetic Uncertainty.
Baele, Guy; Lemey, Philippe; Suchard, Marc A
2016-03-01
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.
Predicting brain activity using a Bayesian spatial model.
Derado, Gordana; Bowman, F Dubois; Zhang, Lijun
2013-08-01
Increasing the clinical applicability of functional neuroimaging technology is an emerging objective, e.g. for diagnostic and treatment purposes. We propose a novel Bayesian spatial hierarchical framework for predicting follow-up neural activity based on an individual's baseline functional neuroimaging data. Our approach attempts to overcome some shortcomings of the modeling methods used in other neuroimaging settings, by borrowing strength from the spatial correlations present in the data. Our proposed methodology is applicable to data from various imaging modalities including functional magnetic resonance imaging and positron emission tomography, and we provide an illustration here using positron emission tomography data from a study of Alzheimer's disease to predict disease progression.
Objective Bayesian Comparison of Constrained Analysis of Variance Models.
Consonni, Guido; Paroli, Roberta
2016-10-04
In the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints. For instance, when examining three group means [Formula: see text] through an analysis of variance (ANOVA), a model may specify that [Formula: see text], while another one may state that [Formula: see text], and finally a third model may instead suggest that all means are unrestricted. This is a challenging problem, because it involves a combination of nonnested models, as well as nested models having the same dimension. We adopt an objective Bayesian approach, requiring no prior specification from the user, and derive the posterior probability of each model under consideration. Our method is based on the intrinsic prior methodology, suitably modified to accommodate equality and inequality constraints. Focussing on normal ANOVA models, a comparative assessment is carried out through simulation studies. We also present an application to real data collected in a psychological experiment.
Markov chain Monte Carlo simulation for Bayesian Hidden Markov Models
NASA Astrophysics Data System (ADS)
Chan, Lay Guat; Ibrahim, Adriana Irawati Nur Binti
2016-10-01
A hidden Markov model (HMM) is a mixture model which has a Markov chain with finite states as its mixing distribution. HMMs have been applied to a variety of fields, such as speech and face recognitions. The main purpose of this study is to investigate the Bayesian approach to HMMs. Using this approach, we can simulate from the parameters' posterior distribution using some Markov chain Monte Carlo (MCMC) sampling methods. HMMs seem to be useful, but there are some limitations. Therefore, by using the Mixture of Dirichlet processes Hidden Markov Model (MDPHMM) based on Yau et. al (2011), we hope to overcome these limitations. We shall conduct a simulation study using MCMC methods to investigate the performance of this model.
Estimating anatomical trajectories with Bayesian mixed-effects modeling.
Ziegler, G; Penny, W D; Ridgway, G R; Ourselin, S; Friston, K J
2015-11-01
We introduce a mass-univariate framework for the analysis of whole-brain structural trajectories using longitudinal Voxel-Based Morphometry data and Bayesian inference. Our approach to developmental and aging longitudinal studies characterizes heterogeneous structural growth/decline between and within groups. In particular, we propose a probabilistic generative model that parameterizes individual and ensemble average changes in brain structure using linear mixed-effects models of age and subject-specific covariates. Model inversion uses Expectation Maximization (EM), while voxelwise (empirical) priors on the size of individual differences are estimated from the data. Bayesian inference on individual and group trajectories is realized using Posterior Probability Maps (PPM). In addition to parameter inference, the framework affords comparisons of models with varying combinations of model order for fixed and random effects using model evidence. We validate the model in simulations and real MRI data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) project. We further demonstrate how subject specific characteristics contribute to individual differences in longitudinal volume changes in healthy subjects, Mild Cognitive Impairment (MCI), and Alzheimer's Disease (AD).
Estimating anatomical trajectories with Bayesian mixed-effects modeling
Ziegler, G.; Penny, W.D.; Ridgway, G.R.; Ourselin, S.; Friston, K.J.
2015-01-01
We introduce a mass-univariate framework for the analysis of whole-brain structural trajectories using longitudinal Voxel-Based Morphometry data and Bayesian inference. Our approach to developmental and aging longitudinal studies characterizes heterogeneous structural growth/decline between and within groups. In particular, we propose a probabilistic generative model that parameterizes individual and ensemble average changes in brain structure using linear mixed-effects models of age and subject-specific covariates. Model inversion uses Expectation Maximization (EM), while voxelwise (empirical) priors on the size of individual differences are estimated from the data. Bayesian inference on individual and group trajectories is realized using Posterior Probability Maps (PPM). In addition to parameter inference, the framework affords comparisons of models with varying combinations of model order for fixed and random effects using model evidence. We validate the model in simulations and real MRI data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) project. We further demonstrate how subject specific characteristics contribute to individual differences in longitudinal volume changes in healthy subjects, Mild Cognitive Impairment (MCI), and Alzheimer's Disease (AD). PMID:26190405
A multivariate Bayesian model for embryonic growth.
Willemsen, Sten P; Eilers, Paul H C; Steegers-Theunissen, Régine P M; Lesaffre, Emmanuel
2015-04-15
Most longitudinal growth curve models evaluate the evolution of each of the anthropometric measurements separately. When applied to a 'reference population', this exercise leads to univariate reference curves against which new individuals can be evaluated. However, growth should be evaluated in totality, that is, by evaluating all body characteristics jointly. Recently, Cole et al. suggested the Superimposition by Translation and Rotation (SITAR) model, which expresses individual growth curves by three subject-specific parameters indicating their deviation from a flexible overall growth curve. This model allows the characterization of normal growth in a flexible though compact manner. In this paper, we generalize the SITAR model in a Bayesian way to multiple dimensions. The multivariate SITAR model allows us to create multivariate reference regions, which is advantageous for prediction. The usefulness of the model is illustrated on longitudinal measurements of embryonic growth obtained in the first semester of pregnancy, collected in the ongoing Rotterdam Predict study. Further, we demonstrate how the model can be used to find determinants of embryonic growth.
Implementing Relevance Feedback in the Bayesian Network Retrieval Model.
ERIC Educational Resources Information Center
de Campos, Luis M.; Fernandez-Luna, Juan M.; Huete, Juan F.
2003-01-01
Discussion of relevance feedback in information retrieval focuses on a proposal for the Bayesian Network Retrieval Model. Bases the proposal on the propagation of partial evidences in the Bayesian network, representing new information obtained from the user's relevance judgments to compute the posterior relevance probabilities of the documents…
NASA Astrophysics Data System (ADS)
Minsley, B. J.; Brodie, R. C.; Bedrosian, P.; Esfahani, A.
2013-12-01
Geophysical data are typically used to infer a single ';best' model consistent with observations and prior information. However, because of non-uniqueness, limited resolution, and data errors, many models satisfy both the data and reasonable prior assumptions. Instead of seeking to describe the properties of any single model, we developed a trans-dimensional Bayesian Markov chain Monte Carlo (McMC) algorithm for the analysis of airborne electromagnetic (AEM) surveys that assesses the characteristics of models that are consistent with observations and prior assumptions. This is a powerful tool for model assessment and uncertainty analysis, and provides a wealth of information that can be used to make inferences about plausible subsurface properties. For example, we can estimate the likelihood of geological interfaces as a function of depth, quantify the probability that resistivity is above or below a certain threshold within a given depth range, assess model resolution and depth of investigation, or query subsets of models that are consistent with auxiliary datasets. Model assessment and uncertainty analysis is compounded by the large volume of data that are typically acquired for AEM surveys. Here, we discuss the mechanics of a McMC algorithm developed for the analysis of time- or frequency-domain airborne electromagnetic data, along with examples where this algorithm has been used to add new insight into model uncertainty and geological interpretations. Specific aspects of the algorithm that will be discussed include: the trans-dimensional nature of the program, which allows the number of layers to be a free parameter; the capability to assess random and/or systematic data errors as unknown parameters; the use of parallel computing tools to run multiple chains for a single dataset in order to assess convergence, and to analyze many datasets simultaneously; the use of stochastic Newton sampling to optimize sampling efficiency; and the ability to integrate multiple
Bayesian analysis. II. Signal detection and model selection
NASA Astrophysics Data System (ADS)
Bretthorst, G. Larry
In the preceding. paper, Bayesian analysis was applied to the parameter estimation problem, given quadrature NMR data. Here Bayesian analysis is extended to the problem of selecting the model which is most probable in view of the data and all the prior information. In addition to the analytic calculation, two examples are given. The first example demonstrates how to use Bayesian probability theory to detect small signals in noise. The second example uses Bayesian probability theory to compute the probability of the number of decaying exponentials in simulated T1 data. The Bayesian answer to this question is essentially a microcosm of the scientific method and a quantitative statement of Ockham's razor: theorize about possible models, compare these to experiment, and select the simplest model that "best" fits the data.
A Bayesian network approach to the database search problem in criminal proceedings
2012-01-01
Background The ‘database search problem’, that is, the strengthening of a case - in terms of probative value - against an individual who is found as a result of a database search, has been approached during the last two decades with substantial mathematical analyses, accompanied by lively debate and centrally opposing conclusions. This represents a challenging obstacle in teaching but also hinders a balanced and coherent discussion of the topic within the wider scientific and legal community. This paper revisits and tracks the associated mathematical analyses in terms of Bayesian networks. Their derivation and discussion for capturing probabilistic arguments that explain the database search problem are outlined in detail. The resulting Bayesian networks offer a distinct view on the main debated issues, along with further clarity. Methods As a general framework for representing and analyzing formal arguments in probabilistic reasoning about uncertain target propositions (that is, whether or not a given individual is the source of a crime stain), this paper relies on graphical probability models, in particular, Bayesian networks. This graphical probability modeling approach is used to capture, within a single model, a series of key variables, such as the number of individuals in a database, the size of the population of potential crime stain sources, and the rarity of the corresponding analytical characteristics in a relevant population. Results This paper demonstrates the feasibility of deriving Bayesian network structures for analyzing, representing, and tracking the database search problem. The output of the proposed models can be shown to agree with existing but exclusively formulaic approaches. Conclusions The proposed Bayesian networks allow one to capture and analyze the currently most well-supported but reputedly counter-intuitive and difficult solution to the database search problem in a way that goes beyond the traditional, purely formulaic expressions
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.
Bayesian joint modeling of longitudinal and spatial survival AIDS data.
Martins, Rui; Silva, Giovani L; Andreozzi, Valeska
2016-08-30
Joint analysis of longitudinal and survival data has received increasing attention in the recent years, especially for analyzing cancer and AIDS data. As both repeated measurements (longitudinal) and time-to-event (survival) outcomes are observed in an individual, a joint modeling is more appropriate because it takes into account the dependence between the two types of responses, which are often analyzed separately. We propose a Bayesian hierarchical model for jointly modeling longitudinal and survival data considering functional time and spatial frailty effects, respectively. That is, the proposed model deals with non-linear longitudinal effects and spatial survival effects accounting for the unobserved heterogeneity among individuals living in the same region. This joint approach is applied to a cohort study of patients with HIV/AIDS in Brazil during the years 2002-2006. Our Bayesian joint model presents considerable improvements in the estimation of survival times of the Brazilian HIV/AIDS patients when compared with those obtained through a separate survival model and shows that the spatial risk of death is the same across the different Brazilian states. Copyright © 2016 John Wiley & Sons, Ltd.
Chiu, Weihsueh A.; Okino, Miles S.; Evans, Marina V.
2009-11-15
We have developed a comprehensive, Bayesian, PBPK model-based analysis of the population toxicokinetics of trichloroethylene (TCE) and its metabolites in mice, rats, and humans, considering a wider range of physiological, chemical, in vitro, and in vivo data than any previously published analysis of TCE. The toxicokinetics of the 'population average,' its population variability, and their uncertainties are characterized in an approach that strives to be maximally transparent and objective. Estimates of experimental variability and uncertainty were also included in this analysis. The experimental database was expanded to include virtually all available in vivo toxicokinetic data, which permitted, in rats and humans, the specification of separate datasets for model calibration and evaluation. The total combination of these approaches and PBPK analysis provides substantial support for the model predictions. In addition, we feel confident that the approach employed also yields an accurate characterization of the uncertainty in metabolic pathways for which available data were sparse or relatively indirect, such as GSH conjugation and respiratory tract metabolism. Key conclusions from the model predictions include the following: (1) as expected, TCE is substantially metabolized, primarily by oxidation at doses below saturation; (2) GSH conjugation and subsequent bioactivation in humans appear to be 10- to 100-fold greater than previously estimated; and (3) mice had the greatest rate of respiratory tract oxidative metabolism as compared to rats and humans. In a situation such as TCE in which there is large database of studies coupled with complex toxicokinetics, the Bayesian approach provides a systematic method of simultaneously estimating model parameters and characterizing their uncertainty and variability. However, care needs to be taken in its implementation to ensure biological consistency, transparency, and objectivity.
Fienen, Michael N.; D'Oria, Marco; Doherty, John E.; Hunt, Randall J.
2013-01-01
The application bgaPEST is a highly parameterized inversion software package implementing the Bayesian Geostatistical Approach in a framework compatible with the parameter estimation suite PEST. Highly parameterized inversion refers to cases in which parameters are distributed in space or time and are correlated with one another. The Bayesian aspect of bgaPEST is related to Bayesian probability theory in which prior information about parameters is formally revised on the basis of the calibration dataset used for the inversion. Conceptually, this approach formalizes the conditionality of estimated parameters on the speciﬁc data and model available. The geostatistical component of the method refers to the way in which prior information about the parameters is used. A geostatistical autocorrelation function is used to enforce structure on the parameters to avoid overﬁtting and unrealistic results. Bayesian Geostatistical Approach is designed to provide the smoothest solution that is consistent with the data. Optionally, users can specify a level of ﬁt or estimate a balance between ﬁt and model complexity informed by the data. Groundwater and surface-water applications are used as examples in this text, but the possible uses of bgaPEST extend to any distributed parameter applications.
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.
Quantum-Like Bayesian Networks for Modeling Decision Making.
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.
Bayesian Modeling of Biomolecular Assemblies with Cryo-EM Maps
Habeck, Michael
2017-01-01
A growing array of experimental techniques allows us to characterize the three-dimensional structure of large biological assemblies at increasingly higher resolution. In addition to X-ray crystallography and nuclear magnetic resonance in solution, new structure determination methods such cryo-electron microscopy (cryo-EM), crosslinking/mass spectrometry and solid-state NMR have emerged. Often it is not sufficient to use a single experimental method, but complementary data need to be collected by using multiple techniques. The integration of all datasets can only be achieved by computational means. This article describes Inferential structure determination, a Bayesian approach to integrative modeling of biomolecular complexes with hybrid structural data. I will introduce probabilistic models for cryo-EM maps and outline Markov chain Monte Carlo algorithms for sampling model structures from the posterior distribution. I will focus on rigid and flexible modeling with cryo-EM data and discuss some of the computational challenges of Bayesian inference in the context of biomolecular modeling. PMID:28382301
Quantum-Like Bayesian Networks for Modeling Decision Making
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
Efficient multilevel brain tumor segmentation with integrated bayesian model classification.
Corso, J J; Sharon, E; Dube, S; El-Saden, S; Sinha, U; Yuille, A
2008-05-01
We present a new method for automatic segmentation of heterogeneous image data that takes a step toward bridging the gap between bottom-up affinity-based segmentation methods and top-down generative model based approaches. The main contribution of the paper is a Bayesian formulation for incorporating soft model assignments into the calculation of affinities, which are conventionally model free. We integrate the resulting model-aware affinities into the multilevel segmentation by weighted aggregation algorithm, and apply the technique to the task of detecting and segmenting brain tumor and edema in multichannel magnetic resonance (MR) volumes. The computationally efficient method runs orders of magnitude faster than current state-of-the-art techniques giving comparable or improved results. Our quantitative results indicate the benefit of incorporating model-aware affinities into the segmentation process for the difficult case of glioblastoma multiforme brain tumor.
Bayesian Case-deletion Model Complexity and Information Criterion
Zhu, Hongtu; Ibrahim, Joseph G.; Chen, Qingxia
2015-01-01
We establish a connection between Bayesian case influence measures for assessing the influence of individual observations and Bayesian predictive methods for evaluating the predictive performance of a model and comparing different models fitted to the same dataset. Based on such a connection, we formally propose a new set of Bayesian case-deletion model complexity (BCMC) measures for quantifying the effective number of parameters in a given statistical model. Its properties in linear models are explored. Adding some functions of BCMC to a conditional deviance function leads to a Bayesian case-deletion information criterion (BCIC) for comparing models. We systematically investigate some properties of BCIC and its connection with other information criteria, such as the Deviance Information Criterion (DIC). We illustrate the proposed methodology on linear mixed models with simulations and a real data example. PMID:26180578
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.
Nonparametric Bayesian inference of the microcanonical stochastic block model
NASA Astrophysics Data System (ADS)
Peixoto, Tiago P.
2017-01-01
A principled approach to characterize the hidden modular structure of networks is to formulate generative models and then infer their parameters from data. When the desired structure is composed of modules or "communities," a suitable choice for this task is the stochastic block model (SBM), where nodes are divided into groups, and the placement of edges is conditioned on the group memberships. Here, we present a nonparametric Bayesian method to infer the modular structure of empirical networks, including the number of modules and their hierarchical organization. We focus on a microcanonical variant of the SBM, where the structure is imposed via hard constraints, i.e., the generated networks are not allowed to violate the patterns imposed by the model. We show how this simple model variation allows simultaneously for two important improvements over more traditional inference approaches: (1) deeper Bayesian hierarchies, with noninformative priors replaced by sequences of priors and hyperpriors, which not only remove limitations that seriously degrade the inference on large networks but also reveal structures at multiple scales; (2) a very efficient inference algorithm that scales well not only for networks with a large number of nodes and edges but also with an unlimited number of modules. We show also how this approach can be used to sample modular hierarchies from the posterior distribution, as well as to perform model selection. We discuss and analyze the differences between sampling from the posterior and simply finding the single parameter estimate that maximizes it. Furthermore, we expose a direct equivalence between our microcanonical approach and alternative derivations based on the canonical SBM.
Bayesian analysis of a disability model for lung cancer survival.
Armero, C; Cabras, S; Castellanos, M E; Perra, S; Quirós, A; Oruezábal, M J; Sánchez-Rubio, J
2016-02-01
Bayesian reasoning, survival analysis and multi-state models are used to assess survival times for Stage IV non-small-cell lung cancer patients and the evolution of the disease over time. Bayesian estimation is done using minimum informative priors for the Weibull regression survival model, leading to an automatic inferential procedure. Markov chain Monte Carlo methods have been used for approximating posterior distributions and the Bayesian information criterion has been considered for covariate selection. In particular, the posterior distribution of the transition probabilities, resulting from the multi-state model, constitutes a very interesting tool which could be useful to help oncologists and patients make efficient and effective decisions.
Comparison of Bayesian and empirical ranking approaches to visual perception.
Howe, Catherine Q; Beau Lotto, R; Purves, Dale
2006-08-21
Much current vision research is predicated on the idea--and a rapidly growing body of evidence--that visual percepts are generated according to the empirical significance of light stimuli rather than their physical characteristics. As a result, an increasing number of investigators have asked how visual perception can be rationalized in these terms. Here, we compare two different theoretical frameworks for predicting what observers actually see in response to visual stimuli: Bayesian decision theory and empirical ranking theory. Deciding which of these approaches has greater merit is likely to determine how the statistical operations that apparently underlie visual perception are eventually understood.
A Bayesian experimental design approach to structural health monitoring
Farrar, Charles; Flynn, Eric; Todd, Michael
2010-01-01
Optimal system design for SHM involves two primarily challenges. The first is the derivation of a proper performance function for a given system design. The second is the development of an efficient optimization algorithm for choosing a design that maximizes, or nearly maximizes the performance function. In this paper we will outline how an SHM practitioner can construct the proper performance function by casting the entire design problem into a framework of Bayesian experimental design. The approach demonstrates how the design problem necessarily ties together all steps of the SHM process.
Approximate Bayesian computation for forward modeling in cosmology
Akeret, Joël; Refregier, Alexandre; Amara, Adam; Seehars, Sebastian; Hasner, Caspar E-mail: alexandre.refregier@phys.ethz.ch E-mail: sebastian.seehars@phys.ethz.ch
2015-08-01
Bayesian inference is often used in cosmology and astrophysics to derive constraints on model parameters from observations. This approach relies on the ability to compute the likelihood of the data given a choice of model parameters. In many practical situations, the likelihood function may however be unavailable or intractable due to non-gaussian errors, non-linear measurements processes, or complex data formats such as catalogs and maps. In these cases, the simulation of mock data sets can often be made through forward modeling. We discuss how Approximate Bayesian Computation (ABC) can be used in these cases to derive an approximation to the posterior constraints using simulated data sets. This technique relies on the sampling of the parameter set, a distance metric to quantify the difference between the observation and the simulations and summary statistics to compress the information in the data. We first review the principles of ABC and discuss its implementation using a Population Monte-Carlo (PMC) algorithm and the Mahalanobis distance metric. We test the performance of the implementation using a Gaussian toy model. We then apply the ABC technique to the practical case of the calibration of image simulations for wide field cosmological surveys. We find that the ABC analysis is able to provide reliable parameter constraints for this problem and is therefore a promising technique for other applications in cosmology and astrophysics. Our implementation of the ABC PMC method is made available via a public code release.
Greiner, Matthias; Smid, Joost; Havelaar, Arie H; Müller-Graf, Christine
2013-05-15
Quantitative microbiological risk assessment (QMRA) models are used to reflect knowledge about complex real-world scenarios for the propagation of microbiological hazards along the feed and food chain. The aim is to provide insight into interdependencies among model parameters, typically with an interest to characterise the effect of risk mitigation measures. A particular requirement is to achieve clarity about the reliability of conclusions from the model in the presence of uncertainty. To this end, Monte Carlo (MC) simulation modelling has become a standard in so-called probabilistic risk assessment. In this paper, we elaborate on the application of Bayesian computational statistics in the context of QMRA. It is useful to explore the analogy between MC modelling and Bayesian inference (BI). This pertains in particular to the procedures for deriving prior distributions for model parameters. We illustrate using a simple example that the inability to cope with feedback among model parameters is a major limitation of MC modelling. However, BI models can be easily integrated into MC modelling to overcome this limitation. We refer a BI submodel integrated into a MC model to as a "Bayes domain". We also demonstrate that an entire QMRA model can be formulated as Bayesian graphical model (BGM) and discuss the advantages of this approach. Finally, we show example graphs of MC, BI and BGM models, highlighting the similarities among the three approaches.
Nonparametric Bayesian Modeling for Automated Database Schema Matching
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 Dose-Response Modeling in Sparse Data
NASA Astrophysics Data System (ADS)
Kim, Steven B.
This book discusses Bayesian dose-response modeling in small samples applied to two different settings. The first setting is early phase clinical trials, and the second setting is toxicology studies in cancer risk assessment. In early phase clinical trials, experimental units are humans who are actual patients. Prior to a clinical trial, opinions from multiple subject area experts are generally more informative than the opinion of a single expert, but we may face a dilemma when they have disagreeing prior opinions. In this regard, we consider compromising the disagreement and compare two different approaches for making a decision. In addition to combining multiple opinions, we also address balancing two levels of ethics in early phase clinical trials. The first level is individual-level ethics which reflects the perspective of trial participants. The second level is population-level ethics which reflects the perspective of future patients. We extensively compare two existing statistical methods which focus on each perspective and propose a new method which balances the two conflicting perspectives. In toxicology studies, experimental units are living animals. Here we focus on a potential non-monotonic dose-response relationship which is known as hormesis. Briefly, hormesis is a phenomenon which can be characterized by a beneficial effect at low doses and a harmful effect at high doses. In cancer risk assessments, the estimation of a parameter, which is known as a benchmark dose, can be highly sensitive to a class of assumptions, monotonicity or hormesis. In this regard, we propose a robust approach which considers both monotonicity and hormesis as a possibility. In addition, We discuss statistical hypothesis testing for hormesis and consider various experimental designs for detecting hormesis based on Bayesian decision theory. Past experiments have not been optimally designed for testing for hormesis, and some Bayesian optimal designs may not be optimal under a
Calibrating Bayesian Network Representations of Social-Behavioral Models
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 empirical comparison with data taken from the Minorities at Risk Organizational Behaviors database.
Model Selection in Historical Research Using Approximate Bayesian Computation
Rubio-Campillo, Xavier
2016-01-01
Formal Models and History Computational models are increasingly being used to study historical dynamics. This new trend, which could be named Model-Based History, makes use of recently published datasets and innovative quantitative methods to improve our understanding of past societies based on their written sources. The extensive use of formal models allows historians to re-evaluate hypotheses formulated decades ago and still subject to debate due to the lack of an adequate quantitative framework. The initiative has the potential to transform the discipline if it solves the challenges posed by the study of historical dynamics. These difficulties are based on the complexities of modelling social interaction, and the methodological issues raised by the evaluation of formal models against data with low sample size, high variance and strong fragmentation. Case Study This work examines an alternate approach to this evaluation based on a Bayesian-inspired model selection method. The validity of the classical Lanchester’s laws of combat is examined against a dataset comprising over a thousand battles spanning 300 years. Four variations of the basic equations are discussed, including the three most common formulations (linear, squared, and logarithmic) and a new variant introducing fatigue. Approximate Bayesian Computation is then used to infer both parameter values and model selection via Bayes Factors. Impact Results indicate decisive evidence favouring the new fatigue model. The interpretation of both parameter estimations and model selection provides new insights into the factors guiding the evolution of warfare. At a methodological level, the case study shows how model selection methods can be used to guide historical research through the comparison between existing hypotheses and empirical evidence. PMID:26730953
Toman, Blaza
2005-01-01
International experiments called Key Comparisons pose an interesting statistical problem, the estimation of a quantity called a Reference Value. There are many possible forms that this estimator can take. Recently, this topic has received much international attention. In this paper, it is argued that a fully Bayesian approach to this problem is compatible with the current practice of metrology, and can easily be used to create statistical models which satisfy the varied properties and assumptions of these experiments. PMID:27308182
Tests of Bayesian model selection techniques for gravitational wave astronomy
Cornish, Neil J.; Littenberg, Tyson B.
2007-10-15
The analysis of gravitational wave data involves many model selection problems. The most important example is the detection problem of selecting between the data being consistent with instrument noise alone, or instrument noise and a gravitational wave signal. The analysis of data from ground based gravitational wave detectors is mostly conducted using classical statistics, and methods such as the Neyman-Peterson criteria are used for model selection. Future space based detectors, such as the Laser Interferometer Space Antenna (LISA), are expected to produce rich data streams containing the signals from many millions of sources. Determining the number of sources that are resolvable, and the most appropriate description of each source poses a challenging model selection problem that may best be addressed in a Bayesian framework. An important class of LISA sources are the millions of low-mass binary systems within our own galaxy, tens of thousands of which will be detectable. Not only are the number of sources unknown, but so are the number of parameters required to model the waveforms. For example, a significant subset of the resolvable galactic binaries will exhibit orbital frequency evolution, while a smaller number will have measurable eccentricity. In the Bayesian approach to model selection one needs to compute the Bayes factor between competing models. Here we explore various methods for computing Bayes factors in the context of determining which galactic binaries have measurable frequency evolution. The methods explored include a reverse jump Markov chain Monte Carlo algorithm, Savage-Dickie density ratios, the Schwarz-Bayes information criterion, and the Laplace approximation to the model evidence. We find good agreement between all of the approaches.
Advances in Bayesian Model Based Clustering Using Particle Learning
Merl, D M
2009-11-19
Recent work by Carvalho, Johannes, Lopes and Polson and Carvalho, Lopes, Polson and Taddy introduced a sequential Monte Carlo (SMC) alternative to traditional iterative Monte Carlo strategies (e.g. MCMC and EM) for Bayesian inference for a large class of dynamic models. The basis of SMC techniques involves representing the underlying inference problem as one of state space estimation, thus giving way to inference via particle filtering. The key insight of Carvalho et al was to construct the sequence of filtering distributions so as to make use of the posterior predictive distribution of the observable, a distribution usually only accessible in certain Bayesian settings. Access to this distribution allows a reversal of the usual propagate and resample steps characteristic of many SMC methods, thereby alleviating to a large extent many problems associated with particle degeneration. Furthermore, Carvalho et al point out that for many conjugate models the posterior distribution of the static variables can be parametrized in terms of [recursively defined] sufficient statistics of the previously observed data. For models where such sufficient statistics exist, particle learning as it is being called, is especially well suited for the analysis of streaming data do to the relative invariance of its algorithmic complexity with the number of data observations. Through a particle learning approach, a statistical model can be fit to data as the data is arriving, allowing at any instant during the observation process direct quantification of uncertainty surrounding underlying model parameters. Here we describe the use of a particle learning approach for fitting a standard Bayesian semiparametric mixture model as described in Carvalho, Lopes, Polson and Taddy. In Section 2 we briefly review the previously presented particle learning algorithm for the case of a Dirichlet process mixture of multivariate normals. In Section 3 we describe several novel extensions to the original
Bayesian Approach for Reliability Assessment of Sunshield Deployment on JWST
NASA Technical Reports Server (NTRS)
Kaminskiy, Mark P.; Evans, John W.; Gallo, Luis D.
2013-01-01
Deployable subsystems are essential to mission success of most spacecraft. These subsystems enable critical functions including power, communications and thermal control. The loss of any of these functions will generally result in loss of the mission. These subsystems and their components often consist of unique designs and applications, for which various standardized data sources are not applicable for estimating reliability and for assessing risks. In this study, a Bayesian approach for reliability estimation of spacecraft deployment was developed for this purpose. This approach was then applied to the James Webb Space Telescope (JWST) Sunshield subsystem, a unique design intended for thermal control of the observatory's telescope and science instruments. In order to collect the prior information on deployable systems, detailed studies of "heritage information", were conducted extending over 45 years of spacecraft launches. The NASA Goddard Space Flight Center (GSFC) Spacecraft Operational Anomaly and Reporting System (SOARS) data were then used to estimate the parameters of the conjugative beta prior distribution for anomaly and failure occurrence, as the most consistent set of available data and that could be matched to launch histories. This allows for an emperical Bayesian prediction for the risk of an anomaly occurrence of the complex Sunshield deployment, with credibility limits, using prior deployment data and test information.
A fully Bayesian multivariate approach to before-after safety evaluation.
Park, Eun Sug; Park, Jaebeom; Lomax, Timothy J
2010-07-01
This paper presents a fully Bayesian multivariate approach to before-after safety evaluation. Although empirical Bayes (EB) methods have been widely accepted as statistically defensible safety evaluation tools in observational before-after studies for more than a decade, EB has some limitations such that it requires a development and calibration of reliable safety performance functions (SPFs) and the uncertainty in the EB safety effectiveness estimates may be underestimated when a fairly large reference group is not available. This is because uncertainty (standard errors) of the estimated regression coefficients and dispersion parameter in SPFs is not reflected in the final safety effectiveness estimate of EB. Fully Bayesian (FB) methodologies in safety evaluation are emerging as the state-of-the-art methods that have a potential to overcome the limitations of EB in that uncertainty in regression parameters in the FB approach is propagated throughout the model and carries through to the final safety effectiveness estimate. Nonetheless, there have not yet been many applications of fully Bayesian methods in before-after studies. Part of reasons is the lack of documentation for a step-by-step FB implementation procedure for practitioners as well as an increased complexity in computation. As opposed to the EB methods of which steps are well-documented in the literature for practitioners, the steps for implementing before-after FB evaluations have not yet been clearly established, especially in more general settings such as a before-after study with a comparison group/comparison groups. The objectives of this paper are two-fold: (1) to develop a fully Bayesian multivariate approach jointly modeling crash counts of different types or severity levels for a before-after evaluation with a comparison group/comparison groups and (2) to establish a step-by-step procedure for implementing the FB methods for a before-after evaluation with a comparison group/comparison groups
Binary Classifier Calibration Using a Bayesian Non-Parametric Approach.
Naeini, Mahdi Pakdaman; Cooper, Gregory F; Hauskrecht, Milos
Learning probabilistic predictive models that are well calibrated is critical for many prediction and decision-making tasks in Data mining. This paper presents two new non-parametric methods for calibrating outputs of binary classification models: a method based on the Bayes optimal selection and a method based on the Bayesian model averaging. The advantage of these methods is that they are independent of the algorithm used to learn a predictive model, and they can be applied in a post-processing step, after the model is learned. This makes them applicable to a wide variety of machine learning models and methods. These calibration methods, as well as other methods, are tested on a variety of datasets in terms of both discrimination and calibration performance. The results show the methods either outperform or are comparable in performance to the state-of-the-art calibration methods.
A Semiparametric Bayesian Model for Detecting Synchrony Among Multiple Neurons
Shahbaba, Babak; Zhou, Bo; Lan, Shiwei; Ombao, Hernando; Moorman, David; Behseta, Sam
2015-01-01
We propose a scalable semiparametric Bayesian model to capture dependencies among multiple neurons by detecting their co-firing (possibly with some lag time) patterns over time. After discretizing time so there is at most one spike at each interval, the resulting sequence of 1’s (spike) and 0’s (silence) for each neuron is modeled using the logistic function of a continuous latent variable with a Gaussian process prior. For multiple neurons, the corresponding marginal distributions are coupled to their joint probability distribution using a parametric copula model. The advantages of our approach are as follows: the nonparametric component (i.e., the Gaussian process model) provides a flexible framework for modeling the underlying firing rates; the parametric component (i.e., the copula model) allows us to make inference regarding both contemporaneous and lagged relationships among neurons; using the copula model, we construct multivariate probabilistic models by separating the modeling of univariate marginal distributions from the modeling of dependence structure among variables; our method is easy to implement using a computationally efficient sampling algorithm that can be easily extended to high dimensional problems. Using simulated data, we show that our approach could correctly capture temporal dependencies in firing rates and identify synchronous neurons. We also apply our model to spike train data obtained from prefrontal cortical areas. PMID:24922500
Disentangling micro from mesostructure by diffusion MRI: A Bayesian approach.
Reisert, Marco; Kellner, Elias; Dhital, Bibek; Hennig, Jürgen; Kiselev, Valerij G
2017-02-15
Diffusion-sensitized magnetic resonance imaging probes the cellular structure of the human brain, but the primary microstructural information gets lost in averaging over higher-level, mesoscopic tissue organization such as different orientations of neuronal fibers. While such averaging is inevitable due to the limited imaging resolution, we propose a method for disentangling the microscopic cell properties from the effects of mesoscopic structure. We further avoid the classical fitting paradigm and use supervised machine learning in terms of a Bayesian estimator to estimate the microstructural properties. The method finds detectable parameters of a given microstructural model and calculates them within seconds, which makes it suitable for a broad range of neuroscientific applications.
A Bayesian-style approach to estimating LISA science capability
NASA Astrophysics Data System (ADS)
Baker, John; Marsat, Sylvain
2017-01-01
A full understanding of LISA's science capability will require accurate models of incident waveform signals and the instrumental response. While Fisher matrix analysis is useful for some estimates, a Bayesian characterization of simulated probability distributions is needed for understanding important cases at the limit of LISA's capability. We apply fast analysis algorithms enabling accurate treatment using EOB waveforms with relevant higher modes and the full-featured LISA response to study these aspects of LISA science capability. Supported by NASA grant 11-ATP-046.
A Generalizable Hierarchical Bayesian Model for Persistent SAR Change Detection
2012-04-01
6] K. Ranney and M. Soumekh, “Signal subspace change detection in averaged multilook sar imagery,” Geoscience and Remote Sensing, IEEE Transactions on...A Generalizable Hierarchical Bayesian Model for Persistent SAR Change Detection Gregory E. Newstadta, Edmund G. Zelniob, and Alfred O. Hero IIIa...Base, OH, 45433, USA ABSTRACT This paper proposes a hierarchical Bayesian model for multiple-pass, multiple antenna synthetic aperture radar ( SAR
Continuous event monitoring via a Bayesian predictive approach.
Di, Jianing; Wang, Daniel; Brashear, H Robert; Dragalin, Vladimir; Krams, Michael
2016-01-01
In clinical trials, continuous monitoring of event incidence rate plays a critical role in making timely decisions affecting trial outcome. For example, continuous monitoring of adverse events protects the safety of trial participants, while continuous monitoring of efficacy events helps identify early signals of efficacy or futility. Because the endpoint of interest is often the event incidence associated with a given length of treatment duration (e.g., incidence proportion of an adverse event with 2 years of dosing), assessing the event proportion before reaching the intended treatment duration becomes challenging, especially when the event onset profile evolves over time with accumulated exposure. In particular, in the earlier part of the study, ignoring censored subjects may result in significant bias in estimating the cumulative event incidence rate. Such a problem is addressed using a predictive approach in the Bayesian framework. In the proposed approach, experts' prior knowledge about both the frequency and timing of the event occurrence is combined with observed data. More specifically, during any interim look, each event-free subject will be counted with a probability that is derived using prior knowledge. The proposed approach is particularly useful in early stage studies for signal detection based on limited information. But it can also be used as a tool for safety monitoring (e.g., data monitoring committee) during later stage trials. Application of the approach is illustrated using a case study where the incidence rate of an adverse event is continuously monitored during an Alzheimer's disease clinical trial. The performance of the proposed approach is also assessed and compared with other Bayesian and frequentist methods via simulation.
Bayesian Structural Equation Modeling: A More Flexible Representation of Substantive Theory
ERIC Educational Resources Information Center
Muthen, Bengt; Asparouhov, Tihomir
2012-01-01
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…
Advanced REACH Tool: A Bayesian Model for Occupational Exposure Assessment
McNally, Kevin; Warren, Nicholas; Fransman, Wouter; Entink, Rinke Klein; Schinkel, Jody; van Tongeren, Martie; Cherrie, John W.; Kromhout, Hans; Schneider, Thomas; Tielemans, Erik
2014-01-01
This paper describes a Bayesian model for the assessment of inhalation exposures in an occupational setting; the methodology underpins a freely available web-based application for exposure assessment, the Advanced REACH Tool (ART). The ART is a higher tier exposure tool that combines disparate sources of information within a Bayesian statistical framework. The information is obtained from expert knowledge expressed in a calibrated mechanistic model of exposure assessment, data on inter- and intra-individual variability in exposures from the literature, and context-specific exposure measurements. The ART provides central estimates and credible intervals for different percentiles of the exposure distribution, for full-shift and long-term average exposures. The ART can produce exposure estimates in the absence of measurements, but the precision of the estimates improves as more data become available. The methodology presented in this paper is able to utilize partially analogous data, a novel approach designed to make efficient use of a sparsely populated measurement database although some additional research is still required before practical implementation. The methodology is demonstrated using two worked examples: an exposure to copper pyrithione in the spraying of antifouling paints and an exposure to ethyl acetate in shoe repair. PMID:24665110
A Bayesian approach to traffic light detection and mapping
NASA Astrophysics Data System (ADS)
Hosseinyalamdary, Siavash; Yilmaz, Alper
2017-03-01
Automatic traffic light detection and mapping is an open research problem. The traffic lights vary in color, shape, geolocation, activation pattern, and installation which complicate their automated detection. In addition, the image of the traffic lights may be noisy, overexposed, underexposed, or occluded. In order to address this problem, we propose a Bayesian inference framework to detect and map traffic lights. In addition to the spatio-temporal consistency constraint, traffic light characteristics such as color, shape and height is shown to further improve the accuracy of the proposed approach. The proposed approach has been evaluated on two benchmark datasets and has been shown to outperform earlier studies. The results show that the precision and recall rates for the KITTI benchmark are 95.78 % and 92.95 % respectively and the precision and recall rates for the LARA benchmark are 98.66 % and 94.65 % .
Carabin, Hélène; Escalona, Marisela; Marshall, Clare; Vivas-Martínez, Sarai; Botto, Carlos; Joseph, Lawrence; Basáñez, María-Gloria
2003-01-01
OBJECTIVE: To develop a Bayesian hierarchical model for human onchocerciasis with which to explore the factors that influence prevalence of microfilariae in the Amazonian focus of onchocerciasis and predict the probability of any community being at least mesoendemic (>20% prevalence of microfilariae), and thus in need of priority ivermectin treatment. METHODS: Models were developed with data from 732 individuals aged > or =15 years who lived in 29 Yanomami communities along four rivers of the south Venezuelan Orinoco basin. The models' abilities to predict prevalences of microfilariae in communities were compared. The deviance information criterion, Bayesian P-values, and residual values were used to select the best model with an approximate cross-validation procedure. FINDINGS: A three-level model that acknowledged clustering of infection within communities performed best, with host age and sex included at the individual level, a river-dependent altitude effect at the community level, and additional clustering of communities along rivers. This model correctly classified 25/29 (86%) villages with respect to their need for priority ivermectin treatment. CONCLUSION: Bayesian methods are a flexible and useful approach for public health research and control planning. Our model acknowledges the clustering of infection within communities, allows investigation of links between individual- or community-specific characteristics and infection, incorporates additional uncertainty due to missing covariate data, and informs policy decisions by predicting the probability that a new community is at least mesoendemic. PMID:12973640
Buyukada, Musa
2017-05-01
The main purpose of the present study was to incorporate the uncertainties in the thermal behavior of walnut hull (WH), lignite coal, and their various blends using Bayesian approach. First of all, thermal behavior of related materials were investigated under different temperatures, blend ratios, and heating rates. Results of ultimate and proximate analyses showed the main steps of oxidation mechanism of (co-)combustion process. Thermal degradation started with the (hemi-)cellulosic compounds and finished with lignin. Finally, a partial sensitivity analysis based on Bayesian approach (Markov Chain Monte Carlo simulations) were applied to data driven regression model (the best fit). The main purpose of uncertainty analysis was to point out the importance of operating conditions (explanatory variables). The other important aspect of the present work was the first performance evaluation study on various uncertainty estimation techniques in (co-)combustion literature.
Textual and visual content-based anti-phishing: a Bayesian approach.
Zhang, Haijun; Liu, Gang; Chow, Tommy W S; Liu, Wenyin
2011-10-01
A novel framework using a Bayesian approach for content-based phishing web page detection is presented. Our model takes into account textual and visual contents to measure the similarity between the protected web page and suspicious web pages. A text classifier, an image classifier, and an algorithm fusing the results from classifiers are introduced. An outstanding feature of this paper is the exploration of a Bayesian model to estimate the matching threshold. This is required in the classifier for determining the class of the web page and identifying whether the web page is phishing or not. In the text classifier, the naive Bayes rule is used to calculate the probability that a web page is phishing. In the image classifier, the earth mover's distance is employed to measure the visual similarity, and our Bayesian model is designed to determine the threshold. In the data fusion algorithm, the Bayes theory is used to synthesize the classification results from textual and visual content. The effectiveness of our proposed approach was examined in a large-scale dataset collected from real phishing cases. Experimental results demonstrated that the text classifier and the image classifier we designed deliver promising results, the fusion algorithm outperforms either of the individual classifiers, and our model can be adapted to different phishing cases.
Bayesian approach for three-dimensional aquifer characterization at the Hanford 300 Area
Murakami, Haruko; Chen, X.; Hahn, Melanie S.; Liu, Yi; Rockhold, Mark L.; Vermeul, Vincent R.; Zachara, John M.; Rubin, Yoram
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 its ability to integrate multi-scale, multi-type data within a Bayesian framework and to compute a nonparametric posterior distribution. After we combined the distribution of transmissivities with depth-discrete relative-conductivity profile from 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.
Illan, Ignacio A.; Górriz, Juan M.; Ramírez, Javier; Meyer-Base, Anke
2014-01-01
This work presents a spatial-component (SC) based approach to aid the diagnosis of Alzheimer's disease (AD) using magnetic resonance images. In this approach, the whole brain image is subdivided in regions or spatial components, and a Bayesian network is used to model the dependencies between affected regions of AD. The structure of relations between affected regions allows to detect neurodegeneration with an estimated performance of 88% on more than 400 subjects and predict neurodegeneration with 80% accuracy, supporting the conclusion that modeling the dependencies between components increases the recognition of different patterns of brain degeneration in AD. PMID:25505408
Parameterizing Bayesian network Representations of Social-Behavioral Models by Expert Elicitation
Walsh, Stephen J.; Dalton, Angela C.; Whitney, Paul D.; White, Amanda M.
2010-05-23
Bayesian networks provide a general framework with which to model many natural phenomena. The mathematical nature of Bayesian networks enables a plethora of model validation and calibration techniques: e.g parameter estimation, goodness of fit tests, and diagnostic checking of the model assumptions. However, they are not free of shortcomings. Parameter estimation from relevant extant data is a common approach to calibrating the model parameters. In practice it is not uncommon to find oneself lacking adequate data to reliably estimate all model parameters. In this paper we present the early development of a novel application of conjoint analysis as a method for eliciting and modeling expert opinions and using the results in a methodology for calibrating the parameters of a Bayesian network.
NASA Astrophysics Data System (ADS)
Placek, Ben; Knuth, Kevin H.; Angerhausen, Daniel
2014-11-01
EXONEST is an algorithm dedicated to detecting and characterizing the photometric signatures of exoplanets, which include reflection and thermal emission, Doppler boosting, and ellipsoidal variations. Using Bayesian inference, we can test between competing models that describe the data as well as estimate model parameters. We demonstrate this approach by testing circular versus eccentric planetary orbital models, as well as testing for the presence or absence of four photometric effects. In addition to using Bayesian model selection, a unique aspect of EXONEST is the potential capability to distinguish between reflective and thermal contributions to the light curve. A case study is presented using Kepler data recorded from the transiting planet KOI-13b. By considering only the nontransiting portions of the light curve, we demonstrate that it is possible to estimate the photometrically relevant model parameters of KOI-13b. Furthermore, Bayesian model testing confirms that the orbit of KOI-13b has a detectable eccentricity.
Placek, Ben; Knuth, Kevin H.; Angerhausen, Daniel E-mail: kknuth@albany.edu
2014-11-10
EXONEST is an algorithm dedicated to detecting and characterizing the photometric signatures of exoplanets, which include reflection and thermal emission, Doppler boosting, and ellipsoidal variations. Using Bayesian inference, we can test between competing models that describe the data as well as estimate model parameters. We demonstrate this approach by testing circular versus eccentric planetary orbital models, as well as testing for the presence or absence of four photometric effects. In addition to using Bayesian model selection, a unique aspect of EXONEST is the potential capability to distinguish between reflective and thermal contributions to the light curve. A case study is presented using Kepler data recorded from the transiting planet KOI-13b. By considering only the nontransiting portions of the light curve, we demonstrate that it is possible to estimate the photometrically relevant model parameters of KOI-13b. Furthermore, Bayesian model testing confirms that the orbit of KOI-13b has a detectable eccentricity.
Modeling Non-Gaussian Time Series with Nonparametric Bayesian Model.
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.
ERIC Educational Resources Information Center
Story, Roger E.
1996-01-01
Discussion of the use of Latent Semantic Indexing to determine relevancy in information retrieval focuses on statistical regression and Bayesian methods. Topics include keyword searching; a multiple regression model; how the regression model can aid search methods; and limitations of this approach, including complexity, linearity, and…
A Non-parametric Bayesian Approach for Predicting RNA Secondary Structures
NASA Astrophysics Data System (ADS)
Sato, Kengo; Hamada, Michiaki; Mituyama, Toutai; Asai, Kiyoshi; Sakakibara, Yasubumi
Since many functional RNAs form stable secondary structures which are related to their functions, RNA secondary structure prediction is a crucial problem in bioinformatics. We propose a novel model for generating RNA secondary structures based on a non-parametric Bayesian approach, called hierarchical Dirichlet processes for stochastic context-free grammars (HDP-SCFGs). Here non-parametric means that some meta-parameters, such as the number of non-terminal symbols and production rules, do not have to be fixed. Instead their distributions are inferred in order to be adapted (in the Bayesian sense) to the training sequences provided. The results of our RNA secondary structure predictions show that HDP-SCFGs are more accurate than the MFE-based and other generative models.
Kercel, Stephen W.
1998-10-11
For several reasons, Bayesian parameter estimation is superior to other methods for extracting features of a weak signal from noise. Since it exploits prior knowledge, the analysis begins from a more advantageous starting point than other methods. Also, since ''nuisance parameters'' can be dropped out of the Bayesian analysis, the description of the model need not be as complete as is necessary for such methods as matched filtering. In the limit for perfectly random noise and a perfect description of the model, the signal-to-noise ratio improves as the square root of the number of samples in the data. Even with the imperfections of real-world data, Bayesian approaches this ideal limit of performance more closely than other methods. A major unsolved problem in landmine detection is the fusion of data from multiple sensor types. Bayesian data fusion is only beginning to be explored as a solution to the problem. In single sensor processes Bayesian analysis can sense multiple parameters from the data stream of the one sensor. It does so by computing a joint probability density function of a set of parameter values from the sensor output. However, there is no inherent requirement that the information must come from a single sensor. If multiple sensors are applied to a single process, where several different parameters are implicit in each sensor output data stream, the joint probability density function of all the parameters of interest can be computed in exactly the same manner as the single sensor case. Thus, it is just as practical to base decisions on multiple sensor outputs as it is for single sensors. This should provide a practical way to combine the outputs of dissimilar sensors, such as ground penetrating radar and electromagnetic induction devices, producing a better detection decision than could be provided by either sensor alone.
Assessing Fit of Unidimensional Graded Response Models Using Bayesian Methods
ERIC Educational Resources Information Center
Zhu, Xiaowen; Stone, Clement A.
2011-01-01
The posterior predictive model checking method is a flexible Bayesian model-checking tool and has recently been used to assess fit of dichotomous IRT models. This paper extended previous research to polytomous IRT models. A simulation study was conducted to explore the performance of posterior predictive model checking in evaluating different…
Tang, An-Min; Tang, Nian-Sheng
2015-02-28
We propose a semiparametric multivariate skew-normal joint model for multivariate longitudinal and multivariate survival data. One main feature of the posited model is that we relax the commonly used normality assumption for random effects and within-subject error by using a centered Dirichlet process prior to specify the random effects distribution and using a multivariate skew-normal distribution to specify the within-subject error distribution and model trajectory functions of longitudinal responses semiparametrically. A Bayesian approach is proposed to simultaneously obtain Bayesian estimates of unknown parameters, random effects and nonparametric functions by combining the Gibbs sampler and the Metropolis-Hastings algorithm. Particularly, a Bayesian local influence approach is developed to assess the effect of minor perturbations to within-subject measurement error and random effects. Several simulation studies and an example are presented to illustrate the proposed methodologies.
Modeling the Climatology of Tornado Occurrence with Bayesian Inference
NASA Astrophysics Data System (ADS)
Cheng, Vincent Y. S.
-related variables are more uniform across seasons. The residual variability of the same modeling framework (a reflection of the fidelity of the statistical formulation considered) is subsequently used to delineate distinct geographical patterns of tornado activity. This piece of information provides the foundation for the Bayesian hierarchical prognostic model presented in the third chapter of my dissertation. The results of the latter approach reinforce my earlier finding that the spatial variability of the annual and warm seasonal tornado occurrence is well explained by convective available potential energy and storm relative helicity alone, while vertical wind shear is better at reproducing the cool season tornado activity. The Bayesian hierarchical modeling framework offers a promising methodological tool for understanding regional tornado environments and obtaining reliable predictions in North America.
Hwang, Kyu-Baek; Zhang, Byoung-Tak
2005-12-01
Bayesian model averaging (BMA) can resolve the overfitting problem by explicitly incorporating the model uncertainty into the analysis procedure. Hence, it can be used to improve the generalization performance of Bayesian network classifiers. Until now, BMA of Bayesian network classifiers has only been performed in some restricted forms, e.g., the model is averaged given a single node-order, because of its heavy computational burden. However, it can be hard to obtain a good node-order when the available training dataset is sparse. To alleviate this problem, we propose BMA of Bayesian network classifiers over several distinct node-orders obtained using the Markov chain Monte Carlo sampling technique. The proposed method was examined using two synthetic problems and four real-life datasets. First, we show that the proposed method is especially effective when the given dataset is very sparse. The classification accuracy of averaging over multiple node-orders was higher in most cases than that achieved using a single node-order in our experiments. We also present experimental results for test datasets with unobserved variables, where the quality of the averaged node-order is more important. Through these experiments, we show that the difference in classification performance between the cases of multiple node-orders and single node-order is related to the level of noise, confirming the relative benefit of averaging over multiple node-orders for incomplete data. We conclude that BMA of Bayesian network classifiers over multiple node-orders has an apparent advantage when the given dataset is sparse and noisy, despite the method's heavy computational cost.
Bayesian approaches for adaptive spatial sampling : an example application.
Johnson, R. L.; LePoire, D.; Huttenga, A.; Quinn, J.
2005-05-25
BAASS (Bayesian Approaches for Adaptive Spatial Sampling) is a set of computational routines developed to support the design and deployment of spatial sampling programs for delineating contamination footprints, such as those that might result from the accidental or intentional environmental release of radionuclides. BAASS presumes the existence of real-time measurement technologies that provide information quickly enough to affect the progress of data collection. This technical memorandum describes the application of BAASS to a simple example, compares the performance of a BAASS-based program with that of a traditional gridded program, and explores the significance of several of the underlying assumptions required by BAASS. These assumptions include the range of spatial autocorrelation present, the value of prior information, the confidence level required for decision making, and ''inside-out'' versus ''outside-in'' sampling strategies. In the context of the example, adaptive sampling combined with prior information significantly reduced the number of samples required to delineate the contamination footprint.
Lee, Sik-Yum; Song, Xin-Yuan
2004-05-01
Missing data are very common in behavioural and psychological research. In this paper, we develop a Bayesian approach in the context of a general nonlinear structural equation model with missing continuous and ordinal categorical data. In the development, the missing data are treated as latent quantities, and provision for the incompleteness of the data is made by a hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm. We show by means of a simulation study that the Bayesian estimates are accurate. A Bayesian model comparison procedure based on the Bayes factor and path sampling is proposed. The required observations from the posterior distribution for computing the Bayes factor are simulated by the hybrid algorithm in Bayesian estimation. Our simulation results indicate that the correct model is selected more frequently when the incomplete records are used in the analysis than when they are ignored. The methodology is further illustrated with a real data set from a study concerned with an AIDS preventative intervention for Filipina sex workers.
Evaluating impacts using a BACI design, ratios, and a Bayesian approach with a focus on restoration.
Conner, Mary M; Saunders, W Carl; Bouwes, Nicolaas; Jordan, Chris
2015-10-01
Before-after-control-impact (BACI) designs are an effective method to evaluate natural and human-induced perturbations on ecological variables when treatment sites cannot be randomly chosen. While effect sizes of interest can be tested with frequentist methods, using Bayesian Markov chain Monte Carlo (MCMC) sampling methods, probabilities of effect sizes, such as a ≥20 % increase in density after restoration, can be directly estimated. Although BACI and Bayesian methods are used widely for assessing natural and human-induced impacts for field experiments, the application of hierarchal Bayesian modeling with MCMC sampling to BACI designs is less common. Here, we combine these approaches and extend the typical presentation of results with an easy to interpret ratio, which provides an answer to the main study question-"How much impact did a management action or natural perturbation have?" As an example of this approach, we evaluate the impact of a restoration project, which implemented beaver dam analogs, on survival and density of juvenile steelhead. Results indicated the probabilities of a ≥30 % increase were high for survival and density after the dams were installed, 0.88 and 0.99, respectively, while probabilities for a higher increase of ≥50 % were variable, 0.17 and 0.82, respectively. This approach demonstrates a useful extension of Bayesian methods that can easily be generalized to other study designs from simple (e.g., single factor ANOVA, paired t test) to more complicated block designs (e.g., crossover, split-plot). This approach is valuable for estimating the probabilities of restoration impacts or other management actions.
Using consensus bayesian network to model the reactive oxygen species regulatory pathway.
Hu, Liangdong; Wang, Limin
2013-01-01
Bayesian network is one of the most successful graph models for representing the reactive oxygen species regulatory pathway. With the increasing number of microarray measurements, it is possible to construct the bayesian network from microarray data directly. Although large numbers of bayesian network learning algorithms have been developed, when applying them to learn bayesian networks from microarray data, the accuracies are low due to that the databases they used to learn bayesian networks contain too few microarray data. In this paper, we propose a consensus bayesian network which is constructed by combining bayesian networks from relevant literatures and bayesian networks learned from microarray data. It would have a higher accuracy than the bayesian networks learned from one database. In the experiment, we validated the bayesian network combination algorithm on several classic machine learning databases and used the consensus bayesian network to model the Escherichia coli's ROS pathway.
Bayesian Geostatistical Modeling of Malaria Indicator Survey Data in Angola
Gosoniu, Laura; Veta, Andre Mia; Vounatsou, Penelope
2010-01-01
The 2006–2007 Angola Malaria Indicator Survey (AMIS) is the first nationally representative household survey in the country assessing coverage of the key malaria control interventions and measuring malaria-related burden among children under 5 years of age. In this paper, the Angolan MIS data were analyzed to produce the first smooth map of parasitaemia prevalence based on contemporary nationwide empirical data in the country. Bayesian geostatistical models were fitted to assess the effect of interventions after adjusting for environmental, climatic and socio-economic factors. Non-linear relationships between parasitaemia risk and environmental predictors were modeled by categorizing the covariates and by employing two non-parametric approaches, the B-splines and the P-splines. The results of the model validation showed that the categorical model was able to better capture the relationship between parasitaemia prevalence and the environmental factors. Model fit and prediction were handled within a Bayesian framework using Markov chain Monte Carlo (MCMC) simulations. Combining estimates of parasitaemia prevalence with the number of children under we obtained estimates of the number of infected children in the country. The population-adjusted prevalence ranges from in Namibe province to in Malanje province. The odds of parasitaemia in children living in a household with at least ITNs per person was by 41% lower (CI: 14%, 60%) than in those with fewer ITNs. The estimates of the number of parasitaemic children produced in this paper are important for planning and implementing malaria control interventions and for monitoring the impact of prevention and control activities. PMID:20351775
D. L. Kelly
2007-06-01
Markov chain Monte Carlo (MCMC) techniques represent an extremely flexible and powerful approach to Bayesian modeling. This work illustrates the application of such techniques to time-dependent reliability of components with repair. The WinBUGS package is used to illustrate, via examples, how Bayesian techniques can be used for parametric statistical modeling of time-dependent component reliability. Additionally, the crucial, but often overlooked subject of model validation is discussed, and summary statistics for judging the model’s ability to replicate the observed data are developed, based on the posterior predictive distribution for the parameters of interest.
Bayesian nonparametric centered random effects models with variable selection.
Yang, Mingan
2013-03-01
In a linear mixed effects model, it is common practice to assume that the random effects follow a parametric distribution such as a normal distribution with mean zero. However, in the case of variable selection, substantial violation of the normality assumption can potentially impact the subset selection and result in poor interpretation and even incorrect results. In nonparametric random effects models, the random effects generally have a nonzero mean, which causes an identifiability problem for the fixed effects that are paired with the random effects. In this article, we focus on a Bayesian method for variable selection. We characterize the subject-specific random effects nonparametrically with a Dirichlet process and resolve the bias simultaneously. In particular, we propose flexible modeling of the conditional distribution of the random effects with changes across the predictor space. The approach is implemented using a stochastic search Gibbs sampler to identify subsets of fixed effects and random effects to be included in the model. Simulations are provided to evaluate and compare the performance of our approach to the existing ones. We then apply the new approach to a real data example, cross-country and interlaboratory rodent uterotrophic bioassay.
Guided wave-based identification of multiple cracks in beams using a Bayesian approach
NASA Astrophysics Data System (ADS)
He, Shuai; Ng, Ching-Tai
2017-02-01
A guided wave damage identification method using a model-based approach is proposed to identify multiple cracks in beam-like structures. The guided wave propagation is simulated using spectral finite element method and a crack element is proposed to take into account the mode conversion effect. The Bayesian model class selection algorithm is employed to determine the crack number and then the Bayesian statistical framework is used to identify the crack parameters and the associated uncertainties. In order to improve the efficiency and ensure the reliability of identification, the Transitional Markov Chain Monte Carlo (TMCMC) method is implemented in the Bayesian approach. A series of numerical case studies are carried out to assess the performance of the proposed method, in which the sensitivity of different guided wave modes and effect of different levels of measurement noise in identifying different numbers of cracks is studied in detail. The proposed method is also experimentally verified using guided wave data obtained from laser vibrometer. The results show that the proposed method is able to accurately identify the number, locations and sizes of the cracks, and also quantify the associated uncertainties. In addition the proposed method is robust under measurement noise and different situations of the cracks.
A Bayesian modelling framework for tornado occurrences in North America
NASA Astrophysics Data System (ADS)
Cheng, Vincent Y. S.; Arhonditsis, George B.; Sills, David M. L.; Gough, William A.; Auld, Heather
2015-03-01
Tornadoes represent one of nature’s most hazardous phenomena that have been responsible for significant destruction and devastating fatalities. Here we present a Bayesian modelling approach for elucidating the spatiotemporal patterns of tornado activity in North America. Our analysis shows a significant increase in the Canadian Prairies and the Northern Great Plains during the summer, indicating a clear transition of tornado activity from the United States to Canada. The linkage between monthly-averaged atmospheric variables and likelihood of tornado events is characterized by distinct seasonality; the convective available potential energy is the predominant factor in the summer; vertical wind shear appears to have a strong signature primarily in the winter and secondarily in the summer; and storm relative environmental helicity is most influential in the spring. The present probabilistic mapping can be used to draw inference on the likelihood of tornado occurrence in any location in North America within a selected time period of the year.
A Bayesian modelling framework for tornado occurrences in North America.
Cheng, Vincent Y S; Arhonditsis, George B; Sills, David M L; Gough, William A; Auld, Heather
2015-03-25
Tornadoes represent one of nature's most hazardous phenomena that have been responsible for significant destruction and devastating fatalities. Here we present a Bayesian modelling approach for elucidating the spatiotemporal patterns of tornado activity in North America. Our analysis shows a significant increase in the Canadian Prairies and the Northern Great Plains during the summer, indicating a clear transition of tornado activity from the United States to Canada. The linkage between monthly-averaged atmospheric variables and likelihood of tornado events is characterized by distinct seasonality; the convective available potential energy is the predominant factor in the summer; vertical wind shear appears to have a strong signature primarily in the winter and secondarily in the summer; and storm relative environmental helicity is most influential in the spring. The present probabilistic mapping can be used to draw inference on the likelihood of tornado occurrence in any location in North America within a selected time period of the year.
Reginal Frequency Analysis Based on Scaling Properties and Bayesian Models
NASA Astrophysics Data System (ADS)
Kwon, Hyun-Han; Lee, Jeong-Ju; Moon, Young-Il
2010-05-01
A regional frequency analysis based on Hierarchical Bayesian Network (HBN) and scaling theory was developmed. Many recording rain gauges over South Korea were used for the analysis. First, a scaling approach combined with extreme distribution was employed to derive regional formula for frequency analysis. Second, HBN model was used to represent additional information about the regional structure of the scaling parameters, especially the location parameter and shape parameter. The location and shape parameters of the extreme distribution were estimated by utilizing scaling properties in a regression framework, and the scaling parameters linking the parameters (location and shape) to various duration times were simultaneously estimated. It was found that the regional frequency analysis combined with HBN and scaling properties show promising results in terms of establishing regional IDF curves.
NASA Astrophysics Data System (ADS)
Durand, M. T.; Liu, D.
2010-12-01
Estimates of snow water equivalent (SWE) for hydrologic applications from passive microwave (PM) brightness temperature (Tb) measurements are often subject to errors in mountainous areas. Data assimilation (DA) schemes have typically utilized land surface models (LSMs) coupled with a radiative transfer model (RTM) within an ensemble framework, generating joint ensembles of state variables (SWE, grain size, etc.) and Tb predictions. The posterior states are estimated from the priors and the observations, weighted based on the ensemble-derived correlation between the states and Tb. We have developed a new Bayesian DA scheme utilizing a Monte Carlo Markov Chain (MCMC) to estimate snow states from Tb measurements. Our motivation was two-fold: First, we wanted a platform to better characterize the prior information needed to calculate estimate snow depth or SWE from Tb; e.g., what are the accuracy tradeoffs for different types of snow if an LSM is not used? Second, the often-used correlation-based DA schemes are arguably not ideal to handle the highly non-linear relationship between snow variables and Tb; this issue is bypassed by using a random walk algorithm in the MCMC. Here we present a synthetic data assimilation study. In the MCMC, we treat the number of snow layers as being unknown, as well as the thickness, grain size, density and temperature of each snow layer. We perform the estimation of the posterior state variables in two steps: First, we generate four separate Markov Chains, assuming 1, 2, 3, and 4 snowpack layers. Second, we perform a model selection using a maximum a-posteriori (MAP) estimate to select the optimal Markov Chain. Given the model selection, the posterior Markov Chain is sampled to estimate the full posterior distribution of the snow variables. We performed separate synthetic experiments at each of 191 snowpits sampled in the NASA CLPX-1 campaign in February, 2003. We assimilated synthetic observations at 19, 37, and 89 GHz and at both V
A Variational Bayesian Approach to Multiframe Image Restoration.
Sonogashira, Motoharu; Funatomi, Takuya; Iiyama, Masaaki; Minoh, Michihiko
2017-03-06
Image restoration is a fundamental problem in the field of image processing. The key objective of image restoration is to recover clean images from images degraded by noise and blur. Recently, a family of new statistical techniques called variational Bayes (VB) has been introduced to image restoration, which enables us to automatically tune parameters that control restoration. While information from one image is often insufficient for high-quality restoration, however, current state-of-theart methods of image restoration via VB approaches use only a single degraded image to recover a clean image. In this paper, we propose a novel method of multiframe image restoration via a VB approach, which can achieve higher image quality while tuning parameters automatically. Given multiple degraded images, this method jointly estimates a clean image and other parameters, including an image warping parameter introduced for the use of multiple images, through Bayesian inference that we enable by making full use of VB techniques. Through various experiments, we demonstrate the effectiveness of our multiframe method by comparing it with single-frame one, and also show the advantages of our VB approach over non-VB approaches.
Accurate characterization of weak neutron fields by using a Bayesian approach.
Medkour Ishak-Boushaki, G; Allab, M
2017-04-01
A Bayesian analysis of data derived from neutron spectrometric measurements provides the advantage of determining rigorously integral physical quantities characterizing the neutron field and their respective related uncertainties. The first and essential step in a Bayesian approach is the parameterization of the investigated neutron spectrum. The aim of this paper is to investigate the sensitivity of the Bayesian results, mainly the neutron dose H(*)(10) required for radiation protection purposes and its correlated uncertainty, to the selected neutron spectrum parameterization.
A Bayesian hierarchical model for categorical data with nonignorable nonresponse.
Green, Paul E; Park, Taesung
2003-12-01
Log-linear models have been shown to be useful for smoothing contingency tables when categorical outcomes are subject to nonignorable nonresponse. A log-linear model can be fit to an augmented data table that includes an indicator variable designating whether subjects are respondents or nonrespondents. Maximum likelihood estimates calculated from the augmented data table are known to suffer from instability due to boundary solutions. Park and Brown (1994, Journal of the American Statistical Association 89, 44-52) and Park (1998, Biometrics 54, 1579-1590) developed empirical Bayes models that tend to smooth estimates away from the boundary. In those approaches, estimates for nonrespondents were calculated using an EM algorithm by maximizing a posterior distribution. As an extension of their earlier work, we develop a Bayesian hierarchical model that incorporates a log-linear model in the prior specification. In addition, due to uncertainty in the variable selection process associated with just one log-linear model, we simultaneously consider a finite number of models using a stochastic search variable selection (SSVS) procedure due to George and McCulloch (1997, Statistica Sinica 7, 339-373). The integration of the SSVS procedure into a Markov chain Monte Carlo (MCMC) sampler is straightforward, and leads to estimates of cell frequencies for the nonrespondents that are averages resulting from several log-linear models. The methods are demonstrated with a data example involving serum creatinine levels of patients who survived renal transplants. A simulation study is conducted to investigate properties of the model.
A Flexible Bayesian Model for Testing for Transmission Ratio Distortion
Casellas, Joaquim; Manunza, Arianna; Mercader, Anna; Quintanilla, Raquel; Amills, Marcel
2014-01-01
Current statistical approaches to investigate the nature and magnitude of transmission ratio distortion (TRD) are scarce and restricted to the most common experimental designs such as F2 populations and backcrosses. In this article, we describe a new Bayesian approach to check TRD within a given biallelic genetic marker in a diploid species, providing a highly flexible framework that can accommodate any kind of population structure. This model relies on the genotype of each offspring and thus integrates all available information from either the parents’ genotypes or population-specific allele frequencies and yields TRD estimates that can be corroborated by the calculation of a Bayes factor (BF). This approach has been evaluated on simulated data sets with appealing statistical performance. As a proof of concept, we have also tested TRD in a porcine population with five half-sib families and 352 offspring. All boars and piglets were genotyped with the Porcine SNP60 BeadChip, whereas genotypes from the sows were not available. The SNP-by-SNP screening of the pig genome revealed 84 SNPs with decisive evidences of TRD (BF > 100) after accounting for multiple testing. Many of these regions contained genes related to biological processes (e.g., nucleosome assembly and co-organization, DNA conformation and packaging, and DNA complex assembly) that are critically associated with embryonic viability. The implementation of this method, which overcomes many of the limitations of previous approaches, should contribute to fostering research on TRD in both model and nonmodel organisms. PMID:25271302
The Appeal to Expert Opinion: Quantitative Support for a Bayesian Network Approach.
Harris, Adam J L; Hahn, Ulrike; Madsen, Jens K; Hsu, Anne S
2016-08-01
The appeal to expert opinion is an argument form that uses the verdict of an expert to support a position or hypothesis. A previous scheme-based treatment of the argument form is formalized within a Bayesian network that is able to capture the critical aspects of the argument form, including the central considerations of the expert's expertise and trustworthiness. We propose this as an appropriate normative framework for the argument form, enabling the development and testing of quantitative predictions as to how people evaluate this argument, suggesting that such an approach might be beneficial to argumentation research generally. We subsequently present two experiments as an example of the potential for future research in this vein, demonstrating that participants' quantitative ratings of the convincingness of a proposition that has been supported with an appeal to expert opinion were broadly consistent with the predictions of the Bayesian model.
A Bayesian Semiparametric Model for Radiation Dose-Response Estimation.
Furukawa, Kyoji; Misumi, Munechika; Cologne, John B; Cullings, Harry M
2016-06-01
In evaluating the risk of exposure to health hazards, characterizing the dose-response relationship and estimating acceptable exposure levels are the primary goals. In analyses of health risks associated with exposure to ionizing radiation, while there is a clear agreement that moderate to high radiation doses cause harmful effects in humans, little has been known about the possible biological effects at low doses, for example, below 0.1 Gy, which is the dose range relevant to most radiation exposures of concern today. A conventional approach to radiation dose-response estimation based on simple parametric forms, such as the linear nonthreshold model, can be misleading in evaluating the risk and, in particular, its uncertainty at low doses. As an alternative approach, we consider a Bayesian semiparametric model that has a connected piece-wise-linear dose-response function with prior distributions having an autoregressive structure among the random slope coefficients defined over closely spaced dose categories. With a simulation study and application to analysis of cancer incidence data among Japanese atomic bomb survivors, we show that this approach can produce smooth and flexible dose-response estimation while reasonably handling the risk uncertainty at low doses and elsewhere. With relatively few assumptions and modeling options to be made by the analyst, the method can be particularly useful in assessing risks associated with low-dose radiation exposures.
Kim, D; Burge, J; Lane, T; Pearlson, G D; Kiehl, K A; Calhoun, V D
2008-10-01
We utilized a discrete dynamic Bayesian network (dDBN) approach (Burge, J., Lane, T., Link, H., Qiu, S., Clark, V.P., 2007. Discrete dynamic Bayesian network analysis of fMRI data. Hum Brain Mapp.) to determine differences in brain regions between patients with schizophrenia and healthy controls on a measure of effective connectivity, termed the approximate conditional likelihood score (ACL) (Burge, J., Lane, T., 2005. Learning Class-Discriminative Dynamic Bayesian Networks. Proceedings of the International Conference on Machine Learning, Bonn, Germany, pp. 97-104.). The ACL score represents a class-discriminative measure of effective connectivity by measuring the relative likelihood of the correlation between brain regions in one group versus another. The algorithm is capable of finding non-linear relationships between brain regions because it uses discrete rather than continuous values and attempts to model temporal relationships with a first-order Markov and stationary assumption constraint (Papoulis, A., 1991. Probability, random variables, and stochastic processes. McGraw-Hill, New York.). Since Bayesian networks are overly sensitive to noisy data, we introduced an independent component analysis (ICA) filtering approach that attempted to reduce the noise found in fMRI data by unmixing the raw datasets into a set of independent spatial component maps. Components that represented noise were removed and the remaining components reconstructed into the dimensions of the original fMRI datasets. We applied the dDBN algorithm to a group of 35 patients with schizophrenia and 35 matched healthy controls using an ICA filtered and unfiltered approach. We determined that filtering the data significantly improved the magnitude of the ACL score. Patients showed the greatest ACL scores in several regions, most markedly the cerebellar vermis and hemispheres. Our findings suggest that schizophrenia patients exhibit weaker connectivity than healthy controls in multiple regions
A Bayesian Attractor Model for Perceptual Decision Making
Bitzer, Sebastian; Bruineberg, Jelle; Kiebel, Stefan J.
2015-01-01
Even for simple perceptual decisions, the mechanisms that the brain employs are still under debate. Although current consensus states that the brain accumulates evidence extracted from noisy sensory information, open questions remain about how this simple model relates to other perceptual phenomena such as flexibility in decisions, decision-dependent modulation of sensory gain, or confidence about a decision. We propose a novel approach of how perceptual decisions are made by combining two influential formalisms into a new model. Specifically, we embed an attractor model of decision making into a probabilistic framework that models decision making as Bayesian inference. We show that the new model can explain decision making behaviour by fitting it to experimental data. In addition, the new model combines for the first time three important features: First, the model can update decisions in response to switches in the underlying stimulus. Second, the probabilistic formulation accounts for top-down effects that may explain recent experimental findings of decision-related gain modulation of sensory neurons. Finally, the model computes an explicit measure of confidence which we relate to recent experimental evidence for confidence computations in perceptual decision tasks. PMID:26267143
Bayesian Networks for Modeling Dredging Decisions
2011-10-01
position unless so designated by other authorized documents. DESTROY THIS REPORT WHEN NO LONGER NEEDED. DO NOT RETURN IT TO THE ORIGINATOR. ERDC/EL TR...links within a network often do indicate causality and it is usually best to work from information about... work in this area. ERDC/EL TR-11-14 16 Table 1. Bayesian network applications reviewed in the literature. Author(s) Year Substantive issue
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…
A Hierarchical Bayesian Approach to Ecological Count Data: A Flexible Tool for Ecologists
Fordyce, James A.; Gompert, Zachariah; Forister, Matthew L.; Nice, Chris C.
2011-01-01
Many ecological studies use the analysis of count data to arrive at biologically meaningful inferences. Here, we introduce a hierarchical Bayesian approach to count data. This approach has the advantage over traditional approaches in that it directly estimates the parameters of interest at both the individual-level and population-level, appropriately models uncertainty, and allows for comparisons among models, including those that exceed the complexity of many traditional approaches, such as ANOVA or non-parametric analogs. As an example, we apply this method to oviposition preference data for butterflies in the genus Lycaeides. Using this method, we estimate the parameters that describe preference for each population, compare the preference hierarchies among populations, and explore various models that group populations that share the same preference hierarchy. PMID:22132077
Back to basics for Bayesian model building in genomic selection.
Kärkkäinen, Hanni P; Sillanpää, Mikko J
2012-07-01
Numerous Bayesian methods of phenotype prediction and genomic breeding value estimation based on multilocus association models have been proposed. Computationally the methods have been based either on Markov chain Monte Carlo or on faster maximum a posteriori estimation. The demand for more accurate and more efficient estimation has led to the rapid emergence of workable methods, unfortunately at the expense of well-defined principles for Bayesian model building. In this article we go back to the basics and build a Bayesian multilocus association model for quantitative and binary traits with carefully defined hierarchical parameterization of Student's t and Laplace priors. In this treatment we consider alternative model structures, using indicator variables and polygenic terms. We make the most of the conjugate analysis, enabled by the hierarchical formulation of the prior densities, by deriving the fully conditional posterior densities of the parameters and using the acquired known distributions in building fast generalized expectation-maximization estimation algorithms.
Bayesian Case Influence Measures for Statistical Models with Missing Data
Zhu, Hongtu; Ibrahim, Joseph G.; Cho, Hyunsoon; Tang, Niansheng
2011-01-01
We examine three Bayesian case influence measures including the φ-divergence, Cook's posterior mode distance and Cook's posterior mean distance for identifying a set of influential observations for a variety of statistical models with missing data including models for longitudinal data and latent variable models in the absence/presence of missing data. Since it can be computationally prohibitive to compute these Bayesian case influence measures in models with missing data, we derive simple first-order approximations to the three Bayesian case influence measures by using the Laplace approximation formula and examine the applications of these approximations to the identification of influential sets. All of the computations for the first-order approximations can be easily done using Markov chain Monte Carlo samples from the posterior distribution based on the full data. Simulated data and an AIDS dataset are analyzed to illustrate the methodology. PMID:23399928
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…
A General Bayesian Model for Testlets: Theory and Applications.
ERIC Educational Resources Information Center
Wang, Xiaohui; Bradlow, Eric T.; Wainer, Howard
2002-01-01
Proposes a modified version of commonly employed item response models in a fully Bayesian framework and obtains inferences under the model using Markov chain Monte Carlo techniques. Demonstrates use of the model in a series of simulations and with operational data from the North Carolina Test of Computer Skills and the Test of Spoken English…
Bayesian Network Models for Local Dependence among Observable Outcome Variables
ERIC Educational Resources Information Center
Almond, Russell G.; Mulder, Joris; Hemat, Lisa A.; Yan, Duanli
2009-01-01
Bayesian network models offer a large degree of flexibility for modeling dependence among observables (item outcome variables) from the same task, which may be dependent. This article explores four design patterns for modeling locally dependent observations: (a) no context--ignores dependence among observables; (b) compensatory context--introduces…
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…
Bayesian network models for error detection in radiotherapy plans.
Kalet, Alan M; Gennari, John H; Ford, Eric C; Phillips, Mark H
2015-04-07
The purpose of this study is to design and develop a probabilistic network for detecting errors in radiotherapy plans for use at the time of initial plan verification. Our group has initiated a multi-pronged approach to reduce these errors. We report on our development of Bayesian models of radiotherapy plans. Bayesian networks consist of joint probability distributions that define the probability of one event, given some set of other known information. Using the networks, we find the probability of obtaining certain radiotherapy parameters, given a set of initial clinical information. A low probability in a propagated network then corresponds to potential errors to be flagged for investigation. To build our networks we first interviewed medical physicists and other domain experts to identify the relevant radiotherapy concepts and their associated interdependencies and to construct a network topology. Next, to populate the network's conditional probability tables, we used the Hugin Expert software to learn parameter distributions from a subset of de-identified data derived from a radiation oncology based clinical information database system. These data represent 4990 unique prescription cases over a 5 year period. Under test case scenarios with approximately 1.5% introduced error rates, network performance produced areas under the ROC curve of 0.88, 0.98, and 0.89 for the lung, brain and female breast cancer error detection networks, respectively. Comparison of the brain network to human experts performance (AUC of 0.90 ± 0.01) shows the Bayes network model performs better than domain experts under the same test conditions. Our results demonstrate the feasibility and effectiveness of comprehensive probabilistic models as part of decision support systems for improved detection of errors in initial radiotherapy plan verification procedures.
Bayesian network models for error detection in radiotherapy plans
NASA Astrophysics Data System (ADS)
Kalet, Alan M.; Gennari, John H.; Ford, Eric C.; Phillips, Mark H.
2015-04-01
The purpose of this study is to design and develop a probabilistic network for detecting errors in radiotherapy plans for use at the time of initial plan verification. Our group has initiated a multi-pronged approach to reduce these errors. We report on our development of Bayesian models of radiotherapy plans. Bayesian networks consist of joint probability distributions that define the probability of one event, given some set of other known information. Using the networks, we find the probability of obtaining certain radiotherapy parameters, given a set of initial clinical information. A low probability in a propagated network then corresponds to potential errors to be flagged for investigation. To build our networks we first interviewed medical physicists and other domain experts to identify the relevant radiotherapy concepts and their associated interdependencies and to construct a network topology. Next, to populate the network’s conditional probability tables, we used the Hugin Expert software to learn parameter distributions from a subset of de-identified data derived from a radiation oncology based clinical information database system. These data represent 4990 unique prescription cases over a 5 year period. Under test case scenarios with approximately 1.5% introduced error rates, network performance produced areas under the ROC curve of 0.88, 0.98, and 0.89 for the lung, brain and female breast cancer error detection networks, respectively. Comparison of the brain network to human experts performance (AUC of 0.90 ± 0.01) shows the Bayes network model performs better than domain experts under the same test conditions. Our results demonstrate the feasibility and effectiveness of comprehensive probabilistic models as part of decision support systems for improved detection of errors in initial radiotherapy plan verification procedures.
NASA Astrophysics Data System (ADS)
Shen, Chien-wen
2009-01-01
During the processes of TFT-LCD manufacturing, steps like visual inspection of panel surface defects still heavily rely on manual operations. As the manual inspection time of TFT-LCD manufacturing could range from 4 hours to 1 day, the reliability of time forecasting is thus important for production planning, scheduling and customer response. This study would like to propose a practical and easy-to-implement prediction model through the approach of Bayesian networks for time estimation of manual operated procedures in TFT-LCD manufacturing. Given the lack of prior knowledge about manual operation time, algorithms of necessary path condition and expectation-maximization are used for structural learning and estimation of conditional probability distributions respectively. This study also applied Bayesian inference to evaluate the relationships between explanatory variables and manual operation time. With the empirical applications of this proposed forecasting model, approach of Bayesian networks demonstrates its practicability and prediction accountability.
Parameter Expanded Algorithms for Bayesian Latent Variable Modeling of Genetic Pleiotropy Data.
Xu, Lizhen; Craiu, Radu V; Sun, Lei; Paterson, Andrew D
2016-01-01
Motivated by genetic association studies of pleiotropy, we propose a Bayesian latent variable approach to jointly study multiple outcomes. The models studied here can incorporate both continuous and binary responses, and can account for serial and cluster correlations. We consider Bayesian estimation for the model parameters, and we develop a novel MCMC algorithm that builds upon hierarchical centering and parameter expansion techniques to efficiently sample from the posterior distribution. We evaluate the proposed method via extensive simulations and demonstrate its utility with an application to aa association study of various complication outcomes related to type 1 diabetes. This article has supplementary material online.
Bayesian non-parametric inference for stochastic epidemic models using Gaussian Processes
Xu, Xiaoguang; Kypraios, Theodore; O'Neill, Philip D.
2016-01-01
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. PMID:26993062
Toward diagnostic model calibration and evaluation: Approximate Bayesian computation
NASA Astrophysics Data System (ADS)
Vrugt, Jasper A.; Sadegh, Mojtaba
2013-07-01
The ever increasing pace of computational power, along with continued advances in measurement technologies and improvements in process understanding has stimulated the development of increasingly complex hydrologic models that simulate soil moisture flow, groundwater recharge, surface runoff, root water uptake, and river discharge at different spatial and temporal scales. Reconciling these high-order system models with perpetually larger volumes of field data is becoming more and more difficult, particularly because classical likelihood-based fitting methods lack the power to detect and pinpoint deficiencies in the model structure. Gupta et al. (2008) has recently proposed steps (amongst others) toward the development of a more robust and powerful method of model evaluation. Their diagnostic approach uses signature behaviors and patterns observed in the input-output data to illuminate to what degree a representation of the real world has been adequately achieved and how the model should be improved for the purpose of learning and scientific discovery. In this paper, we introduce approximate Bayesian computation (ABC) as a vehicle for diagnostic model evaluation. This statistical methodology relaxes the need for an explicit likelihood function in favor of one or multiple different summary statistics rooted in hydrologic theory that together have a clearer and more compelling diagnostic power than some average measure of the size of the error residuals. Two illustrative case studies are used to demonstrate that ABC is relatively easy to implement, and readily employs signature based indices to analyze and pinpoint which part of the model is malfunctioning and in need of further improvement.
Bridging groundwater models and decision support with a Bayesian network
Fienen, Michael N.; Masterson, John P.; Plant, Nathaniel G.; Gutierrez, Benjamin T.; Thieler, E. Robert
2013-01-01
Resource managers need to make decisions to plan for future environmental conditions, particularly sea level rise, in the face of substantial uncertainty. Many interacting processes factor in to the decisions they face. Advances in process models and the quantification of uncertainty have made models a valuable tool for this purpose. Long-simulation runtimes and, often, numerical instability make linking process models impractical in many cases. A method for emulating the important connections between model input and forecasts, while propagating uncertainty, has the potential to provide a bridge between complicated numerical process models and the efficiency and stability needed for decision making. We explore this using a Bayesian network (BN) to emulate a groundwater flow model. We expand on previous approaches to validating a BN by calculating forecasting skill using cross validation of a groundwater model of Assateague Island in Virginia and Maryland, USA. This BN emulation was shown to capture the important groundwater-flow characteristics and uncertainty of the groundwater system because of its connection to island morphology and sea level. Forecast power metrics associated with the validation of multiple alternative BN designs guided the selection of an optimal level of BN complexity. Assateague island is an ideal test case for exploring a forecasting tool based on current conditions because the unique hydrogeomorphological variability of the island includes a range of settings indicative of past, current, and future conditions. The resulting BN is a valuable tool for exploring the response of groundwater conditions to sea level rise in decision support.
Bayesian spatially dependent variable selection for small area health modeling.
Choi, Jungsoon; Lawson, Andrew B
2016-06-16
Statistical methods for spatial health data to identify the significant covariates associated with the health outcomes are of critical importance. Most studies have developed variable selection approaches in which the covariates included appear within the spatial domain and their effects are fixed across space. However, the impact of covariates on health outcomes may change across space and ignoring this behavior in spatial epidemiology may cause the wrong interpretation of the relations. Thus, the development of a statistical framework for spatial variable selection is important to allow for the estimation of the space-varying patterns of covariate effects as well as the early detection of disease over space. In this paper, we develop flexible spatial variable selection approaches to find the spatially-varying subsets of covariates with significant effects. A Bayesian hierarchical latent model framework is applied to account for spatially-varying covariate effects. We present a simulation example to examine the performance of the proposed models with the competing models. We apply our models to a county-level low birth weight incidence dataset in Georgia.
The Bayesian Evaluation of Categorization Models: Comment on Wills and Pothos (2012)
ERIC Educational Resources Information Center
Vanpaemel, Wolf; Lee, Michael D.
2012-01-01
Wills and Pothos (2012) reviewed approaches to evaluating formal models of categorization, raising a series of worthwhile issues, challenges, and goals. Unfortunately, in discussing these issues and proposing solutions, Wills and Pothos (2012) did not consider Bayesian methods in any detail. This means not only that their review excludes a major…
Bayesian Analysis of Structural Equation Models with Nonlinear Covariates and Latent Variables
ERIC Educational Resources Information Center
Song, Xin-Yuan; Lee, Sik-Yum
2006-01-01
In this article, we formulate a nonlinear structural equation model (SEM) that can accommodate covariates in the measurement equation and nonlinear terms of covariates and exogenous latent variables in the structural equation. The covariates can come from continuous or discrete distributions. A Bayesian approach is developed to analyze the…
Bayesian Analysis for Linearized Multi-Stage Models in Quantal Bioassay.
ERIC Educational Resources Information Center
Kuo, Lynn; Cohen, Michael P.
Bayesian methods for estimating dose response curves in quantal bioassay are studied. A linearized multi-stage model is assumed for the shape of the curves. A Gibbs sampling approach with data augmentation is employed to compute the Bayes estimates. In addition, estimation of the "relative additional risk" and the "risk specific…
Bayesian Approaches to Imputation, Hypothesis Testing, and Parameter Estimation
ERIC Educational Resources Information Center
Ross, Steven J.; Mackey, Beth
2015-01-01
This chapter introduces three applications of Bayesian inference to common and novel issues in second language research. After a review of the critiques of conventional hypothesis testing, our focus centers on ways Bayesian inference can be used for dealing with missing data, for testing theory-driven substantive hypotheses without a default null…
Webb, J Angus; Koster, Wayne M; Stuart, Ivor G; Reich, Paul; Stewardson, Michael J
2017-03-03
Environmental water managers must make best use of allocations, and adaptive management is one means of improving effectiveness of environmental water delivery. Adaptive management relies on generation of new knowledge from monitoring and evaluation, but it is often difficult to make clear inferences from available monitoring data. Alternative approaches to assessment of flow benefits may offer an improved pathway to adaptive management. We developed Bayesian statistical models to inform adaptive management of the threatened Australian grayling (Prototroctes maraena) in the coastal Thomson River, South-East Victoria Australia. The models assessed the importance of flows in spring and early summer (migration flows) for upstream dispersal and colonization of juveniles of this diadromous species. However, Australian grayling young-of-year were recorded in low numbers, and models provided no indication of the benefit of migration flows. To overcome this limitation, we applied the same models to young-of-year of a surrogate species (tupong-Pseudaphritis urvilli)-a more common diadromous species expected to respond to flow similarly to Australian grayling-and found strong positive responses to migration flows. Our results suggest two complementary approaches to supporting adaptive management of Australian grayling. First, refine monitoring approaches to allow direct measurement of effects of migration flows, a process currently under way. Second, while waiting for improved data, further investigate the use of tupong as a surrogate species. More generally, alternative approaches to assessment can improve knowledge to inform adaptive management, and this can occur while monitoring is being revised to directly target environmental responses of interest.
A Bayesian approach to multiscale inverse problems with on-the-fly scale determination
NASA Astrophysics Data System (ADS)
Ellam, Louis; Zabaras, Nicholas; Girolami, Mark
2016-12-01
A Bayesian computational approach is presented to provide a multi-resolution estimate of an unknown spatially varying parameter from indirect measurement data. In particular, we are interested in spatially varying parameters with multiscale characteristics. In our work, we consider the challenge of not knowing the characteristic length scale(s) of the unknown a priori, and present an algorithm for on-the-fly scale determination. Our approach is based on representing the spatial field with a wavelet expansion. Wavelet basis functions are hierarchically structured, localized in both spatial and frequency domains and tend to provide sparse representations in that a large number of wavelet coefficients are approximately zero. For these reasons, wavelet bases are suitable for representing permeability fields with non-trivial correlation structures. Moreover, the intra-scale correlations between wavelet coefficients form a quadtree, and this structure is exploited to identify additional basis functions to refine the model. Bayesian inference is performed using a sequential Monte Carlo (SMC) sampler with a Markov Chain Monte Carlo (MCMC) transition kernel. The SMC sampler is used to move between posterior densities defined on different scales, thereby providing a computationally efficient method for adaptive refinement of the wavelet representation. We gain insight from the marginal likelihoods, by computing Bayes factors, for model comparison and model selection. The marginal likelihoods provide a termination criterion for our scale determination algorithm. The Bayesian computational approach is rather general and applicable to several inverse problems concerning the estimation of a spatially varying parameter. The approach is demonstrated with permeability estimation for groundwater flow using pressure sensor measurements.
ERIC Educational Resources Information Center
Shuck, Brad; Zigarmi, Drea; Owen, Jesse
2015-01-01
Purpose: The purpose of this study was to empirically examine the utility of self-determination theory (SDT) within the engagement-performance linkage. Design/methodology/approach: Bayesian multi-measurement mediation modeling was used to estimate the relation between SDT, engagement and a proxy measure of performance (e.g. work intentions) (N =…
NASA Astrophysics Data System (ADS)
Hobson, Michael P.; Jaffe, Andrew H.; Liddle, Andrew R.; Mukherjee, Pia; Parkinson, David
2009-12-01
Preface; Part I. Methods: 1. Foundations and algorithms John Skilling; 2. Simple applications of Bayesian methods D. S. Sivia and Steve Rawlings; 3. Parameter estimation using Monte Carlo sampling Antony Lewis and Sarah Bridle; 4. Model selection and multi-model interference Andrew R. Liddle, Pia Mukherjee and David Parkinson; 5. Bayesian experimental design and model selection forecasting Roberto Trotta, Martin Kunz, Pia Mukherjee and David Parkinson; 6. Signal separation in cosmology M. P. Hobson, M. A. J. Ashdown and V. Stolyarov; Part II. Applications: 7. Bayesian source extraction M. P. Hobson, Graça Rocha and R. Savage; 8. Flux measurement Daniel Mortlock; 9. Gravitational wave astronomy Neil Cornish; 10. Bayesian analysis of cosmic microwave background data Andrew H. Jaffe; 11. Bayesian multilevel modelling of cosmological populations Thomas J. Loredo and Martin A. Hendry; 12. A Bayesian approach to galaxy evolution studies Stefano Andreon; 13. Photometric redshift estimation: methods and applications Ofer Lahav, Filipe B. Abdalla and Manda Banerji; Index.
NASA Astrophysics Data System (ADS)
Hobson, Michael P.; Jaffe, Andrew H.; Liddle, Andrew R.; Mukherjee, Pia; Parkinson, David
2014-02-01
Preface; Part I. Methods: 1. Foundations and algorithms John Skilling; 2. Simple applications of Bayesian methods D. S. Sivia and Steve Rawlings; 3. Parameter estimation using Monte Carlo sampling Antony Lewis and Sarah Bridle; 4. Model selection and multi-model interference Andrew R. Liddle, Pia Mukherjee and David Parkinson; 5. Bayesian experimental design and model selection forecasting Roberto Trotta, Martin Kunz, Pia Mukherjee and David Parkinson; 6. Signal separation in cosmology M. P. Hobson, M. A. J. Ashdown and V. Stolyarov; Part II. Applications: 7. Bayesian source extraction M. P. Hobson, Graça Rocha and R. Savage; 8. Flux measurement Daniel Mortlock; 9. Gravitational wave astronomy Neil Cornish; 10. Bayesian analysis of cosmic microwave background data Andrew H. Jaffe; 11. Bayesian multilevel modelling of cosmological populations Thomas J. Loredo and Martin A. Hendry; 12. A Bayesian approach to galaxy evolution studies Stefano Andreon; 13. Photometric redshift estimation: methods and applications Ofer Lahav, Filipe B. Abdalla and Manda Banerji; Index.
Bayesian Estimation in the One-Parameter Latent Trait Model.
1980-03-01
3 MASSACHUSETTS LNIV AMHERST LAB OF PSYCHOMETRIC AND -- ETC F/G 12/1 BAYESIAN ESTIMATION IN THE ONE-PARA1ETER LATENT TRAIT MODEL. (U) MAR 80 H...TEST CHART VVNN lfl’ ,. [’ COD BAYESIAN ESTIMATION IN THE ONE-PARAMETER LATENT TRAIT MODEL 0 wtHAR IHARAN SWA I NATHAN AND JANICE A. GIFFORD Research...block numbef) latent trait theory Bayesain estimation 20. ABSTRACT (Continue on reveso aide If neceaar and identlfy by Nock mambe) ,-When several
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…
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…
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,…
A Bayesian Model of Category-Specific Emotional Brain Responses
Wager, Tor D.; Kang, Jian; Johnson, Timothy D.; Nichols, Thomas E.; Satpute, Ajay B.; Barrett, Lisa Feldman
2015-01-01
Understanding emotion is critical for a science of healthy and disordered brain function, but the neurophysiological basis of emotional experience is still poorly understood. We analyzed human brain activity patterns from 148 studies of emotion categories (2159 total participants) using a novel hierarchical Bayesian model. The model allowed us to classify which of five categories—fear, anger, disgust, sadness, or happiness—is engaged by a study with 66% accuracy (43-86% across categories). Analyses of the activity patterns encoded in the model revealed that each emotion category is associated with unique, prototypical patterns of activity across multiple brain systems including the cortex, thalamus, amygdala, and other structures. The results indicate that emotion categories are not contained within any one region or system, but are represented as configurations across multiple brain networks. The model provides a precise summary of the prototypical patterns for each emotion category, and demonstrates that a sufficient characterization of emotion categories relies on (a) differential patterns of involvement in neocortical systems that differ between humans and other species, and (b) distinctive patterns of cortical-subcortical interactions. Thus, these findings are incompatible with several contemporary theories of emotion, including those that emphasize emotion-dedicated brain systems and those that propose emotion is localized primarily in subcortical activity. They are consistent with componential and constructionist views, which propose that emotions are differentiated by a combination of perceptual, mnemonic, prospective, and motivational elements. Such brain-based models of emotion provide a foundation for new translational and clinical approaches. PMID:25853490
Bayesian methods for characterizing unknown parameters of material models
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
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 to characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.
Capturing changes in flood risk with Bayesian approaches for flood damage assessment
NASA Astrophysics Data System (ADS)
Vogel, Kristin; Schröter, Kai; Kreibich, Heidi; Thieken, Annegret; Müller, Meike; Sieg, Tobias; Laudan, Jonas; Kienzler, Sarah; Weise, Laura; Merz, Bruno; Scherbaum, Frank
2016-04-01
Flood risk is a function of hazard as well as of exposure and vulnerability. All three components are under change over space and time and have to be considered for reliable damage estimations and risk analyses, since this is the basis for an efficient, adaptable risk management. Hitherto, models for estimating flood damage are comparatively simple and cannot sufficiently account for changing conditions. The Bayesian network approach allows for a multivariate modeling of complex systems without relying on expert knowledge about physical constraints. In a Bayesian network each model component is considered to be a random variable. The way of interactions between those variables can be learned from observations or be defined by expert knowledge. Even a combination of both is possible. Moreover, the probabilistic framework captures uncertainties related to the prediction and provides a probability distribution for the damage instead of a point estimate. The graphical representation of Bayesian networks helps to study the change of probabilities for changing circumstances and may thus simplify the communication between scientists and public authorities. In the framework of the DFG-Research Training Group "NatRiskChange" we aim to develop Bayesian networks for flood damage and vulnerability assessments of residential buildings and companies under changing conditions. A Bayesian network learned from data, collected over the last 15 years in flooded regions in the Elbe and Danube catchments (Germany), reveals the impact of many variables like building characteristics, precaution and warning situation on flood damage to residential buildings. While the handling of incomplete and hybrid (discrete mixed with continuous) data are the most challenging issues in the study on residential buildings, a similar study, that focuses on the vulnerability of small to medium sized companies, bears new challenges. Relying on a much smaller data set for the determination of the model
Forecasting unconventional resource productivity - A spatial Bayesian model
NASA Astrophysics Data System (ADS)
Montgomery, J.; O'sullivan, F.
2015-12-01
Today's low prices mean that unconventional oil and gas development requires ever greater efficiency and better development decision-making. Inter and intra-field variability in well productivity, which is a major contemporary driver of uncertainty regarding resource size and its economics is driven by factors including geological conditions, well and completion design (which companies vary as they seek to optimize their performance), and uncertainty about the nature of fracture propagation. Geological conditions are often not be well understood early on in development campaigns, but nevertheless critical assessments and decisions must be made regarding the value of drilling an area and the placement of wells. In these situations, location provides a reasonable proxy for geology and the "rock quality." We propose a spatial Bayesian model for forecasting acreage quality, which improves decision-making by leveraging available production data and provides a framework for statistically studying the influence of different parameters on well productivity. Our approach consists of subdividing a field into sections and forming prior distributions for productivity in each section based on knowledge about the overall field. Production data from wells is used to update these estimates in a Bayesian fashion, improving model accuracy far more rapidly and with less sensitivity to outliers than a model that simply establishes an "average" productivity in each section. Additionally, forecasts using this model capture the importance of uncertainty—either due to a lack of information or for areas that demonstrate greater geological risk. We demonstrate the forecasting utility of this method using public data and also provide examples of how information from this model can be combined with knowledge about a field's geology or changes in technology to better quantify development risk. This approach represents an important shift in the way that production data is used to guide
NASA Astrophysics Data System (ADS)
Dries, M.; Trager, S. C.; Koopmans, L. V. E.
2016-11-01
Recent studies based on the integrated light of distant galaxies suggest that the initial mass function (IMF) might not be universal. Variations of the IMF with galaxy type and/or formation time may have important consequences for our understanding of galaxy evolution. We have developed a new stellar population synthesis (SPS) code specifically designed to reconstruct the IMF. We implement a novel approach combining regularization with hierarchical Bayesian inference. Within this approach, we use a parametrized IMF prior to regulate a direct inference of the IMF. This direct inference gives more freedom to the IMF and allows the model to deviate from parametrized models when demanded by the data. We use Markov chain Monte Carlo sampling techniques to reconstruct the best parameters for the IMF prior, the age and the metallicity of a single stellar population. We present our code and apply our model to a number of mock single stellar populations with different ages, metallicities and IMFs. When systematic uncertainties are not significant, we are able to reconstruct the input parameters that were used to create the mock populations. Our results show that if systematic uncertainties do play a role, this may introduce a bias on the results. Therefore, it is important to objectively compare different ingredients of SPS models. Through its Bayesian framework, our model is well suited for this.
Bayesian Modeling of Haplotype Effects in Multiparent Populations
Zhang, Zhaojun; Wang, Wei; Valdar, William
2014-01-01
A general Bayesian model, Diploffect, is described for estimating the effects of founder haplotypes at quantitative trait loci (QTL) detected in multiparental genetic populations; such populations include the Collaborative Cross (CC), Heterogeneous Socks (HS), and many others for which local genetic variation is well described by an underlying, usually probabilistically inferred, haplotype mosaic. Our aim is to provide a framework for coherent estimation of haplotype and diplotype (haplotype pair) effects that takes into account the following: uncertainty in haplotype composition for each individual; uncertainty arising from small sample sizes and infrequently observed haplotype combinations; possible effects of dominance (for noninbred subjects); genetic background; and that provides a means to incorporate data that may be incomplete or has a hierarchical structure. Using the results of a probabilistic haplotype reconstruction as prior information, we obtain posterior distributions at the QTL for both haplotype effects and haplotype composition. Two alternative computational approaches are supplied: a Markov chain Monte Carlo sampler and a procedure based on importance sampling of integrated nested Laplace approximations. Using simulations of QTL in the incipient CC (pre-CC) and Northport HS populations, we compare the accuracy of Diploffect, approximations to it, and more commonly used approaches based on Haley–Knott regression, describing trade-offs between these methods. We also estimate effects for three QTL previously identified in those populations, obtaining posterior intervals that describe how the phenotype might be affected by diplotype substitutions at the modeled locus. PMID:25236455
Genome Scans for Detecting Footprints of Local Adaptation Using a Bayesian Factor Model
Duforet-Frebourg, Nicolas; Bazin, Eric; Blum, Michael G.B.
2014-01-01
There is a considerable impetus in population genomics to pinpoint loci involved in local adaptation. A powerful approach to find genomic regions subject to local adaptation is to genotype numerous molecular markers and look for outlier loci. One of the most common approaches for selection scans is based on statistics that measure population differentiation such as FST. However, there are important caveats with approaches related to FST because they require grouping individuals into populations and they additionally assume a particular model of population structure. Here, we implement a more flexible individual-based approach based on Bayesian factor models. Factor models capture population structure with latent variables called factors, which can describe clustering of individuals into populations or isolation-by-distance patterns. Using hierarchical Bayesian modeling, we both infer population structure and identify outlier loci that are candidates for local adaptation. In order to identify outlier loci, the hierarchical factor model searches for loci that are atypically related to population structure as measured by the latent factors. In a model of population divergence, we show that it can achieve a 2-fold or more reduction of false discovery rate compared with the software BayeScan or with an FST approach. We show that our software can handle large data sets by analyzing the single nucleotide polymorphisms of the Human Genome Diversity Project. The Bayesian factor model is implemented in the open-source PCAdapt software. PMID:24899666
Improving default risk prediction using Bayesian model uncertainty techniques.
Kazemi, Reza; Mosleh, Ali
2012-11-01
Credit risk is the potential exposure of a creditor to an obligor's failure or refusal to repay the debt in principal or interest. The potential of exposure is measured in terms of probability of default. Many models have been developed to estimate credit risk, with rating agencies dating back to the 19th century. They provide their assessment of probability of default and transition probabilities of various firms in their annual reports. Regulatory capital requirements for credit risk outlined by the Basel Committee on Banking Supervision have made it essential for banks and financial institutions to develop sophisticated models in an attempt to measure credit risk with higher accuracy. The Bayesian framework proposed in this article uses the techniques developed in physical sciences and engineering for dealing with model uncertainty and expert accuracy to obtain improved estimates of credit risk and associated uncertainties. The approach uses estimates from one or more rating agencies and incorporates their historical accuracy (past performance data) in estimating future default risk and transition probabilities. Several examples demonstrate that the proposed methodology can assess default probability with accuracy exceeding the estimations of all the individual models. Moreover, the methodology accounts for potentially significant departures from "nominal predictions" due to "upsetting events" such as the 2008 global banking crisis.
Structure Prior Effects in Bayesian Approaches of Quantitative Susceptibility Mapping
Chen, Weiwei; Wang, Chunmei; Liu, Tian; Wang, Yi; Pan, Chu; Mu, Ketao; Zhu, Ce; Zhang, Xiang; Cheng, Jian
2016-01-01
Quantitative susceptibility mapping (QSM) has shown its potential for anatomical and functional MRI, as it can quantify, for in vivo tissues, magnetic biomarkers and contrast agents which have differential susceptibilities to the surroundings substances. For reconstructing the QSM with a single orientation, various methods have been proposed to identify a unique solution for the susceptibility map. Bayesian QSM approach is the major type which uses various regularization terms, such as a piece-wise constant, a smooth, a sparse, or a morphological prior. Six QSM algorithms with or without structure prior are systematically discussed to address the structure prior effects. The methods are evaluated using simulations, phantom experiments with the given susceptibility, and human brain data. The accuracy and image quality of QSM were increased when using structure prior in the simulation and phantom compared to same regularization term without it, respectively. The image quality of QSM method using the structure prior is better comparing, respectively, to the method without it by either sharpening the image or reducing streaking artifacts in vivo. The structure priors improve the performance of the various QSMs using regularized minimization including L1, L2, and TV norm. PMID:28097129
Helle, Inari; Ahtiainen, Heini; Luoma, Emilia; Hänninen, Maria; Kuikka, Sakari
2015-08-01
Large-scale oil accidents can inflict substantial costs to the society, as they typically result in expensive oil combating and waste treatment operations and have negative impacts on recreational and environmental values. Cost-benefit analysis (CBA) offers a way to assess the economic efficiency of management measures capable of mitigating the adverse effects. However, the irregular occurrence of spills combined with uncertainties related to the possible effects makes the analysis a challenging task. We develop a probabilistic modeling approach for a CBA of oil spill management and apply it in the Gulf of Finland, the Baltic Sea. The model has a causal structure, and it covers a large number of factors relevant to the realistic description of oil spills, as well as the costs of oil combating operations at open sea, shoreline clean-up, and waste treatment activities. Further, to describe the effects on environmental benefits, we use data from a contingent valuation survey. The results encourage seeking for cost-effective preventive measures, and emphasize the importance of the inclusion of the costs related to waste treatment and environmental values in the analysis. Although the model is developed for a specific area, the methodology is applicable also to other areas facing the risk of oil spills as well as to other fields that need to cope with the challenging combination of low probabilities, high losses and major uncertainties.
A Bayesian approach for convex combination of two Gumbel-Barnett copulas
NASA Astrophysics Data System (ADS)
Fernández, M.; González-López, V. A.
2013-10-01
In this paper it was applied a new Bayesian approach to model the dependence between two variables of interest in public policy: "Gonorrhea Rates per 100,000 Population" and "400% Federal Poverty Level and over" with a small number of paired observations (one pair for each U.S. state). We use a mixture of Gumbel-Barnett copulas suitable to represent situations with weak and negative dependence, which is the case treated here. The methodology allows even making a prediction of the dependence between the variables from one year to another, showing whether there was any alteration in the dependence.
ERIC Educational Resources Information Center
Aslan, Burak Galip; Öztürk, Özlem; Inceoglu, Mustafa Murat
2014-01-01
Considering the increasing importance of adaptive approaches in CALL systems, this study implemented a machine learning based student modeling middleware with Bayesian networks. The profiling approach of the student modeling system is based on Felder and Silverman's Learning Styles Model and Felder and Soloman's Index of Learning Styles…
NASA Astrophysics Data System (ADS)
Werner, Johannes; Tingley, Martin
2015-04-01
Reconstructions of late-Holocene climate rely heavily upon proxies that are assumed to be accurately dated by layer counting, such as measurement on tree rings, ice cores, and varved lake sediments. Considerable advances may be achievable if time uncertain proxies could be included within these multiproxy reconstructions, and if time uncertainties were recognized and correctly modeled for proxies commonly treated as free of age model errors. Current approaches to accounting for time uncertainty are generally limited to repeating the reconstruction using each of an ensemble of age models, thereby inflating the final estimated uncertainty - in effect, each possible age model is given equal weighting. Uncertainties can be reduced by exploiting the inferred space-time covariance structure of the climate to re-weight the possible age models. Here we demonstrate how Bayesian Hierarchical climate reconstruction models can be augmented to account for time uncertain proxies. Critically, while a priori all age models are given equal probability of being correct, the probabilities associated with the age models are formally updated within the Bayesian framework, thereby reducing uncertainties. Numerical experiments show that updating the age model probabilities decreases uncertainty in the climate reconstruction, as compared with the current de-facto standard of sampling over all age models, provided there is sufficient information from other data sources in the region of the time-uncertain proxy. This approach can readily be generalized to non-layer counted proxies, such as those derived from marine sediments. Werner and Tingley, Climate of the Past Discussions (2014)
NASA Astrophysics Data System (ADS)
Werner, J. P.; Tingley, M. P.
2015-03-01
Reconstructions of the late-Holocene climate rely heavily upon proxies that are assumed to be accurately dated by layer counting, such as measurements of tree rings, ice cores, and varved lake sediments. Considerable advances could be achieved if time-uncertain proxies were able to be included within these multiproxy reconstructions, and if time uncertainties were recognized and correctly modeled for proxies commonly treated as free of age model errors. Current approaches for accounting for time uncertainty are generally limited to repeating the reconstruction using each one of an ensemble of age models, thereby inflating the final estimated uncertainty - in effect, each possible age model is given equal weighting. Uncertainties can be reduced by exploiting the inferred space-time covariance structure of the climate to re-weight the possible age models. Here, we demonstrate how Bayesian hierarchical climate reconstruction models can be augmented to account for time-uncertain proxies. Critically, although a priori all age models are given equal probability of being correct, the probabilities associated with the age models are formally updated within the Bayesian framework, thereby reducing uncertainties. Numerical experiments show that updating the age model probabilities decreases uncertainty in the resulting reconstructions, as compared with the current de facto standard of sampling over all age models, provided there is sufficient information from other data sources in the spatial region of the time-uncertain proxy. This approach can readily be generalized to non-layer-counted proxies, such as those derived from marine sediments.
NASA Astrophysics Data System (ADS)
Werner, J. P.; Tingley, M. P.
2014-12-01
Reconstructions of late-Holocene climate rely heavily upon proxies that are assumed to be accurately dated by layer counting, such as measurement on tree rings, ice cores, and varved lake sediments. Considerable advances may be achievable if time uncertain proxies could be included within these multiproxy reconstructions, and if time uncertainties were recognized and correctly modeled for proxies commonly treated as free of age model errors. Current approaches to accounting for time uncertainty are generally limited to repeating the reconstruction using each of an ensemble of age models, thereby inflating the final estimated uncertainty - in effect, each possible age model is given equal weighting. Uncertainties can be reduced by exploiting the inferred space-time covariance structure of the climate to re-weight the possible age models. Here we demonstrate how Bayesian Hierarchical climate reconstruction models can be augmented to account for time uncertain proxies. Critically, while a priori all age models are given equal probability of being correct, the probabilities associated with the age models are formally updated within the Bayesian framework, thereby reducing uncertainties. Numerical experiments show that updating the age-model probabilities decreases uncertainty in the climate reconstruction, as compared with the current de-facto standard of sampling over all age models, provided there is sufficient information from other data sources in the region of the time-uncertain proxy. This approach can readily be generalized to non-layer counted proxies, such as those derived from marine sediments.
True versus Apparent Malaria Infection Prevalence: The Contribution of a Bayesian Approach
Claes, Filip; Van Hong, Nguyen; Torres, Kathy; Mao, Sokny; Van den Eede, Peter; Thi Thinh, Ta; Gamboa, Dioni; Sochantha, Tho; Thang, Ngo Duc; Coosemans, Marc; Büscher, Philippe; D'Alessandro, Umberto; Berkvens, Dirk; Erhart, Annette
2011-01-01
Aims To present a new approach for estimating the “true prevalence” of malaria and apply it to datasets from Peru, Vietnam, and Cambodia. Methods Bayesian models were developed for estimating both the malaria prevalence using different diagnostic tests (microscopy, PCR & ELISA), without the need of a gold standard, and the tests' characteristics. Several sources of information, i.e. data, expert opinions and other sources of knowledge can be integrated into the model. This approach resulting in an optimal and harmonized estimate of malaria infection prevalence, with no conflict between the different sources of information, was tested on data from Peru, Vietnam and Cambodia. Results Malaria sero-prevalence was relatively low in all sites, with ELISA showing the highest estimates. The sensitivity of microscopy and ELISA were statistically lower in Vietnam than in the other sites. Similarly, the specificities of microscopy, ELISA and PCR were significantly lower in Vietnam than in the other sites. In Vietnam and Peru, microscopy was closer to the “true” estimate than the other 2 tests while as expected ELISA, with its lower specificity, usually overestimated the prevalence. Conclusions Bayesian methods are useful for analyzing prevalence results when no gold standard diagnostic test is available. Though some results are expected, e.g. PCR more sensitive than microscopy, a standardized and context-independent quantification of the diagnostic tests' characteristics (sensitivity and specificity) and the underlying malaria prevalence may be useful for comparing different sites. Indeed, the use of a single diagnostic technique could strongly bias the prevalence estimation. This limitation can be circumvented by using a Bayesian framework taking into account the imperfect characteristics of the currently available diagnostic tests. As discussed in the paper, this approach may further support global malaria burden estimation initiatives. PMID:21364745
Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring.
Carroll, Carlos; Johnson, Devin S; Dunk, Jeffrey R; Zielinski, William J
2010-12-01
Biologists who develop and apply habitat models are often familiar with the statistical challenges posed by their data's spatial structure but are unsure of whether the use of complex spatial models will increase the utility of model results in planning. We compared the relative performance of nonspatial and hierarchical Bayesian spatial models for three vertebrate and invertebrate taxa of conservation concern (Church's sideband snails [Monadenia churchi], red tree voles [Arborimus longicaudus], and Pacific fishers [Martes pennanti pacifica]) that provide examples of a range of distributional extents and dispersal abilities. We used presence-absence data derived from regional monitoring programs to develop models with both landscape and site-level environmental covariates. We used Markov chain Monte Carlo algorithms and a conditional autoregressive or intrinsic conditional autoregressive model framework to fit spatial models. The fit of Bayesian spatial models was between 35 and 55% better than the fit of nonspatial analogue models. Bayesian spatial models outperformed analogous models developed with maximum entropy (Maxent) methods. Although the best spatial and nonspatial models included similar environmental variables, spatial models provided estimates of residual spatial effects that suggested how ecological processes might structure distribution patterns. Spatial models built from presence-absence data improved fit most for localized endemic species with ranges constrained by poorly known biogeographic factors and for widely distributed species suspected to be strongly affected by unmeasured environmental variables or population processes. By treating spatial effects as a variable of interest rather than a nuisance, hierarchical Bayesian spatial models, especially when they are based on a common broad-scale spatial lattice (here the national Forest Inventory and Analysis grid of 24 km(2) hexagons), can increase the relevance of habitat models to multispecies
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…
Shortlist B: A Bayesian Model of Continuous Speech Recognition
ERIC Educational Resources Information Center
Norris, Dennis; McQueen, James M.
2008-01-01
A Bayesian model of continuous speech recognition is presented. It is based on Shortlist (D. Norris, 1994; D. Norris, J. M. McQueen, A. Cutler, & S. Butterfield, 1997) and shares many of its key assumptions: parallel competitive evaluation of multiple lexical hypotheses, phonologically abstract prelexical and lexical representations, a feedforward…
CRAFFT: An Activity Prediction Model based on Bayesian Networks.
Nazerfard, Ehsan; Cook, Diane J
2015-04-01
Recent advances in the areas of pervasive computing, data mining, and machine learning offer unique opportunities to provide health monitoring and assistance for individuals facing difficulties to live independently in their homes. Several components have to work together to provide health monitoring for smart home residents including, but not limited to, activity recognition, activity discovery, activity prediction, and prompting system. Compared to the significant research done to discover and recognize activities, less attention has been given to predict the future activities that the resident is likely to perform. Activity prediction components can play a major role in design of a smart home. For instance, by taking advantage of an activity prediction module, a smart home can learn context-aware rules to prompt individuals to initiate important activities. In this paper, we propose an activity prediction model using Bayesian networks together with a novel two-step inference process to predict both the next activity features and the next activity label. We also propose an approach to predict the start time of the next activity which is based on modeling the relative start time of the predicted activity using the continuous normal distribution and outlier detection. To validate our proposed models, we used real data collected from physical smart environments.
Bayesian shared frailty models for regional inference about wildlife survival
Heisey, D.M.
2012-01-01
One can joke that 'exciting statistics' is an oxymoron, but it is neither a joke nor an exaggeration to say that these are exciting times to be involved in statistical ecology. As Halstead et al.'s (2012) paper nicely exemplifies, recently developed Bayesian analyses can now be used to extract insights from data using techniques that would have been unavailable to the ecological researcher just a decade ago. Some object to this, implying that the subjective priors of the Bayesian approach is the pathway to perdition (e.g. Lele & Dennis, 2009). It is reasonable to ask whether these new approaches are really giving us anything that we could not obtain with traditional tried-and-true frequentist approaches. I believe the answer is a clear yes.
Fu, Zhibiao; Baker, Daniel; Cheng, Aili; Leighton, Julie; Appelbaum, Edward; Aon, Juan
2016-05-01
The principle of quality by design (QbD) has been widely applied to biopharmaceutical manufacturing processes. Process characterization is an essential step to implement the QbD concept to establish the design space and to define the proven acceptable ranges (PAR) for critical process parameters (CPPs). In this study, we present characterization of a Saccharomyces cerevisiae fermentation process using risk assessment analysis, statistical design of experiments (DoE), and the multivariate Bayesian predictive approach. The critical quality attributes (CQAs) and CPPs were identified with a risk assessment. The statistical model for each attribute was established using the results from the DoE study with consideration given to interactions between CPPs. Both the conventional overlapping contour plot and the multivariate Bayesian predictive approaches were used to establish the region of process operating conditions where all attributes met their specifications simultaneously. The quantitative Bayesian predictive approach was chosen to define the PARs for the CPPs, which apply to the manufacturing control strategy. Experience from the 10,000 L manufacturing scale process validation, including 64 continued process verification batches, indicates that the CPPs remain under a state of control and within the established PARs. The end product quality attributes were within their drug substance specifications. The probability generated with the Bayesian approach was also used as a tool to assess CPP deviations. This approach can be extended to develop other production process characterization and quantify a reliable operating region. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:799-812, 2016.
Bayesian evidence computation for model selection in non-linear geoacoustic inference problems.
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.
Estimation of incident clearance times using Bayesian Networks approach.
Ozbay, Kaan; Noyan, Nebahat
2006-05-01
Effective incident management requires a full understanding of various characteristics of incidents to accurately estimate incident durations and to help make more efficient decisions to reduce the impact of non-recurring congestion due to these accidents. Our goal is thus to have a comprehensive and clear description of incident clearance patterns and to represent these patterns with formalisms based on Bayesian Networks (BNs). BNs can be used to create dynamic incident duration estimation trees that can be extracted in the presence of a real incident for which data might only be partially available. This capability will enable traffic operators to create case-specific incident management strategies in the presence of incomplete information. In this paper, we employ a unique database created using incident data collected in Northern Virginia. This database is then used to demonstrate the advantages of employing BNs as a powerful modeling and analysis tool especially due to their ability to consider the stochastic variations of the data and to allow bi-directional induction in decision-making. In addition to the presentation of the basic theory behind BNs in the context of our problem and the validation of our estimation results, the dependency relations among all variables in the estimated BN that can be used for both quantitative and qualitative analysis are also discussed in detail.
Adaptive Methods within a Sequential Bayesian Approach for Structural Health Monitoring
NASA Astrophysics Data System (ADS)
Huff, Daniel W.
Structural integrity is an important characteristic of performance for critical components used in applications such as aeronautics, materials, construction and transportation. When appraising the structural integrity of these components, evaluation methods must be accurate. In addition to possessing capability to perform damage detection, the ability to monitor the level of damage over time can provide extremely useful information in assessing the operational worthiness of a structure and in determining whether the structure should be repaired or removed from service. In this work, a sequential Bayesian approach with active sensing is employed for monitoring crack growth within fatigue-loaded materials. The monitoring approach is based on predicting crack damage state dynamics and modeling crack length observations. Since fatigue loading of a structural component can change while in service, an interacting multiple model technique is employed to estimate probabilities of different loading modes and incorporate this information in the crack length estimation problem. For the observation model, features are obtained from regions of high signal energy in the time-frequency plane and modeled for each crack length damage condition. Although this observation model approach exhibits high classification accuracy, the resolution characteristics can change depending upon the extent of the damage. Therefore, several different transmission waveforms and receiver sensors are considered to create multiple modes for making observations of crack damage. Resolution characteristics of the different observation modes are assessed using a predicted mean squared error criterion and observations are obtained using the predicted, optimal observation modes based on these characteristics. Calculation of the predicted mean square error metric can be computationally intensive, especially if performed in real time, and an approximation method is proposed. With this approach, the real time
Modeling Unreliable Observations in Bayesian Networks by Credal Networks
NASA Astrophysics Data System (ADS)
Antonucci, Alessandro; Piatti, Alberto
Bayesian networks are probabilistic graphical models widely employed in AI for the implementation of knowledge-based systems. Standard inference algorithms can update the beliefs about a variable of interest in the network after the observation of some other variables. This is usually achieved under the assumption that the observations could reveal the actual states of the variables in a fully reliable way. We propose a procedure for a more general modeling of the observations, which allows for updating beliefs in different situations, including various cases of unreliable, incomplete, uncertain and also missing observations. This is achieved by augmenting the original Bayesian network with a number of auxiliary variables corresponding to the observations. For a flexible modeling of the observational process, the quantification of the relations between these auxiliary variables and those of the original Bayesian network is done by credal sets, i.e., convex sets of probability mass functions. Without any lack of generality, we show how this can be done by simply estimating the bounds of likelihoods of the observations for the different values of the observed variables. Overall, the Bayesian network is transformed into a credal network, for which a standard updating problem has to be solved. Finally, a number of transformations that might simplify the updating of the resulting credal network is provided.
Empirical evaluation of scoring functions for Bayesian network model selection.
Liu, Zhifa; Malone, Brandon; Yuan, Changhe
2012-01-01
In this work, we empirically evaluate the capability of various scoring functions of Bayesian networks for recovering true underlying structures. Similar investigations have been carried out before, but they typically relied on approximate learning algorithms to learn the network structures. The suboptimal structures found by the approximation methods have unknown quality and may affect the reliability of their conclusions. Our study uses an optimal algorithm to learn Bayesian network structures from datasets generated from a set of gold standard Bayesian networks. Because all optimal algorithms always learn equivalent networks, this ensures that only the choice of scoring function affects the learned networks. Another shortcoming of the previous studies stems from their use of random synthetic networks as test cases. There is no guarantee that these networks reflect real-world data. We use real-world data to generate our gold-standard structures, so our experimental design more closely approximates real-world situations. A major finding of our study suggests that, in contrast to results reported by several prior works, the Minimum Description Length (MDL) (or equivalently, Bayesian information criterion (BIC)) consistently outperforms other scoring functions such as Akaike's information criterion (AIC), Bayesian Dirichlet equivalence score (BDeu), and factorized normalized maximum likelihood (fNML) in recovering the underlying Bayesian network structures. We believe this finding is a result of using both datasets generated from real-world applications rather than from random processes used in previous studies and learning algorithms to select high-scoring structures rather than selecting random models. Other findings of our study support existing work, e.g., large sample sizes result in learning structures closer to the true underlying structure; the BDeu score is sensitive to the parameter settings; and the fNML performs pretty well on small datasets. We also
Empirical evaluation of scoring functions for Bayesian network model selection
2012-01-01
In this work, we empirically evaluate the capability of various scoring functions of Bayesian networks for recovering true underlying structures. Similar investigations have been carried out before, but they typically relied on approximate learning algorithms to learn the network structures. The suboptimal structures found by the approximation methods have unknown quality and may affect the reliability of their conclusions. Our study uses an optimal algorithm to learn Bayesian network structures from datasets generated from a set of gold standard Bayesian networks. Because all optimal algorithms always learn equivalent networks, this ensures that only the choice of scoring function affects the learned networks. Another shortcoming of the previous studies stems from their use of random synthetic networks as test cases. There is no guarantee that these networks reflect real-world data. We use real-world data to generate our gold-standard structures, so our experimental design more closely approximates real-world situations. A major finding of our study suggests that, in contrast to results reported by several prior works, the Minimum Description Length (MDL) (or equivalently, Bayesian information criterion (BIC)) consistently outperforms other scoring functions such as Akaike's information criterion (AIC), Bayesian Dirichlet equivalence score (BDeu), and factorized normalized maximum likelihood (fNML) in recovering the underlying Bayesian network structures. We believe this finding is a result of using both datasets generated from real-world applications rather than from random processes used in previous studies and learning algorithms to select high-scoring structures rather than selecting random models. Other findings of our study support existing work, e.g., large sample sizes result in learning structures closer to the true underlying structure; the BDeu score is sensitive to the parameter settings; and the fNML performs pretty well on small datasets. We also
Assessment of uncertainty in chemical models by Bayesian probabilities: Why, when, how?
NASA Astrophysics Data System (ADS)
Sahlin, Ullrika
2015-07-01
A prediction of a chemical property or activity is subject to uncertainty. Which type of uncertainties to consider, whether to account for them in a differentiated manner and with which methods, depends on the practical context. In chemical modelling, general guidance of the assessment of uncertainty is hindered by the high variety in underlying modelling algorithms, high-dimensionality problems, the acknowledgement of both qualitative and quantitative dimensions of uncertainty, and the fact that statistics offers alternative principles for uncertainty quantification. Here, a view of the assessment of uncertainty in predictions is presented with the aim to overcome these issues. The assessment sets out to quantify uncertainty representing error in predictions and is based on probability modelling of errors where uncertainty is measured by Bayesian probabilities. Even though well motivated, the choice to use Bayesian probabilities is a challenge to statistics and chemical modelling. Fully Bayesian modelling, Bayesian meta-modelling and bootstrapping are discussed as possible approaches. Deciding how to assess uncertainty is an active choice, and should not be constrained by traditions or lack of validated and reliable ways of doing it.
Bayesian state space models for dynamic genetic network construction across multiple tissues.
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 Two-Step Bayesian Approach for Propensity Score Analysis: Simulations and Case Study.
Kaplan, David; Chen, Jianshen
2012-07-01
A two-step Bayesian propensity score approach is introduced that incorporates prior information in the propensity score equation and outcome equation without the problems associated with simultaneous Bayesian propensity score approaches. The corresponding variance estimators are also provided. The two-step Bayesian propensity score is provided for three methods of implementation: propensity score stratification, weighting, and optimal full matching. Three simulation studies and one case study are presented to elaborate the proposed two-step Bayesian propensity score approach. Results of the simulation studies reveal that greater precision in the propensity score equation yields better recovery of the frequentist-based treatment effect. A slight advantage is shown for the Bayesian approach in small samples. Results also reveal that greater precision around the wrong treatment effect can lead to seriously distorted results. However, greater precision around the correct treatment effect parameter yields quite good results, with slight improvement seen with greater precision in the propensity score equation. A comparison of coverage rates for the conventional frequentist approach and proposed Bayesian approach is also provided. The case study reveals that credible intervals are wider than frequentist confidence intervals when priors are non-informative.
Bayesian modeling of temporal dependence in large sparse contingency tables
Kunihama, Tsuyoshi; Dunson, David B.
2013-01-01
In many applications, it is of interest to study trends over time in relationships among categorical variables, such as age group, ethnicity, religious affiliation, political party and preference for particular policies. At each time point, a sample of individuals provide responses to a set of questions, with different individuals sampled at each time. In such settings, there tends to be abundant missing data and the variables being measured may change over time. At each time point, one obtains a large sparse contingency table, with the number of cells often much larger than the number of individuals being surveyed. To borrow information across time in modeling large sparse contingency tables, we propose a Bayesian autoregressive tensor factorization approach. The proposed model relies on a probabilistic Parafac factorization of the joint pmf characterizing the categorical data distribution at each time point, with autocorrelation included across times. Efficient computational methods are developed relying on MCMC. The methods are evaluated through simulation examples and applied to social survey data. PMID:24482548
NASA Technical Reports Server (NTRS)
He, Yuning
2015-01-01
The behavior of complex aerospace systems is governed by numerous parameters. For safety analysis it is important to understand how the system behaves with respect to these parameter values. In particular, understanding the boundaries between safe and unsafe regions is of major importance. In this paper, we describe a hierarchical Bayesian statistical modeling approach for the online detection and characterization of such boundaries. Our method for classification with active learning uses a particle filter-based model and a boundary-aware metric for best performance. From a library of candidate shapes incorporated with domain expert knowledge, the location and parameters of the boundaries are estimated using advanced Bayesian modeling techniques. The results of our boundary analysis are then provided in a form understandable by the domain expert. We illustrate our approach using a simulation model of a NASA neuro-adaptive flight control system, as well as a system for the detection of separation violations in the terminal airspace.
Probabilistic detection of volcanic ash using a Bayesian approach
Mackie, Shona; Watson, Matthew
2014-01-01
Airborne volcanic ash can pose a hazard to aviation, agriculture, and both human and animal health. It is therefore important that ash clouds are monitored both day and night, even when they travel far from their source. Infrared satellite data provide perhaps the only means of doing this, and since the hugely expensive ash crisis that followed the 2010 Eyjafjalljökull eruption, much research has been carried out into techniques for discriminating ash in such data and for deriving key properties. Such techniques are generally specific to data from particular sensors, and most approaches result in a binary classification of pixels into “ash” and “ash free” classes with no indication of the classification certainty for individual pixels. Furthermore, almost all operational methods rely on expert-set thresholds to determine what constitutes “ash” and can therefore be criticized for being subjective and dependent on expertise that may not remain with an institution. Very few existing methods exploit available contemporaneous atmospheric data to inform the detection, despite the sensitivity of most techniques to atmospheric parameters. The Bayesian method proposed here does exploit such data and gives a probabilistic, physically based classification. We provide an example of the method's implementation for a scene containing both land and sea observations, and a large area of desert dust (often misidentified as ash by other methods). The technique has already been successfully applied to other detection problems in remote sensing, and this work shows that it will be a useful and effective tool for ash detection. Key Points Presentation of a probabilistic volcanic ash detection scheme Method for calculation of probability density function for ash observations Demonstration of a remote sensing technique for monitoring volcanic ash hazards PMID:25844278
Modelling the presence of disease under spatial misalignment using Bayesian latent Gaussian models.
Barber, Xavier; Conesa, David; Lladosa, Silvia; López-Quílez, Antonio
2016-04-18
Modelling patterns of the spatial incidence of diseases using local environmental factors has been a growing problem in the last few years. Geostatistical models have become popular lately because they allow estimating and predicting the underlying disease risk and relating it with possible risk factors. Our approach to these models is based on the fact that the presence/absence of a disease can be expressed with a hierarchical Bayesian spatial model that incorporates the information provided by the geographical and environmental characteristics of the region of interest. Nevertheless, our main interest here is to tackle the misalignment problem arising when information about possible covariates are partially (or totally) different than those of the observed locations and those in which we want to predict. As a result, we present two different models depending on the fact that there is uncertainty on the covariates or not. In both cases, Bayesian inference on the parameters and prediction of presence/absence in new locations are made by considering the model as a latent Gaussian model, which allows the use of the integrated nested Laplace approximation. In particular, the spatial effect is implemented with the stochastic partial differential equation approach. The methodology is evaluated on the presence of the Fasciola hepatica in Galicia, a North-West region of Spain.
Bayesian Proteoform Modeling Improves Protein Quantification of Global Proteomic Measurements
Webb-Robertson, Bobbie-Jo M.; Matzke, Melissa M.; Datta, Susmita; Payne, Samuel H.; Kang, Jiyun; Bramer, Lisa M.; Nicora, Carrie D.; Shukla, Anil K.; Metz, Thomas O.; Rodland, Karin D.; Smith, Richard D.; Tardiff, Mark F.; McDermott, Jason E.; Pounds, Joel G.; Waters, Katrina M.
2014-12-01
As the capability of mass spectrometry-based proteomics has matured, tens of thousands of peptides can be measured simultaneously, which has the benefit of offering a systems view of protein expression. However, a major challenge is that with an increase in throughput, protein quantification estimation from the native measured peptides has become a computational task. A limitation to existing computationally-driven protein quantification methods is that most ignore protein variation, such as alternate splicing of the RNA transcript and post-translational modifications or other possible proteoforms, which will affect a significant fraction of the proteome. The consequence of this assumption is that statistical inference at the protein level, and consequently downstream analyses, such as network and pathway modeling, have only limited power for biomarker discovery. Here, we describe a Bayesian model (BP-Quant) that uses statistically derived peptides signatures to identify peptides that are outside the dominant pattern, or the existence of multiple over-expressed patterns to improve relative protein abundance estimates. It is a research-driven approach that utilizes the objectives of the experiment, defined in the context of a standard statistical hypothesis, to identify a set of peptides exhibiting similar statistical behavior relating to a protein. This approach infers that changes in relative protein abundance can be used as a surrogate for changes in function, without necessarily taking into account the effect of differential post-translational modifications, processing, or splicing in altering protein function. We verify the approach using a dilution study from mouse plasma samples and demonstrate that BP-Quant achieves similar accuracy as the current state-of-the-art methods at proteoform identification with significantly better specificity. BP-Quant is available as a MatLab ® and R packages at https://github.com/PNNL-Comp-Mass-Spec/BP-Quant.
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 ...
Zhang, Nien Fan; Silver, Richard M; Zhou, Hui; Barnes, Bryan M
2012-09-01
Recently, there has been significant research investigating new optical technologies for dimensional metrology of features 22 nm in critical dimension and smaller. When modeling optical measurements, a library of curves is assembled through the simulation of a multidimensional parameter space. A nonlinear regression routine described in this paper is then used to identify an optimum set of parameters that yields the closest experiment-to-theory agreement. However, parametric correlation, measurement noise, and model inaccuracy all lead to measurement uncertainty in the fitting process for optical critical dimension measurements. To improve the optical measurements, other techniques such as atomic force microscopy and scanning electronic microscopy can also be used to provide supplemental a priori information. In this paper, a Bayesian statistical approach is proposed to allow the combination of different measurement techniques that are based on different physical measurements. The effect of this hybrid metrology approach will be shown to reduce the uncertainties of the parameter estimators.
Number-knower levels in young children: insights from Bayesian modeling.
Lee, Michael D; Sarnecka, Barbara W
2011-09-01
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, the knower-levels theory, is basically a "stage" theory involving real conceptual change. The other, the approximate-meanings theory, assumes that the child's conceptual knowledge is relatively constant, although performance improves over time. In the second extension, the model is used to ask whether the same latent psychological variable (a child's number-knower level) can simultaneously account for behavior on two tasks (the Give-N task and the Fast-Cards task) with different performance demands. Together, these two demonstrations show the potential of the Bayesian modeling approach to improve our understanding of the development of human cognition.
Bayesian inference for kinetic models of biotransformation using a generalized rate equation.
Ying, Shanshan; Zhang, Jiangjiang; Zeng, Lingzao; Shi, Jiachun; Wu, Laosheng
2017-03-06
Selecting proper rate equations for the kinetic models is essential to quantify biotransformation processes in the environment. Bayesian model selection method can be used to evaluate the candidate models. However, comparisons of all plausible models can result in high computational cost, while limiting the number of candidate models may lead to biased results. In this work, we developed an integrated Bayesian method to simultaneously perform model selection and parameter estimation by using a generalized rate equation. In the approach, the model hypotheses were represented by discrete parameters and the rate constants were represented by continuous parameters. Then Bayesian inference of the kinetic models was solved by implementing Markov Chain Monte Carlo simulation for parameter estimation with the mixed (i.e., discrete and continuous) priors. The validity of this approach was illustrated through a synthetic case and a nitrogen transformation experimental study. It showed that our method can successfully identify the plausible models and parameters, as well as uncertainties therein. Thus this method can provide a powerful tool to reveal more insightful information for the complex biotransformation processes.
Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.
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.
Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models
NASA Astrophysics Data System (ADS)
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.
Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models
Daunizeau, J.; Friston, K.J.; Kiebel, S.J.
2009-01-01
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. PMID:19862351
Integrated survival analysis using an event-time approach in a Bayesian framework
Walsh, Daniel P.; Dreitz, VJ; Heisey, Dennis M.
2015-01-01
Event-time or continuous-time statistical approaches have been applied throughout the biostatistical literature and have led to numerous scientific advances. However, these techniques have traditionally relied on knowing failure times. This has limited application of these analyses, particularly, within the ecological field where fates of marked animals may be unknown. To address these limitations, we developed an integrated approach within a Bayesian framework to estimate hazard rates in the face of unknown fates. We combine failure/survival times from individuals whose fates are known and times of which are interval-censored with information from those whose fates are unknown, and model the process of detecting animals with unknown fates. This provides the foundation for our integrated model and permits necessary parameter estimation. We provide the Bayesian model, its derivation, and use simulation techniques to investigate the properties and performance of our approach under several scenarios. Lastly, we apply our estimation technique using a piece-wise constant hazard function to investigate the effects of year, age, chick size and sex, sex of the tending adult, and nesting habitat on mortality hazard rates of the endangered mountain plover (Charadrius montanus) chicks. Traditional models were inappropriate for this analysis because fates of some individual chicks were unknown due to failed radio transmitters. Simulations revealed biases of posterior mean estimates were minimal (≤ 4.95%), and posterior distributions behaved as expected with RMSE of the estimates decreasing as sample sizes, detection probability, and survival increased. We determined mortality hazard rates for plover chicks were highest at <5 days old and were lower for chicks with larger birth weights and/or whose nest was within agricultural habitats. Based on its performance, our approach greatly expands the range of problems for which event-time analyses can be used by eliminating the
Integrated survival analysis using an event-time approach in a Bayesian framework
Walsh, Daniel P; Dreitz, Victoria J; Heisey, Dennis M
2015-01-01
Event-time or continuous-time statistical approaches have been applied throughout the biostatistical literature and have led to numerous scientific advances. However, these techniques have traditionally relied on knowing failure times. This has limited application of these analyses, particularly, within the ecological field where fates of marked animals may be unknown. To address these limitations, we developed an integrated approach within a Bayesian framework to estimate hazard rates in the face of unknown fates. We combine failure/survival times from individuals whose fates are known and times of which are interval-censored with information from those whose fates are unknown, and model the process of detecting animals with unknown fates. This provides the foundation for our integrated model and permits necessary parameter estimation. We provide the Bayesian model, its derivation, and use simulation techniques to investigate the properties and performance of our approach under several scenarios. Lastly, we apply our estimation technique using a piece-wise constant hazard function to investigate the effects of year, age, chick size and sex, sex of the tending adult, and nesting habitat on mortality hazard rates of the endangered mountain plover (Charadrius montanus) chicks. Traditional models were inappropriate for this analysis because fates of some individual chicks were unknown due to failed radio transmitters. Simulations revealed biases of posterior mean estimates were minimal (≤ 4.95%), and posterior distributions behaved as expected with RMSE of the estimates decreasing as sample sizes, detection probability, and survival increased. We determined mortality hazard rates for plover chicks were highest at <5 days old and were lower for chicks with larger birth weights and/or whose nest was within agricultural habitats. Based on its performance, our approach greatly expands the range of problems for which event-time analyses can be used by eliminating the
The Bayesian approach to reporting GSR analysis results: some first-hand experiences
NASA Astrophysics Data System (ADS)
Charles, Sebastien; Nys, Bart
2010-06-01
The use of Bayesian principles in the reporting of forensic findings has been a matter of interest for some years. Recently, also the GSR community is gradually exploring the advantages of this method, or rather approach, for writing reports. Since last year, our GSR group is adapting reporting procedures to the use of Bayesian principles. The police and magistrates find the reports more directly accessible and useful in their part of the criminal investigation. In the lab we find that, through applying the Bayesian principles, unnecessary analyses can be eliminated and thus time can be freed on the instruments.
Predicting individual brain functional connectivity using a Bayesian hierarchical model.
Dai, Tian; Guo, Ying
2017-02-15
Network-oriented analysis of functional magnetic resonance imaging (fMRI), especially resting-state fMRI, has revealed important association between abnormal connectivity and brain disorders such as schizophrenia, major depression and Alzheimer's disease. Imaging-based brain connectivity measures have become a useful tool for investigating the pathophysiology, progression and treatment response of psychiatric disorders and neurodegenerative diseases. Recent studies have started to explore the possibility of using functional neuroimaging to help predict disease progression and guide treatment selection for individual patients. These studies provide the impetus to develop statistical methodology that would help provide predictive information on disease progression-related or treatment-related changes in neural connectivity. To this end, we propose a prediction method based on Bayesian hierarchical model that uses individual's baseline fMRI scans, coupled with relevant subject characteristics, to predict the individual's future functional connectivity. A key advantage of the proposed method is that it can improve the accuracy of individualized prediction of connectivity by combining information from both group-level connectivity patterns that are common to subjects with similar characteristics as well as individual-level connectivity features that are particular to the specific subject. Furthermore, our method also offers statistical inference tools such as predictive intervals that help quantify the uncertainty or variability of the predicted outcomes. The proposed prediction method could be a useful approach to predict the changes in individual patient's brain connectivity with the progression of a disease. It can also be used to predict a patient's post-treatment brain connectivity after a specified treatment regimen. Another utility of the proposed method is that it can be applied to test-retest imaging data to develop a more reliable estimator for individual
Bayesian Hidden Markov Modeling of Array CGH Data.
Guha, Subharup; Li, Yi; Neuberg, Donna
2008-06-01
Genomic alterations have been linked to the development and progression of cancer. The technique of comparative genomic hybridization (CGH) yields data consisting of fluorescence intensity ratios of test and reference DNA samples. The intensity ratios provide information about the number of copies in DNA. Practical issues such as the contamination of tumor cells in tissue specimens and normalization errors necessitate the use of statistics for learning about the genomic alterations from array CGH data. As increasing amounts of array CGH data become available, there is a growing need for automated algorithms for characterizing genomic profiles. Specifically, there is a need for algorithms that can identify gains and losses in the number of copies based on statistical considerations, rather than merely detect trends in the data.We adopt a Bayesian approach, relying on the hidden Markov model to account for the inherent dependence in the intensity ratios. Posterior inferences are made about gains and losses in copy number. Localized amplifications (associated with oncogene mutations) and deletions (associated with mutations of tumor suppressors) are identified using posterior probabilities. Global trends such as extended regions of altered copy number are detected. Because the posterior distribution is analytically intractable, we implement a Metropolis-within-Gibbs algorithm for efficient simulation-based inference. Publicly available data on pancreatic adenocarcinoma, glioblastoma multiforme, and breast cancer are analyzed, and comparisons are made with some widely used algorithms to illustrate the reliability and success of the technique.
Estimating seabed scattering mechanisms via Bayesian model selection.
Steininger, Gavin; Dosso, Stan E; Holland, Charles W; Dettmer, Jan
2014-10-01
A quantitative inversion procedure is developed and applied to determine the dominant scattering mechanism (surface roughness and/or volume scattering) from seabed scattering-strength data. The classification system is based on trans-dimensional Bayesian inversion with the deviance information criterion used to select the dominant scattering mechanism. Scattering is modeled using first-order perturbation theory as due to one of three mechanisms: Interface scattering from a rough seafloor, volume scattering from a heterogeneous sediment layer, or mixed scattering combining both interface and volume scattering. The classification system is applied to six simulated test cases where it correctly identifies the true dominant scattering mechanism as having greater support from the data in five cases; the remaining case is indecisive. The approach is also applied to measured backscatter-strength data where volume scattering is determined as the dominant scattering mechanism. Comparison of inversion results with core data indicates the method yields both a reasonable volume heterogeneity size distribution and a good estimate of the sub-bottom depths at which scatterers occur.
Nursing Home Care Quality: Insights from a Bayesian Network Approach
ERIC Educational Resources Information Center
Goodson, Justin; Jang, Wooseung; Rantz, Marilyn
2008-01-01
Purpose: The purpose of this research is twofold. The first purpose is to utilize a new methodology (Bayesian networks) for aggregating various quality indicators to measure the overall quality of care in nursing homes. The second is to provide new insight into the relationships that exist among various measures of quality and how such measures…
Bayesian model updating using incomplete modal data without mode matching
NASA Astrophysics Data System (ADS)
Sun, Hao; Büyüköztürk, Oral
2016-04-01
This study investigates a new probabilistic strategy for model updating using incomplete modal data. A hierarchical Bayesian inference is employed to model the updating problem. A Markov chain Monte Carlo technique with adaptive random-work steps is used to draw parameter samples for uncertainty quantification. Mode matching between measured and predicted modal quantities is not required through model reduction. We employ an iterated improved reduced system technique for model reduction. The reduced model retains the dynamic features as close as possible to those of the model before reduction. The proposed algorithm is finally validated by an experimental example.
A Bayesian Approach to Identifying New Risk Factors for Dementia
Wen, Yen-Hsia; Wu, Shihn-Sheng; Lin, Chun-Hung Richard; Tsai, Jui-Hsiu; Yang, Pinchen; Chang, Yang-Pei; Tseng, Kuan-Hua
2016-01-01
Abstract Dementia is one of the most disabling and burdensome health conditions worldwide. In this study, we identified new potential risk factors for dementia from nationwide longitudinal population-based data by using Bayesian statistics. We first tested the consistency of the results obtained using Bayesian statistics with those obtained using classical frequentist probability for 4 recognized risk factors for dementia, namely severe head injury, depression, diabetes mellitus, and vascular diseases. Then, we used Bayesian statistics to verify 2 new potential risk factors for dementia, namely hearing loss and senile cataract, determined from the Taiwan's National Health Insurance Research Database. We included a total of 6546 (6.0%) patients diagnosed with dementia. We observed older age, female sex, and lower income as independent risk factors for dementia. Moreover, we verified the 4 recognized risk factors for dementia in the older Taiwanese population; their odds ratios (ORs) ranged from 3.469 to 1.207. Furthermore, we observed that hearing loss (OR = 1.577) and senile cataract (OR = 1.549) were associated with an increased risk of dementia. We found that the results obtained using Bayesian statistics for assessing risk factors for dementia, such as head injury, depression, DM, and vascular diseases, were consistent with those obtained using classical frequentist probability. Moreover, hearing loss and senile cataract were found to be potential risk factors for dementia in the older Taiwanese population. Bayesian statistics could help clinicians explore other potential risk factors for dementia and for developing appropriate treatment strategies for these patients. PMID:27227925
Robust video object tracking via Bayesian model averaging-based feature fusion
NASA Astrophysics Data System (ADS)
Dai, Yi; Liu, Bin
2016-08-01
We are concerned with tracking an object of interest in a video stream. We propose an algorithm that is robust against occlusion, the presence of confusing colors, abrupt changes in the object features and changes in scale. We develop the algorithm within a Bayesian modeling framework. The state-space model is used for capturing the temporal correlation in the sequence of frame images by modeling the underlying dynamics of the tracking system. The Bayesian model averaging (BMA) strategy is proposed for fusing multiclue information in the observations. Any number of object features is allowed to be involved in the proposed framework. Every feature represents one source of information to be fused and is associated with an observation model. The state inference is performed by employing the particle filter methods. In comparison with the related approaches, the BMA-based tracker is shown to have robustness, expressivity, and comprehensibility.
Bayesian Estimation of Categorical Dynamic Factor Models
ERIC Educational Resources Information Center
Zhang, Zhiyong; Nesselroade, John R.
2007-01-01
Dynamic factor models have been used to analyze continuous time series behavioral data. We extend 2 main dynamic factor model variations--the direct autoregressive factor score (DAFS) model and the white noise factor score (WNFS) model--to categorical DAFS and WNFS models in the framework of the underlying variable method and illustrate them with…
Fu, Zhibiao; Leighton, Julie; Cheng, Aili; Appelbaum, Edward; Aon, Juan C
2012-07-01
Various approaches have been applied to optimize biological product fermentation processes and define design space. In this article, we present a stepwise approach to optimize a Saccharomyces cerevisiae fermentation process through risk assessment analysis, statistical design of experiments (DoE), and multivariate Bayesian predictive approach. The critical process parameters (CPPs) were first identified through a risk assessment. The response surface for each attribute was modeled using the results from the DoE study with consideration given to interactions between CPPs. A multivariate Bayesian predictive approach was then used to identify the region of process operating conditions where all attributes met their specifications simultaneously. The model prediction was verified by twelve consistency runs where all batches achieved broth titer more than 1.53 g/L of broth and quality attributes within the expected ranges. The calculated probability was used to define the reliable operating region. To our knowledge, this is the first case study to implement the multivariate Bayesian predictive approach to the process optimization for the industrial application and its corresponding verification at two different production scales. This approach can be extended to other fermentation process optimizations and reliable operating region quantitation.
A hierarchical Bayesian-MAP approach to inverse problems in imaging
NASA Astrophysics Data System (ADS)
Raj, Raghu G.
2016-07-01
We present a novel approach to inverse problems in imaging based on a hierarchical Bayesian-MAP (HB-MAP) formulation. In this paper we specifically focus on the difficult and basic inverse problem of multi-sensor (tomographic) imaging wherein the source object of interest is viewed from multiple directions by independent sensors. Given the measurements recorded by these sensors, the problem is to reconstruct the image (of the object) with a high degree of fidelity. We employ a probabilistic graphical modeling extension of the compound Gaussian distribution as a global image prior into a hierarchical Bayesian inference procedure. Since the prior employed by our HB-MAP algorithm is general enough to subsume a wide class of priors including those typically employed in compressive sensing (CS) algorithms, HB-MAP algorithm offers a vehicle to extend the capabilities of current CS algorithms to include truly global priors. After rigorously deriving the regression algorithm for solving our inverse problem from first principles, we demonstrate the performance of the HB-MAP algorithm on Monte Carlo trials and on real empirical data (natural scenes). In all cases we find that our algorithm outperforms previous approaches in the literature including filtered back-projection and a variety of state-of-the-art CS algorithms. We conclude with directions of future research emanating from this work.
Bayesian Safety Risk Modeling of Human-Flightdeck Automation Interaction
NASA Technical Reports Server (NTRS)
Ancel, Ersin; Shih, Ann T.
2015-01-01
Usage of automatic systems in airliners has increased fuel efficiency, added extra capabilities, enhanced safety and reliability, as well as provide improved passenger comfort since its introduction in the late 80's. However, original automation benefits, including reduced flight crew workload, human errors or training requirements, were not achieved as originally expected. Instead, automation introduced new failure modes, redistributed, and sometimes increased workload, brought in new cognitive and attention demands, and increased training requirements. Modern airliners have numerous flight modes, providing more flexibility (and inherently more complexity) to the flight crew. However, the price to pay for the increased flexibility is the need for increased mode awareness, as well as the need to supervise, understand, and predict automated system behavior. Also, over-reliance on automation is linked to manual flight skill degradation and complacency in commercial pilots. As a result, recent accidents involving human errors are often caused by the interactions between humans and the automated systems (e.g., the breakdown in man-machine coordination), deteriorated manual flying skills, and/or loss of situational awareness due to heavy dependence on automated systems. This paper describes the development of the increased complexity and reliance on automation baseline model, named FLAP for FLightdeck Automation Problems. The model development process starts with a comprehensive literature review followed by the construction of a framework comprised of high-level causal factors leading to an automation-related flight anomaly. The framework was then converted into a Bayesian Belief Network (BBN) using the Hugin Software v7.8. The effects of automation on flight crew are incorporated into the model, including flight skill degradation, increased cognitive demand and training requirements along with their interactions. Besides flight crew deficiencies, automation system
The Bayesian approximation error approach for electrical impedance tomography—experimental results
NASA Astrophysics Data System (ADS)
Nissinen, A.; Heikkinen, L. M.; Kaipio, J. P.
2008-01-01
Inverse problems can be characterized as problems that tolerate measurement and modelling errors poorly. While the measurement error issue has been widely considered as a solved problem, the modelling errors have remained largely untreated. The approximation and modelling errors can, however, be argued to dominate the measurement errors in most applications. There are several applications in which the temporal and memory requirements dictate that the computational complexity of the forward solver be radically reduced. For example, in process tomography the reconstructions have to be carried out typically in a few tens of milliseconds. Recently, a Bayesian approach for the treatment of approximation and modelling errors for inverse problems has been proposed. This approach has proven to work well in several classes of problems, but the approach has not been verified in any problem with real data. In this paper, we study two different types of modelling errors in the case of electrical impedance tomography: one related to model reduction and one concerning partially unknown geometry. We show that the approach is also feasible in practice and may facilitate the reduction of the computational complexity of the nonlinear EIT problem at least by an order of magnitude.
Hierarchical Bayesian approaches for detecting inconsistency in network meta-analysis.
Zhao, Hong; Hodges, James S; Ma, Haijun; Jiang, Qi; Carlin, Bradley P
2016-09-10
Network meta-analysis (NMA), also known as multiple treatment comparisons, is commonly used to incorporate direct and indirect evidence comparing treatments. With recent advances in methods and software, Bayesian approaches to NMA have become quite popular and allow models of previously unanticipated complexity. However, when direct and indirect evidence differ in an NMA, the model is said to suffer from inconsistency. Current inconsistency detection in NMA is usually based on contrast-based (CB) models; however, this approach has certain limitations. In this work, we propose an arm-based random effects model, where we detect discrepancy of direct and indirect evidence for comparing two treatments using the fixed effects in the model while flagging extreme trials using the random effects. We define discrepancy factors to characterize evidence of inconsistency for particular treatment comparisons, which is novel in NMA research. Our approaches permit users to address issues previously tackled via CB models. We compare sources of inconsistency identified by our approach and existing loop-based CB methods using real and simulated datasets and demonstrate that our methods can offer powerful inconsistency detection. Copyright © 2016 John Wiley & Sons, Ltd.
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.
Wu, Wei; Chen, Zhe; Gao, Shangkai; Brown, Emery N.
2011-01-01
Multichannel electroencephalography (EEG) offers a non-invasive tool to explore spatio-temporal dynamics of brain activity. With EEG recordings consisting of multiple trials, traditional signal processing approaches that ignore inter-trial variability in the data may fail to accurately estimate the underlying spatio-temporal brain patterns. Moreover, precise characterization of such inter-trial variability per se can be of high scientific value in establishing the relationship between brain activity and behavior. In this paper, a statistical modeling framework is introduced for learning spatiotemporal decomposition of multiple-trial EEG data recorded under two contrasting experimental conditions. By modeling the variance of source signals as random variables varying across trials, the proposed two-stage hierarchical Bayesian model is able to capture inter-trial amplitude variability in the data in a sparse way where a parsimonious representation of the data can be obtained. A variational Bayesian (VB) algorithm is developed for statistical inference of the hierarchical model. The efficacy of the proposed modeling framework is validated with the analysis of both synthetic and real EEG data. In the simulation study we show that even at low signal-to-noise ratios our approach is able to recover with high precision the underlying spatiotemporal patterns and the evolution of source amplitude across trials; on two brain-computer interface (BCI) data sets we show that our VB algorithm can extract physiologically meaningful spatio-temporal patterns and make more accurate predictions than other two widely used algorithms: the common spatial patterns (CSP) algorithm and the Infomax algorithm for independent component analysis (ICA). The results demonstrate that our statistical modeling framework can serve as a powerful tool for extracting brain patterns, characterizing trial-to-trial brain dynamics, and decoding brain states by exploiting useful structures in the data. PMID
RELION: Implementation of a Bayesian approach to cryo-EM structure determination
Scheres, Sjors H.W.
2012-01-01
RELION, for REgularized LIkelihood OptimizatioN, is an open-source computer program for the refinement of macromolecular structures by single-particle analysis of electron cryo-microscopy (cryo-EM) data. Whereas alternative approaches often rely on user expertise for the tuning of parameters, RELION uses a Bayesian approach to infer parameters of a statistical model from the data. This paper describes developments that reduce the computational costs of the underlying maximum a posteriori (MAP) algorithm, as well as statistical considerations that yield new insights into the accuracy with which the relative orientations of individual particles may be determined. A so-called gold-standard Fourier shell correlation (FSC) procedure to prevent overfitting is also described. The resulting implementation yields high-quality reconstructions and reliable resolution estimates with minimal user intervention and at acceptable computational costs. PMID:23000701
A Bayesian Approach for Apparent Inter-plate Coupling in the Central Andes Subduction Zone
NASA Astrophysics Data System (ADS)
Ortega Culaciati, F. H.; Simons, M.; Genrich, J. F.; Galetzka, J.; Comte, D.; Glass, B.; Leiva, C.; Gonzalez, G.; Norabuena, E. O.
2010-12-01
We aim to characterize the extent of apparent plate coupling on the subduction zone megathrust with the eventual goal of understanding spatial variations of fault zone rheology, inferring relationships between apparent coupling and the rupture zone of big earthquakes, as well as the implications for earthquake and tsunami hazard. Unlike previous studies, we approach the problem from a Bayesian perspective, allowing us to completely characterize the model parameter space by searching a posteriori estimates of the range of allowable models instead of seeking a single optimum model. Two important features of the Bayesian approach are the possibility to easily implement any kind of physically plausible a priori information and to perform the inversion without regularization, other than that imposed by the way in which we parameterize the forward model. Adopting a simple kinematic back-slip model and a 3D geometry of the inter-plate contact zone, we can estimate the probability of apparent coupling (Pc) along the plate interface that is consistent with a priori information (e.g., approximate rake of back-slip) and available geodetic measurements. More generally, the Bayesian approach adopted here is applicable to any region and eventually would allow one to evaluate the spatial relationship between various inferred distributions of fault behavior (e.g., seismic rupture, postseismic creep, and apparent interseismic coupling) in a quantifiable manner. We apply this methodology to evaluate the state of apparent inter-seismic coupling in the Chilean-Peruvian subduction margin (12 S - 25 S). As observational constraints, we use previously published horizontal velocities from campaign GPS [Kendrick et al., 2001, 2006] as well as 3 component velocities from a recently established continuous GPS network in the region (CAnTO). We compare results from both joint and independent use of these data sets. We obtain patch like features for Pc with higher values located above 60 km
Theory-Based Bayesian Models of Inductive Inference
2010-06-30
Oxford University Press . 28. Griffiths, T. L. and Tenenbaum, J.B. (2007). Two proposals for causal grammar. In A. Gopnik and L. Schulz (eds.). ( ausal Learning. Oxford University Press . 29. Tenenbaum. J. B.. Kemp, C, Shafto. P. (2007). Theory-based Bayesian models for inductive reasoning. In A. Feeney and E. Heit (eds.). Induction. Cambridge University Press. 30. Goodman, N. D., Tenenbaum, J. B., Griffiths. T. L.. & Feldman, J. (2008). Compositionality in rational analysis: Grammar-based induction for concept
Slice sampling technique in Bayesian extreme of gold price modelling
NASA Astrophysics Data System (ADS)
Rostami, Mohammad; Adam, Mohd Bakri; Ibrahim, Noor Akma; Yahya, Mohamed Hisham
2013-09-01
In this paper, a simulation study of Bayesian extreme values by using Markov Chain Monte Carlo via slice sampling algorithm is implemented. We compared the accuracy of slice sampling with other methods for a Gumbel model. This study revealed that slice sampling algorithm offers more accurate and closer estimates with less RMSE than other methods . Finally we successfully employed this procedure to estimate the parameters of Malaysia extreme gold price from 2000 to 2011.
Prediction and assimilation of surf-zone processes using a Bayesian network: Part I: Forward models
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.
A joint inter- and intrascale statistical model for Bayesian wavelet based image denoising.
Pizurica, Aleksandra; Philips, Wilfried; Lemahieu, Ignace; Acheroy, Marc
2002-01-01
This paper presents a new wavelet-based image denoising method, which extends a "geometrical" Bayesian framework. The new method combines three criteria for distinguishing supposedly useful coefficients from noise: coefficient magnitudes, their evolution across scales and spatial clustering of large coefficients near image edges. These three criteria are combined in a Bayesian framework. The spatial clustering properties are expressed in a prior model. The statistical properties concerning coefficient magnitudes and their evolution across scales are expressed in a joint conditional model. The three main novelties with respect to related approaches are (1) the interscale-ratios of wavelet coefficients are statistically characterized and different local criteria for distinguishing useful coefficients from noise are evaluated, (2) a joint conditional model is introduced, and (3) a novel anisotropic Markov random field prior model is proposed. The results demonstrate an improved denoising performance over related earlier techniques.
Bayesian inference using two-stage Laplace approximation for differential equation models
NASA Astrophysics Data System (ADS)
Dass, Sarat C.; Lee, Jaeyong; Lee, Kyoungjae
2016-11-01
We consider the problem of Bayesian inference for parameters in non-linear regression models whereby the underlying unknown response functions are formed by a set of differential equations. Bayesian methods of inference for unknown parameters rely primarily on the posterior obtained by Bayes rule. For differential equation models, analytic and closed forms for the posterior are not available and one has to resort to approximations. We propose a two-stage Laplace expansion to approximate the marginal likelihood, and hence, the posterior, to obtain an approximate closed form solution. For large sample sizes, the method of inference borrows from non-linear regression theory for maximum likelihood estimates, and is therefore, consistent. Our approach is exact in the limit and does not need the specification of an additional penalty parameter. Examples in this paper include the exponential model and SIR (Susceptible-Infected-Recovered) disease spread model.
Bayesian latent variable models for the analysis of experimental psychology data.
Merkle, Edgar C; Wang, Ting
2016-03-18
In this paper, we address the use of Bayesian factor analysis and structural equation models to draw inferences from experimental psychology data. While such application is non-standard, the models are generally useful for the unified analysis of multivariate data that stem from, e.g., subjects' responses to multiple experimental stimuli. We first review the models and the parameter identification issues inherent in the models. We then provide details on model estimation via JAGS and on Bayes factor estimation. Finally, we use the models to re-analyze experimental data on risky choice, comparing the approach to simpler, alternative methods.
How to Address Measurement Noise in Bayesian Model Averaging
NASA Astrophysics Data System (ADS)
Schöniger, A.; Wöhling, T.; Nowak, W.
2014-12-01
When confronted with the challenge of selecting one out of several competing conceptual models for a specific modeling task, Bayesian model averaging is a rigorous choice. It ranks the plausibility of models based on Bayes' theorem, which yields an optimal trade-off between performance and complexity. With the resulting posterior model probabilities, their individual predictions are combined into a robust weighted average and the overall predictive uncertainty (including conceptual uncertainty) can be quantified. This rigorous framework does, however, not yet explicitly consider statistical significance of measurement noise in the calibration data set. This is a major drawback, because model weights might be instable due to the uncertainty in noisy data, which may compromise the reliability of model ranking. We present a new extension to the Bayesian model averaging framework that explicitly accounts for measurement noise as a source of uncertainty for the weights. This enables modelers to assess the reliability of model ranking for a specific application and a given calibration data set. Also, the impact of measurement noise on the overall prediction uncertainty can be determined. Technically, our extension is built within a Monte Carlo framework. We repeatedly perturb the observed data with random realizations of measurement error. Then, we determine the robustness of the resulting model weights against measurement noise. We quantify the variability of posterior model weights as weighting variance. We add this new variance term to the overall prediction uncertainty analysis within the Bayesian model averaging framework to make uncertainty quantification more realistic and "complete". We illustrate the importance of our suggested extension with an application to soil-plant model selection, based on studies by Wöhling et al. (2013, 2014). Results confirm that noise in leaf area index or evaporation rate observations produces a significant amount of weighting
Eacker, Daniel R; Lukacs, Paul M; Proffitt, Kelly M; Hebblewhite, Mark
2017-02-11
To successfully respond to changing habitat, climate or harvest, managers need to identify the most effective strategies to reverse population trends of declining species and/or manage harvest of game species. A classic approach in conservation biology for the last two decades has been the use of matrix population models to determine the most important vital rates affecting population growth rate (λ), that is, sensitivity. Ecologists quickly realized the critical role of environmental variability in vital rates affecting population growth rate by developing approaches such as life-stage simulation analysis (LSA) that account for both sensitivity and variability of a vital rate. These LSA methods used matrix-population modeling and Monte Carlo simulation methods, but faced challenges in integrating data from different sources, disentangling process and sampling variation, and in their flexibility. Here, we developed a Bayesian integrated population model (IPM) for two populations of a large herbivore, elk (Cervus canadensis) in Montana, USA. We then extended the IPM to evaluate sensitivity in a Bayesian framework. We integrated known-fate survival data from radio-marked adults and juveniles, fecundity data, and population counts in a hierarchical population model that explicitly accounted for process and sampling variance. Next, we tested the prevailing paradigm in large herbivore population ecology that juvenile survival of neonates <90 days old drives λ using our Bayesian LSA approach. In contrast to the prevailing paradigm in large herbivore ecology, we found that adult female survival explained more of the variation in λ than elk calf survival, and that summer and winter elk calf survival periods were nearly equivalent in importance for λ. Our Bayesian IPM improved precision of our vital rate estimates and highlighted discrepancies between count and vital rate data that could refine population monitoring, demonstrating that combining sensitivity analysis
A Bayesian Developmental Approach to Robotic Goal-Based Imitation Learning
Chung, Michael Jae-Yoon; Friesen, Abram L.; Fox, Dieter; Meltzoff, Andrew N.; Rao, Rajesh P. N.
2015-01-01
A fundamental challenge in robotics today is building robots that can learn new skills by observing humans and imitating human actions. We propose a new Bayesian approach to robotic learning by imitation inspired by the developmental hypothesis that children use self-experience to bootstrap the process of intention recognition and goal-based imitation. Our approach allows an autonomous agent to: (i) learn probabilistic models of actions through self-discovery and experience, (ii) utilize these learned models for inferring the goals of human actions, and (iii) perform goal-based imitation for robotic learning and human-robot collaboration. Such an approach allows a robot to leverage its increasing repertoire of learned behaviors to interpret increasingly complex human actions and use the inferred goals for imitation, even when the robot has very different actuators from humans. We demonstrate our approach using two different scenarios: (i) a simulated robot that learns human-like gaze following behavior, and (ii) a robot that learns to imitate human actions in a tabletop organization task. In both cases, the agent learns a probabilistic model of its own actions, and uses this model for goal inference and goal-based imitation. We also show that the robotic agent can use its probabilistic model to seek human assistance when it recognizes that its inferred actions are too uncertain, risky, or impossible to perform, thereby opening the door to human-robot collaboration. PMID:26536366
A Bayesian Developmental Approach to Robotic Goal-Based Imitation Learning.
Chung, Michael Jae-Yoon; Friesen, Abram L; Fox, Dieter; Meltzoff, Andrew N; Rao, Rajesh P N
2015-01-01
A fundamental challenge in robotics today is building robots that can learn new skills by observing humans and imitating human actions. We propose a new Bayesian approach to robotic learning by imitation inspired by the developmental hypothesis that children use self-experience to bootstrap the process of intention recognition and goal-based imitation. Our approach allows an autonomous agent to: (i) learn probabilistic models of actions through self-discovery and experience, (ii) utilize these learned models for inferring the goals of human actions, and (iii) perform goal-based imitation for robotic learning and human-robot collaboration. Such an approach allows a robot to leverage its increasing repertoire of learned behaviors to interpret increasingly complex human actions and use the inferred goals for imitation, even when the robot has very different actuators from humans. We demonstrate our approach using two different scenarios: (i) a simulated robot that learns human-like gaze following behavior, and (ii) a robot that learns to imitate human actions in a tabletop organization task. In both cases, the agent learns a probabilistic model of its own actions, and uses this model for goal inference and goal-based imitation. We also show that the robotic agent can use its probabilistic model to seek human assistance when it recognizes that its inferred actions are too uncertain, risky, or impossible to perform, thereby opening the door to human-robot collaboration.
Bayesian Isotonic Regression Dose-response (BIRD) Model.
Li, Wen; Fu, Haoda
2016-12-21
Understanding dose-response relationship is a crucial step in drug development. There are a few parametric methods to estimate dose-response curves, such as the Emax model and the logistic model. These parametric models are easy to interpret and, hence, widely used. However, these models often require the inclusion of patients on high-dose levels; otherwise, the model parameters cannot be reliably estimated. To have robust estimation, nonparametric models are used. However, these models are not able to estimate certain important clinical parameters, such as ED50 and Emax. Furthermore, in many therapeutic areas, dose-response curves can be assumed as non-decreasing functions. This creates an additional challenge for nonparametric methods. In this paper, we propose a new Bayesian isotonic regression dose-response model which features advantages from both parametric and nonparametric models. The ED50 and Emax can be derived from this model. Simulations are provided to evaluate the Bayesian isotonic regr