Use Of Bayesian Models Research Articles

Exploration of the use of Bayesian modeling of gradients for censored spatiotemporal data from the Deepwater Horizon oil spill

This paper develops a hierarchical framework for identifying spatiotemporal patterns in data with a high degree of censoring using the gradient process. To do this, we impute censored values using a sampling-based inverse CDF method within our Markov chain Monte Carlo algorithm, thereby avoiding burdensome integration and facilitating efficient estimation of other model parameters. We illustrate use of our methodology using a simulated data example, and uncover the danger of simply substituting a space- and time-constant function of the level of detection for all missing values. We then fit our model to area measurement data of volatile organic compound (VOC) air concentrations collected on vessels supporting the response and clean-up efforts of the Deepwater Horizon oil release that occurred starting April 20, 2010. These data contained a high percentage of observations below the detectable limits of the measuring instrument. Despite this, we were still able to make some interesting discoveries, including elevated levels of VOC near the site of the oil well on June 26th. Using the results from this preliminary analysis, we hope to inform future research on the Deepwater Horizon study, including the use of gradient methods for assigning workers to exposure categories.

An application of MCMC simulation in mortality projection for populations with limited data

IIn this paper, we investigate the use of Bayesian modeling and Markov chain Monte Carlo (MCMC) simulation, via the software WinBUGS, to project future mortality for populations with limited data. In particular, we adapt some extensions of the Lee-Carter m

Spatial analysis of distribution of dengue cases in Espírito Santo, Brazil, in 2010: use of Bayesian model.

To study the relationship between the risk of dengue and sociodemographic variables through the use of spatial regression models fully Bayesian in the municipalities of Espírito Santo in 2010. This is an ecological study and exploration that used spatial analysis tools in preparing thematic maps with data obtained from SinanNet. An analysis by area, taking as unit the municipalities of the state, was performed. Thematic maps were constructed by the computer program R 2.15.00 and Deviance Information Criterion (DIC), calculated in WinBugs, Absolut and Normalized Mean Error (NMAE) were the criteria used to compare the models. We were able to geocode 21,933 dengue cases (rate of 623.99 cases per 100 thousand habitants) with a higher incidence in the municipalities of Vitória, Serra and Colatina; model with spatial effect with the covariates trash and income showed the best performance at DIC and Nmae criteria. It was possible to identify the relationship of dengue with factors outside the health sector and to identify areas with higher risk of disease.

Exploration of the use of Bayesian modeling of gradients for censored spatiotemporal data from the Deepwater Horizon oil spill

Exploration of the use of Bayesian modeling of gradients for censored spatiotemporal data from the Deepwater Horizon oil spill

The Mini-IPIP6: Tiny yet highly stable markers of Big Six personality

We assessed the stability of a short-form six-factor personality measure over a one-year period in a large national probability sample (N=4289). Personality was assessed using the Mini-IPIP6—a short-form measure assessing Extraversion, Agreeableness, Conscientiousness, Neuroticism, Openness to Experience, and Honesty-Humility. Standardized estimates calculated using Bayesian Structural Equation Modelling (BSEM) indicated that all six personality dimensions were extremely stable. An alternative model using Maximum Likelihood estimation, in which residual item variances were associated over repeated assessments, yielded similar findings. These results highlight the stability of personality in the general population, even when assessed using short-form scales. The use of Bayesian models to examine the stability of personality and their application for study of change in specific developmental periods is discussed.

Bayesian calibration of mathematical models: Optimization of model structure and examination of the role of process error covariance

The integration of Bayesian inference techniques with mathematical modeling offers a promising means to improve ecological forecasts and management actions over space and time, while accounting for the uncertainty underlying model predictions. In this study, we address two important questions related to the ramifications of the statistical assumptions typically made about the model structural error and the prospect of Bayesian calibration to guide the optimization of model complexity. Regarding the former issue, we examine statistical formulations that whether postulate conditional independence or explicitly accommodate the covariance among the error terms for various model endpoints. Our analysis evaluates the differences in the posterior parameter patterns and predictive performance of a limiting nutrient (phosphate)–phytoplankton–zooplankton–detritus (particulate phosphorus) model calibrated with three alternative statistical configurations. The lessons learned from this exercise are combined with those from a second comparative analysis that aims to optimize model structure. In particular, we selected three formulas of the zooplankton mortality term (linear, hyperbolic, sigmoidal) and examine their capacity to determine the posterior parameterization as well as the reproduction of the observed ecosystem patterns. Our analysis suggests that the statistical characterization of the model error as well as the mathematical representation of specific ecological processes can be influential to the inference drawn by a modeling exercise. Our findings could be useful when selecting the most suitable statistical framework for model calibration and/or making informative decisions about model structure optimization. In the absence of adequate prior knowledge, we also advocate the use of Bayesian model averaging for obtaining weighted averages of the forecasts from different model structures and/or statistical descriptions of the process error terms.

Evaluating the Impact of Unmeasured Confounding with Internal Validation Data: An Example Cost Evaluation in Type 2 Diabetes

The quantitative assessment of the potential influence of unmeasured confounders in the analysis of observational data is rare, despite reliance on the “no unmeasured confounders” assumption. In a recent comparison of costs of care between two treatments for type 2 diabetes using a health care claims database, propensity score matching was implemented to adjust for selection bias though it was noted that information on baseline glycemic control was not available for the propensity model. Using data from a linked laboratory file, data on this potential “unmeasured confounder” were obtained for a small subset of the original sample. By using this information, we demonstrate how Bayesian modeling, propensity score calibration, and multiple imputation can utilize this additional information to perform sensitivity analyses to quantitatively assess the potential impact of unmeasured confounding. Bayesian regression models were developed to utilize the internal validation data as informative prior distributions for all parameters, retaining information on the correlation between the confounder and other covariates. While assumptions supporting the use of propensity score calibration were not met in this sample, the use of Bayesian modeling and multiple imputation provided consistent results, suggesting that the lack of data on the unmeasured confounder did not have a strong impact on the original analysis, due to the lack of strong correlation between the confounder and the cost outcome variable. Bayesian modeling with informative priors and multiple imputation may be useful tools for unmeasured confounding sensitivity analysis in these situations. Further research to understand the operating characteristics of these methods in a variety of situations, however, remains.

On the Use of Bayesian Model Averaging for Covariate Selection in Epidemiological Modeling

Bayesian model averaging (BMA) is a powerful technique to address model selection uncertainty and recent computational advances have led to a proliferation of usage. BMA methods are of particular interest in environmental health risk assessment because of the high degree of uncertainty that typically arises in that context. In this article, we review a variety of approaches to conducting BMA and compare four implementations in a setting where there are a number of potential predictors. We then use these four methods to calculate risk assessment measures that account for the uncertainty involved in modeling environmental exposures. These methods are used to reexamine data from a study conducted by Walkowiak et al. (2001) to investigate the effects of maternal polychlorinated biphenyl exposure on cognitive development in early childhood. This case study reveals that different strategies for implementing BMA can yield varying risk assessment results. We conclude with some practical recommendations.

Bayesian model averaging in astrophysics: a review

AbstractWe review the use of Bayesian model averaging in astrophysics. We first introduce the statistical basis of Bayesian model selection and model averaging. We discuss methods to calculate the model‐averaged posteriors, including Markov chain Monte Carlo (MCMC), nested sampling, population Monte Carlo, and reversible jump MCMC (RJMCMC). We then review some applications of Bayesian model averaging in astrophysics, including measurements of the dark energy and primordial power spectrum parameters in cosmology, cluster weak lensing, and Sunyaev–Zel'dovich effect data, estimating distances to Cepheids and classifying variable stars. © 2013 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 6: 3–14, 2013

Ordering copy number alteration data to analyze colorectal cancer progression

Ordering copy number alteration data to analyze colorectal cancer progression

Applying Bayesian Model Averaging for Quantile Estimation in Accelerated Life Tests

In an accelerated life test, inferences on extreme quantiles of the lifetime distribution at the use condition are obtained via extrapolation in two directions: in time, and in stress levels. Extrapolation is known to highly depend on the working model, and ignoring model uncertainty can result in over-confidence. This paper explores the use of Bayesian model averaging for estimating quantiles in an accelerated life test. Two of the most commonly used lifetime regression models, lognormal, and Weibull log-location-scale regression models, are considered in this paper as candidate models. To illustrate, we analyse complementary metal-oxide semiconductor integrated circuit data. We also construct a simulation study to compare the performance of the Bayesian model averaging -credibility intervals with other exiting interval estimators. The simulation study shows that, for estimating extreme quantiles, both the standard Bayesian and the maximum likelihood approaches can lead to an over-confident result, and Bayesian model averaging provides a -credibility interval with a wider average length, but a more accurate coverage probability.

Bayes in the Brain—On Bayesian Modelling in Neuroscience

According to a growing trend in theoretical neuroscience, the human perceptual system is akin to a Bayesian machine. The aim of this article is to clearly articulate the claims that perception can be considered Bayesian inference and that the brain can be considered a Bayesian machine, some of the epistemological challenges to these claims; and some of the implications of these claims. We address two questions: (i) How are Bayesian models used in theoretical neuroscience? (ii) From the use of Bayesian models in theoretical neuroscience, have we learned or can we hope to learn that perception is Bayesian inference or that the brain is a Bayesian machine? From actual practice in theoretical neuroscience, we argue for three claims. First, currently Bayesian models do not provide mechanistic explanations; instead they are useful devices for predicting and systematizing observational statements about people’s performances in a variety of perceptual tasks. That is, currently we should have an instrumentalist attitude towards Bayesian models in neuroscience. Second, the inference typically drawn from Bayesian behavioural performance in a variety of perceptual tasks to underlying Bayesian mechanisms should be understood within the three-level framework laid out by David Marr ([1982]). Third, we can hope to learn that perception is Bayesian inference or that the brain is a Bayesian machine to the extent that Bayesian models will prove successful in yielding secure and informative predictions of both subjects’ perceptual performance and features of the underlying neural mechanisms.

Bayesian statistical modeling of spatially correlated error structure in atmospheric tracer inverse analysis

Abstract. We present and discuss the use of Bayesian modeling and computational methods for atmospheric chemistry inverse analyses that incorporate evaluation of spatial structure in model-data residuals. Motivated by problems of refining bottom-up estimates of source/sink fluxes of trace gas and aerosols based on satellite retrievals of atmospheric chemical concentrations, we address the need for formal modeling of spatial residual error structure in global scale inversion models. We do this using analytically and computationally tractable conditional autoregressive (CAR) spatial models as components of a global inversion framework. We develop Markov chain Monte Carlo methods to explore and fit these spatial structures in an overall statistical framework that simultaneously estimates source fluxes. Additional aspects of the study extend the statistical framework to utilize priors on source fluxes in a physically realistic manner, and to formally address and deal with missing data in satellite retrievals. We demonstrate the analysis in the context of inferring carbon monoxide (CO) sources constrained by satellite retrievals of column CO from the Measurement of Pollution in the Troposphere (MOPITT) instrument on the TERRA satellite, paying special attention to evaluating performance of the inverse approach using various statistical diagnostic metrics. This is developed using synthetic data generated to resemble MOPITT data to define a proof-of-concept and model assessment, and then in analysis of real MOPITT data. These studies demonstrate the ability of these simple spatial models to substantially improve over standard non-spatial models in terms of statistical fit, ability to recover sources in synthetic examples, and predictive match with real data.

Infant mortality in South Africa--distribution, associations and policy implications, 2007: an ecological spatial analysis.

BackgroundMany sub-Saharan countries are confronted with persistently high levels of infant mortality because of the impact of a range of biological and social determinants. In particular, infant mortality has increased in sub-Saharan Africa in recent decades due to the HIV/AIDS epidemic. The geographic distribution of health problems and their relationship to potential risk factors can be invaluable for cost effective intervention planning. The objective of this paper is to determine and map the spatial nature of infant mortality in South Africa at a sub district level in order to inform policy intervention. In particular, the paper identifies and maps high risk clusters of infant mortality, as well as examines the impact of a range of determinants on infant mortality. A Bayesian approach is used to quantify the spatial risk of infant mortality, as well as significant associations (given spatial correlation between neighbouring areas) between infant mortality and a range of determinants. The most attributable determinants in each sub-district are calculated based on a combination of prevalence and model risk factor coefficient estimates. This integrated small area approach can be adapted and applied in other high burden settings to assist intervention planning and targeting.ResultsInfant mortality remains high in South Africa with seemingly little reduction since previous estimates in the early 2000's. Results showed marked geographical differences in infant mortality risk between provinces as well as within provinces as well as significantly higher risk in specific sub-districts and provinces. A number of determinants were found to have a significant adverse influence on infant mortality at the sub-district level. Following multivariable adjustment increasing maternal mortality, antenatal HIV prevalence, previous sibling mortality and male infant gender remained significantly associated with increased infant mortality risk. Of these antenatal HIV sero-prevalence, previous sibling mortality and maternal mortality were found to be the most attributable respectively.ConclusionsThis study demonstrates the usefulness of advanced spatial analysis to both quantify excess infant mortality risk at the lowest administrative unit, as well as the use of Bayesian modelling to quantify determinant significance given spatial correlation. The "novel" integration of determinant prevalence at the sub-district and coefficient estimates to estimate attributable fractions further elucidates the "high impact" factors in particular areas and has considerable potential to be applied in other locations. The usefulness of the paper, therefore, not only suggests where to intervene geographically, but also what specific interventions policy makers should prioritize in order to reduce the infant mortality burden in specific administration areas.

Bayesian quantitative electrophysiology and its multiple applications in bioengineering.

Bayesian interpretation of observations began in the early 1700s, and scientific electrophysiology began in the late 1700s. For two centuries these two fields developed mostly separately. In part that was because quantitative Bayesian interpretation, in principle a powerful method of relating measurements to their underlying sources, often required too many steps to be feasible with hand calculation in real applications. As computer power became widespread in the later 1900s, Bayesian models and interpretation moved rapidly but unevenly from the domain of mathematical statistics into applications. Use of Bayesian models now is growing rapidly in electrophysiology. Bayesian models are well suited to the electrophysiological environment, allowing a direct and natural way to express what is known (and unknown) and to evaluate which one of many alternatives is most likely the source of the observations, and the closely related receiver operating characteristic (ROC) curve is a powerful tool in making decisions. Yet, in general, many people would ask what such models are for, in electrophysiology, and what particular advantages such models provide. So to examine this question in particular, this review identifies a number of electrophysiological papers in bioengineering arising from questions in several organ systems to see where Bayesian electrophysiological models or ROC curves were important to the results that were achieved.

Additive Genetic Variability and the Bayesian Alphabet

The use of all available molecular markers in statistical models for prediction of quantitative traits has led to what could be termed a genomic-assisted selection paradigm in animal and plant breeding. This article provides a critical review of some theoretical and statistical concepts in the context of genomic-assisted genetic evaluation of animals and crops. First, relationships between the (Bayesian) variance of marker effects in some regression models and additive genetic variance are examined under standard assumptions. Second, the connection between marker genotypes and resemblance between relatives is explored, and linkages between a marker-based model and the infinitesimal model are reviewed. Third, issues associated with the use of Bayesian models for marker-assisted selection, with a focus on the role of the priors, are examined from a theoretical angle. The sensitivity of a Bayesian specification that has been proposed (called "Bayes A") with respect to priors is illustrated with a simulation. Methods that can solve potential shortcomings of some of these Bayesian regression procedures are discussed briefly.

Use of Bayesian Modeling to Estimate the Sensitivity of Stereotactic Directional Vacuum-Assisted Breast Biopsy When the Gold Standard is Incomplete

This study is conducted to estimate the sensitivity of stereotactic directional vacuum-assisted breast biopsy (ST DVAB) using Bayesian modeling and to predict how many more cancers can be inferred from those lesions without surgical correlation. We retrospectively reviewed the 103 lesions from 84 women who underwent ST DVAB. The study was approved by the Institutional Review Board of our hospital. We estimated the sensitivity and prevalence of the study population for ST DVAB by two types of approaches: for the type I approach, the gold standards were surgical correlation or postbiopsy mammographic follow-up. For the type II approach using Bayesian modeling by a beta-binomial model, the only gold standard was surgical correlation and the predicted number of cancerous lesions in those patients without surgical correlation was estimated. For the type I approach, the sensitivity was 92.3%, and the prevalence 12.6%. For the type II approach, the mean sensitivity of ST DVAB was 89%, and the mean prevalence was 15%. We predicted that an average of 1.7 cancerous lesions occurred among those lesions without surgical correlation by the Bayesian estimation. The mean sensitivity of ST DVAB using the Bayesian (type II) approach was lower than that using the type I approach, because we regarded the surgery as the only gold standard in Bayesian modeling and the nonoperated lesions were thought to be with unknown true disease status. The Bayesian approach is thus more appropriate to use than the type I approach when the gold standard is incomplete.

Bayesian estimation of quantile distributions

Use of Bayesian modelling and analysis has become commonplace in many disciplines (finance, genetics and image analysis, for example). Many complex data sets are collected which do not readily admit standard distributions, and often comprise skew and kurtotic data. Such data is well-modelled by the very flexibly-shaped distributions of the quantile distribution family, whose members are defined by the inverse of their cumulative distribution functions and rarely have analytical likelihood functions defined. Without explicit likelihood functions, Bayesian methodologies such as Gibbs sampling cannot be applied to parameter estimation for this valuable class of distributions without resorting to numerical inversion. Approximate Bayesian computation provides an alternative approach requiring only a sampling scheme for the distribution of interest, enabling easier use of quantile distributions under the Bayesian framework. Parameter estimates for simulated and experimental data are presented.

Incorporating model uncertainty in cost-effectiveness analysis: A Bayesian model averaging approach

Recently, several authors have proposed the use of linear regression models in cost-effectiveness analysis. In this paper, by modelling costs and outcomes using patient and Health Centre covariates, we seek to identify the part of the cost or outcome difference that is not attributable to the treatment itself, but to the patients’ condition or to characteristics of the Centres. Selection of the covariates to be included as predictors of effectiveness and cost is usually assumed by the researcher. This behaviour ignores the uncertainty associated with model selection and leads to underestimation of the uncertainty about quantities of interest. We propose the use of Bayesian model averaging as a mechanism to account for such uncertainty about the model. Data from a clinical trial are used to analyze the effect of incorporating model uncertainty, by comparing two highly active antiretroviral treatments applied to asymptomatic HIV patients. The joint posterior density of incremental effectiveness and cost and cost-effectiveness acceptability curves are proposed as decision-making measures.

Bayesian Copulae Distributions, with Application to Operational Risk Management

The aim of this paper is to introduce a new methodology for operational risk management, based on Bayesian copulae. One of the main problems related to operational risk management is understanding the complex dependence structure of the associated variables. In order to model this structure in a flexible way, we construct a method based on copulae. This allows us to split the joint multivariate probability distribution of a random vector of losses into individual components characterized by univariate marginals. Thus, copula functions embody all the information about the correlation between variables and provide a useful technique for modelling the dependency of a high number of marginals. Another important problem in operational risk modelling is the lack of loss data. This suggests the use of Bayesian models, computed via simulation methods and, in particular, Markov chain Monte Carlo. We propose a new methodology for modelling operational risk and for estimating the required capital. This methodology combines the use of copulae and Bayesian models.