Bayesian Diagnostics Research Articles

Spatial Prediction of Diameter Distributions for the Alpine Protection Forests in Ebensee, Austria, Using ALS/PLS and Spatial Distributional Regression Models

A novel Bayesian spatial distributional regression model is presented to predict forest structural diversity in terms of the distributions of the stem diameter at breast height (DBH) in the protection forests in Ebensee, Austria. The distributional regression approach overcomes the limitations and uncertainties of traditional regression modeling, in which the conditional mean of the response is regressed against explanatory variables. The distributional regression addresses the complete conditional response distribution, instead. In total 36,338 sample trees were measured via a handheld mobile personal laser scanning system (PLS) on 273 sample plots each having a 20 m radius. Recent airborne laser scanning (ALS) data were used to derive regression covariates from the normalized digital vegetation height model (DVHM) and the digital terrain model (DTM). Candidate models were constructed that differed in their linear predictors of the two gamma distribution parameters. In the distributional regression approach, covariates can enter the model in a flexible form, such as via nonlinear smooth curves, cyclic smooths, or spatial effects. Supported by Bayesian diagnostics DIC and WAIC, nonlinear smoothing splines outperformed linear parametric slope coefficients, and the best implementation of spatial structured effects was achieved by a Gaussian process smooth. Model fitting and posterior parameter inference was achieved by using full Bayesian methodology and MCMC sampling algorithms implemented in the R-package BAMLSS. With BAMLSS, spatial interval predictions of the DBH distribution at any new geo-locations were enabled via straightforward access to the posterior predictive distributions of the model terms and by offering simple plug-in solutions for new covariate values. A cross-validation analysis validated the robustness of the proposed method’s parameter estimation and out-of-sample prediction. Spatial predictions of stem count proportions per DBH classes revealed that regeneration of smaller trees was lacking in certain areas of the protection forest landscape. Therefore, the intensity of final felling needs to be increased to reduce shading from the dense, overmature shelter trees and to promote sunlight for the young regeneration trees.

Bayesian Diagnostics for Chain Event Graphs

Bayesian Diagnostics for Chain Event Graphs

A Bayesian small area model with order restrictions for contingency tables

Estimating the probabilities of possible outcomes for small areas can be difficult, due to a lack of available data from national surveys. One of the statistical techniques for small area estimation is using multinomial Dirichlet models to borrow information among small areas. We study Bayesian diagnostics for multinomial counts from small areas. Within each area, the probabilities of counts for possible outcomes are ordered (e.g., unimodal ordering). Specifically we consider Bayesian diagnostics for a multinomial Dirichlet model with order restriction which shares a common effect among areas. The log pseudo marginal likelihood (LPML) is a well-known Bayesian criterion for comparing models. Since the order restriction significantly increases the difficulty, we develop an algorithm to compute LPML. We use a special-designed importance function to increase the efficiency of Monte Carlo integration, thereby gaining a higher precision for estimation of LPML. The proposed methodology is applied to a case study of body mass index (BMI) and a simulation study to test different scenarios.

Application of a Vine Copula for Multi-Line Insurance Reserving

This article introduces a novel use of the vine copula which captures dependence among multi-line claim triangles, especially when an insurance portfolio consists of more than two lines of business. First, we suggest a way to choose an optimal joint loss development model for multiple lines of business that considers marginal distribution, vine copula structure, and choice of family for each pair of copulas. The performance of the model is also demonstrated with Bayesian model diagnostics and out-of-sample validation measures. Finally, we provide an implication of the dependence modeling, which allows a company to analyze and establish the risk capital for whole portfolio.

Experience in Developing an FHIR Medical Data Management Platform to Provide Clinical Decision Support.

This paper is an extension of work originally presented to pHealth 2019—16th International Conference on Wearable, Micro and Nano Technologies for Personalized Health. To provide an efficient decision support, it is necessary to integrate clinical decision support systems (CDSSs) in information systems routinely operated by healthcare professionals, such as hospital information systems (HISs), or by patients deploying their personal health records (PHR). CDSSs should be able to use the semantics and the clinical context of the data imported from other systems and data repositories. A CDSS platform was developed as a set of separate microservices. In this context, we implemented the core components of a CDSS platform, namely its communication services and logical inference components. A fast healthcare interoperability resources (FHIR)-based CDSS platform addresses the ease of access to clinical decision support services by providing standard-based interfaces and workflows. This type of CDSS may be able to improve the quality of care for doctors who are using HIS without CDSS features. The HL7 FHIR interoperability standards provide a platform usable by all HISs that are FHIR enabled. The platform has been implemented and is now productive, with a rule-based engine processing around 50,000 transactions a day with more than 400 decision support models and a Bayes Engine processing around 2000 transactions a day with 128 Bayesian diagnostics models.

Bayesian Diagnostics of Hidden Markov Structural Equation Models with Missing Data

ABSTRACTCocaine is a type of drug that functions to increase the availability of the neurotransmitter dopamine in the brain. However, cocaine dependence or abuse is highly related to an increased risk of psychiatric disorders and deficits in cognitive performance, attention, and decision-making abilities. Given the chronic and persistent features of drug addiction, the progression of abstaining from cocaine often evolves across several states, such as addiction to, moderate dependence on, and swearing off cocaine. Hidden Markov models (HMMs) are well suited to the characterization of longitudinal data in terms of a set of unobservable states, and have increasingly been used to uncover the dynamic heterogeneity in progressive diseases or activities. However, the existence of outliers or influential points may misidentify the hidden states and distort the associated inference. In this study, we develop a Bayesian local influence procedure for HMMs with latent variables in the presence of missing data. The proposed model enables us to investigate the dynamic heterogeneity of multivariate longitudinal data, reveal how the interrelationships among latent variables change from one state to another, and simultaneously conduct statistical diagnosis for the given data, model assumptions, and prior inputs. We apply the proposed procedure to analyze a dataset collected by the UCLA center for advancing longitudinal drug abuse research. Several outliers or influential points that seriously influence estimation results are identified and removed. The proposed procedure also discovers the effects of treatment and individuals’ psychological problems on cocaine use behavior and delineates their dynamic changes across the cocaine-addiction states.

BAYESIAN DIAGNOSTICS FOR TEST DESIGN AND ANALYSIS

This paper attempts to bridge the gap between classical test theory and item response theory. It is demonstrated that the familiar and popular statistics used in classical test theory can be translated into a Bayesian framework where all of the advantages of the Bayesian paradigm can be realized. In particular, prior opinion can be introduced and inferences can be obtained using posterior distributions. In addition, the use of the JAGS programming language facilitates extensions to more complex scenarios involving the assessment of tests and questionnaires.

On the Bayesian estimation and influence diagnostics for the Weibull-Negative-Binomial regression model with cure rate under latent failure causes

ABSTRACTThe purpose of this paper is to develop a Bayesian approach for the Weibull-Negative-Binomial regression model with cure rate under latent failure causes and presence of randomized activation mechanisms. We assume the number of competing causes of the event of interest follows a Negative Binomial (NB) distribution while the latent lifetimes are assumed to follow a Weibull distribution. Markov chain Monte Carlos (MCMC) methods are used to develop the Bayesian procedure. Model selection to compare the fitted models is discussed. Moreover, we develop case deletion influence diagnostics for the joint posterior distribution based on the ψ-divergence, which has several divergence measures as particular cases. The developed procedures are illustrated with a real data set.

Semiparametric Bayesian inference on generalized linear measurement error models

The classical assumption in generalized linear measurement error models (GLMEMs) is that measurement errors (MEs) for covariates are distributed as a fully parametric distribution such as the multivariate normal distribution. This paper uses a centered Dirichlet process mixture model to relax the fully parametric distributional assumption of MEs, and develops a semiparametric Bayesian approach to simultaneously obtain Bayesian estimations of parameters and covariates subject to MEs by combining the stick-breaking prior and the Gibbs sampler together with the Metropolis–Hastings algorithm. Two Bayesian case-deletion diagnostics are proposed to identify influential observations in GLMEMs via the Kullback–Leibler divergence and Cook’s distance. Computationally feasible formulae for evaluating Bayesian case-deletion diagnostics are presented. Several simulation studies and a real example are used to illustrate our proposed methodologies.

Bayesian estimation and influence diagnostics of generalized partially linear mixed-effects models for longitudinal data

This paper develops a Bayesian approach to obtain the joint estimates of unknown parameters, nonparametric functions and random effects in generalized partially linear mixed models (GPLMMs), and presents three case deletion influence measures to identify influential observations based on the φ-divergence, Cook's posterior mean distance and Cook's posterior mode distance of parameters. Fisher's iterative scoring algorithm is developed to evaluate the posterior modes of parameters in GPLMMs. The first-order approximation to Cook's posterior mode distance is presented. The computationally feasible formulae for the φ-divergence diagnostic and Cook's posterior mean distance are given. Several simulation studies and an example are presented to illustrate our proposed methodologies.

Evidence evaluation: Measure Z corresponds to human utility judgments better than measure L and optimal-experimental-design models.

Evidence evaluation is a crucial process in many human activities, spanning from medical diagnosis to impression formation. The present experiments investigated which, if any, normative model best conforms to people's intuition about the value of the obtained evidence. Psychologists, epistemologists, and philosophers of science have proposed several models to account for people's intuition about the utility of the obtained evidence with respect either to a focal hypothesis or to a constellation of hypotheses. We pitted against each other the so-called optimal-experimental-design models (i.e., Bayesian diagnosticity, log₁₀ diagnosticity, information gain, Kullback-Leibler distance, probability gain, and impact) and measures L and Z to compare their ability to describe humans' intuition about the value of the obtained evidence. Participants received words-and-numbers scenarios concerning 2 hypotheses and binary features. They were asked to evaluate the utility of "yes" and "no" answers to questions about some features possessed in different proportions (i.e., the likelihoods) by 2 types of extraterrestrial creatures (corresponding to 2 mutually exclusive and exhaustive hypotheses). Participants evaluated either how an answer was helpful or how an answer decreased/increased their beliefs with respect either to a single hypothesis or to both hypotheses. We fitted mixed-effects models and used the Akaike information criterion and the Bayesian information criterion values to compare the competing models of the value of the obtained evidence. Overall, the experiments showed that measure Z was the best fitting model of participants' judgments of the value of obtained answers. We discussed the implications for the human hypothesis-evaluation process.

Bayesian diagnostics of transformation structural equation models

In the behavioral, social, psychological, and the medical sciences, the most widely used models in assessing latent variables are the structural equation models (SEMs). However, most of the existin...

Bayesian Nonparametric Models for Community Detection

We propose a series of Bayesian nonparametric statistical models for community detection in graphs. We model the probability of the presence or absence of edges within the graph. Using these models, we naturally incorporate uncertainty and variability and take advantage of nonparametric techniques, such as the Chinese restaurant process and the Dirichlet process. Some of the contributions include: (a) the community structure is directly modeled without specifying the number of communities a priori; (b) the probabilities of edges within or between communities may be modeled as varying by community or pairs of communities; (c) some nodes can be classified as not belonging to any community; and (d) Bayesian model diagnostics are used to compare models and help with appropriate model selection. We start by fitting an initial model to a well-known network dataset, and we develop a series of increasingly complex models. We propose Markov chain Monte Carlo algorithms to carry out the estimation as well as an approach for community detection using the posterior distributions under a decision theoretical framework. Bayesian nonparametric techniques allow us to estimate the number and structure of communities from the data. To evaluate the proposed models for the example dataset, we discuss model comparison using the deviance information criterion and model checking using posterior predictive distributions. Supplementary materials are available online.

Bayesian diagnostics of transformation structural equation models

In the behavioral, social, psychological, and the medical sciences, the most widely used models in assessing latent variables are the structural equation models (SEMs). However, most of the existing statistical methods for analyzing SEMs have been developed for normally distributed data. Transformation SEMs are useful tools for tackling the non-normality of multidimensional data and simultaneously revealing the interrelationships among latent variables. The main objective of this paper is to develop a Bayesian diagnostic procedure for transformation SEMs. The first- and second-order local inference measures are established with the objective functions that are defined based on the logarithm of Bayes Factor. Markov chain Monte Carlo (MCMC) methods with the Bayesian P-splines approach are developed to compute the local influence measures and to estimate nonparametric transformations, latent variables, and unknown parameters. Compared with conventional maximum likelihood-based diagnostic procedures, the Bayesian diagnostic approach could detect outliers and/or influential points in the observed data, as well as conduct model comparison and sensitivity analysis through various perturbations of the data, sampling distributions, or prior distributions of the model parameters. Simulation studies reveal the empirical performance of the proposed Bayesian diagnostic procedure. An actual data set that is extracted from a study based on the Hong Kong Diabetes Registry is used to illustrate the application of our methodology.

Bayesian influence diagnostics in radiocarbon dating

Linear models constitute the primary statistical technique for any experimental science. A major topic in this area is the detection of influential subsets of data, that is, of observations that are influential in terms of their effect on the estimation of parameters in linear regression or of the total population parameters. Numerous studies exist on radiocarbon dating which propose a value consensus and remove possible outliers after the corresponding testing. An influence analysis for the value consensus from a Bayesian perspective is developed in this article.

Bayesian diagnostic techniques for detecting hierarchical structure

Motivated by an increasing number of Bayesian hierarchical model applications, the objective of this paper is to evaluate properties of several diagnostic techniques when the fitted model includes some hierarchical structure, but the data are from a model with additional, unknown hierarchical structure. Because there has been no apparent evaluation of Bayesian diagnostics used for this purpose, we start by studying the simple situation where the data come from a normal model with two-stage hierarchical structure while the fitted model does not have any hierarchical structure, and then extend this to the case where the fitted model has two-stage normal hierarchical structure while the data come from a model with three-stage normal structure. We use exact derivations, large sample approximations and numerical examples to evaluate the quality of the diagnostic techniques. Our investigation suggests two promising techniques: distribution of individual posterior predictive $p$ values and the conventional posterior predictive $p$ value with the $F$ statistic as a checking function. We show that (at least) for large sample sizes these $p$ values are uniformly distributed under the null model and are effective in detecting hierarchical structure not included in the null model. Finally, we apply these two techniques to examine the fit of a model for data from the Patterns of Care Study, a two-stage cluster sample of cancer patients undergoing radiation therapy.

A Conversation with Seymour Geisser

A Conversation with Seymour Geisser

"Finding useful questions: On Bayesian diagnosticity, probability, impact, and information gain": Correction to Nelson (2005).

"Finding useful questions: On Bayesian diagnosticity, probability, impact, and information gain": Correction to Nelson (2005).

Finding Useful Questions: On Bayesian Diagnosticity, Probability, Impact, and Information Gain.

Several norms for how people should assess a question's usefulness have been proposed, notably Bayesian diagnosticity, information gain (mutual information), Kullback-Liebler distance, probability gain (error minimization), and impact (absolute change). Several probabilistic models of previous experiments on categorization, covariation assessment, medical diagnosis, and the selection task are shown to not discriminate among these norms as descriptive models of human intuitions and behavior. Computational optimization found situations in which information gain, probability gain, and impact strongly contradict Bayesian diagnosticity. In these situations, diagnosticity's claims are normatively inferior. Results of a new experiment strongly contradict the predictions of Bayesian diagnosticity. Normative theoretical concerns also argue against use of diagnosticity. It is concluded that Bayesian diagnosticity is normatively flawed and empirically unjustified.

Supplemental Material for Finding Useful Questions: On Bayesian Diagnosticity, Probability, Impact, and Information Gain

Supplemental Material for Finding Useful Questions: On Bayesian Diagnosticity, Probability, Impact, and Information Gain