Abstract Stochastic substitution, the Gibbs sampler, and sampling-importance-resampling algorithm can be viewed as three alternative sampling- (or Monte Carlo-) based approaches to calculation of numerical estimates marginal probability distributions. The will reviewed, compared, contrasted in relation various joint structures frequently encountered applications. In particular, relevance calculating Bayesian posterior densities for a variety structured models discussed illustrated.

Abstract Stochastic substitution, the Gibbs sampler, and sampling-importance-resampling algorithm can be viewed as three alternative sampling- (or Monte Carlo-) based approaches to calculation of numerical estimates marginal probability distributions. The will reviewed, compared, contrasted in relation various joint structures frequently encountered applications. In particular, relevance calculating Bayesian posterior densities for a variety structured models discussed illustrated.

SUMMARY Model determination is a fundamental data analytic task. Here we consider the problem of choosing among finite (without loss generality assume two) set models. After briefly reviewing classical and Bayesian model choice strategies present general predictive density which includes all proposed approaches that are aware of. Using Laplace approximations can conveniently assess compare asymptotic behaviour these approaches. Concern regarding accuracy for small to moderate sample sizes...

Summary With scientific data available at geocoded locations, investigators are increasingly turning to spatial process models for carrying out statistical inference. Over the last decade, hierarchical implemented through Markov chain Monte Carlo methods have become especially popular modelling, given their flexibility and power fit that would be infeasible with classical as well avoidance of possibly inappropriate asymptotics. However, fitting often involves expensive matrix decompositions...

Abstract The use of the Gibbs sampler as a method for calculating Bayesian marginal posterior and predictive densities is reviewed illustrated with range normal data models, including variance components, unordered ordered means, hierarchical growth curves, missing in crossover trial. In all cases approach straightforward to specify distributionally implement computationally, output readily adapted required inference summaries.

Abstract Even to the initiated, statistical calculations based on Bayes's Theorem can be daunting because of numerical integrations required in all but simplest applications. Moreover, from a teaching perspective, introductions Bayesian statistics—if they are given at all—are circumscribed by these apparent calculational difficulties. Here we offer straightforward sampling-resampling perspective inference, which has both pedagogic appeal and suggests easily implemented calculation...

Journal Article Model choice: A minimum posterior predictive loss approach Get access ALAN E. GELFAND, GELFAND Department of Statistics, University ConnecticutStorrs, Connecticut 06269-3120, U.S.A.alan@stat.uconn.edu Search for other works by this author on: Oxford Academic Google Scholar SUJIT K. GHOSH North Carolina State UniversityRaleigh, Carolina, 27695-8203, U.S.A.sghosh@stat.ncsu.edu Biometrika, Volume 85, Issue 1, March 1998, Pages 1–11, https://doi.org/10.1093/biomet/85.1.1...

SUMMARY A general approach to hierarchical Bayes changepoint models is presented. In particular, desired marginal posterior densities are obtained utilizing the Gibbs sampler, an iterative Monte Carlo method. This avoids sophisticated analytic and numerical high dimensional integration procedures. We include application changing regressions, Poisson processes Markov chains. Within these contexts we handle several previously inaccessible problems.

In many applications, the objective is to build regression models explain a response variable over region of interest under assumption that responses are spatially correlated. nearly all this work, coefficients assumed be constant region. However, in some expected vary at local or subregional level. Here we focus on case. Although parametric modeling spatial surface for coefficient possible, here argue it more natural and flexible view as realization from process. We show how such can...

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations large. This article develops a class highly scalable nearest-neighbor Gaussian (NNGP) to provide fully model-based inference large datasets. We establish NNGP is well-defined providing legitimate finite-dimensional densities with sparse precision matrices. embed sparsity-inducing prior within rich hierarchical modeling framework and outline how...

Abstract Maps of regional morbidity and mortality rates are useful tools in determining spatial patterns disease. Combined with sociodemographic census information, they also permit assessment environmental justice; that is, whether certain subgroups suffer disproportionately from diseases or other adverse effects harmful exposures. Bayes empirical methods have proven smoothing crude maps disease risk, eliminating the instability estimates low-population areas while maintaining geographic...

In the past decade conditional autoregressive modelling specifications have found considerable application for analysis of spatial data. Nearly all this work is done in univariate case and employs an improper specification. Our contribution here to move multivariate models provide rich, flexible classes which yield proper distributions. approach introduce autoregression parameters. We first clarify what can be developed from family Mardia (1988) contrast with recent Kim et al. (2000). then...

Abstract Constrained parameter problems arise in a wide variety of applications, including bioassay, actuarial graduation, ordinal categorical data, response surfaces, reliability development testing, and variance component models. Truncated data naturally survival failure time studies, models, studies aimed at uncovering underlying continuous distributions. In many applications both constraints truncation are present. The statistical literature on such is very extensive, reflecting the...

Customary modeling for continuous point-referenced data assumes a Gaussian process that is often taken to be stationary. When such models are fitted within Bayesian framework, the unknown parameters of assumed random, so random results. Here we propose novel spatial Dirichlet mixture model produce neither nor We first develop and discuss its properties. Because familiar limitations associated with direct use models, introduce mixing by convolving this pure error process. then examine...

Models of the geographic distributions species have wide application in ecology. But nonspatial, single-level, regression models that ecologists often employed do not deal with problems irregular sampling intensity or spatial dependence, and adequately quantify uncertainty. We show here how to build statistical can handle these features prediction provide richer, more powerful inference about niche relations, distributions, effects human disturbance. begin a familiar generalized linear model...

In multicenter studies, subjects in different centers may have outcome distributions. This article is motivated by the problem of nonparametric modeling these distributions, borrowing information across while also allowing to be clustered. Starting with a stick-breaking representation Dirichlet process (DP), we replace random atoms probability measures drawn from DP. results nested DP prior, which can placed on collection distributions for centers, same component automatically clustered...

The perceived threat of climate change is often evaluated from species distribution models that are fitted to many independently and then added together. This approach ignores the fact jointly distributed limit one another. Species respond same underlying climatic variables, abundance any can be constrained by competition; a large increase in inevitably linked declines others. Omitting this basic relationship explains why responses modeled do not agree with richness or basal areas actual...

Even to the initiated, statistical calculations based on Bayes's Theorem can be daunting because of numerical integrations required in all but simplest applications.Moreover, from a teaching perspective, introductions Bayesian statistics-if they are given at all-are circumscribed by these apparent calculational difficulties.Here we offer straightforward samplingresampling perspective inference, which has both pedagogic appeal and suggests easily implemented calculation strategies.

Abstract : A fully Bayesian analysis of linear and nonlinear population models has previously been unavailable, as a consequence the seeming impossibility performing necessary numerical Integrations in complex multi- parameter structures typically arising such models. It is demonstrated that, for variety models, can be implemented straightforward manner using Gibbs sampler. The approach illustrated with examples involving challenging problems outliers mean-variance relationships modelling.

The generality and easy programmability of modern sampling-based methods for maximisation likelihoods summarisation posterior distributions have led to a tremendous increase in the complexity dimensionality statistical models used practice. However, these can often be extremely slow converge, due high correlations between, or weak identifiability of, certain model parameters. We present simple hierarchical centring reparametrisations that give improved convergence broad class normal linear...