2,259 research outputs found
Updating schemes, correlation structure, blocking and parameterisation for the Gibbs sampler
No full textIn this paper many convergence issues concerning the implementation of the Gibbs sampler are investigated. Exact computable rates of convergence for Gaussian target distributions are obtained. Different random and non-random updating strategies and blocking combinations are compared using the rates. The effect of dimensionality and correlation structure on the convergence rates are studied. Some examples are considered to demonstrate the results. For a Gaussian image analysis problem several updating strategies are described and compared. For problems in Bayesian linear models several possible parameterizations are analysed in terms of their convergence rates characterizing the optimal choice
Approximate predetermined convergence properties of the Gibbs sampler
No full textThis article aims to provide a method for approximately predetermining convergence properties of the Gibbs sampler. This is to be done by first finding an approximate rate of convergence for a normal approximation of the target distribution. The rates of convergence for different implementation strategies of the Gibbs sampler are compared to find the best one. In general, the limiting convergence properties of the Gibbs sampler on a sequence of target distributions (approaching a limit) are not the same as the convergence properties of the Gibbs sampler on the limiting target distribution. Theoretical results are given in this article to justify that under conditions, the convergence properties of the Gibbs sampler can be approximated as well. A number of practical examples are given for illustration
A fast distance based approach for determining the number of components in mixtures
No full textThe authors propose a procedure for determining the unknown number of components in mixtures by generalizing a Bayesian testing method proposed by Mengersen & Robert (1996). The testing criterion they propose involves a Kullback-Leibler distance, which may be weighted or not. They give explicit formulas for the weighted distance for a number of mixture distributions and propose a stepwise testing procedure to select the minimum number of components adequate for the data. Their procedure, which is implemented using the BUGS software, exploits a fast collapsing approach which accelerates the search for the minimum number of components by avoiding full refitting at each step. The performance of their method is compared, using both distances, to the Bayes factor approach
Bayesian models for relative archaeological chronology building
No full textFor many years now, archaeologists have postulated that the presence or absence of various artefact types within excavated features should give insight as to their relative dates of deposition even when stratigraphic information is not present. A typical data set used in such studies can be reported as a cross-classification table (often called an abundance matrix or, equivalently, a contingency table) of excavated features against artefact types. Each entry of the table represents the number of a particular artefact type found in a particular archaeological feature. Methodologies for attempting to identify temporal sequence on the basis of such data are commonly referred to as seriation techniques. Several different procedures for seriation including both parametric and non-parametric statistics have been used in an attempt to reconstruct relative chronological orders on the basis of such contingency tables. In this paper we develop a number of possible model-based approaches that might be used to aid in relative, archaeological chronology building. We use the recently developed Markov chain Monte Carlo method based on Langevin diffusions to fit some of the proposed models. Predictive Bayesian model choice techniques are then employed to ascertain which of the models we develop are most plausible. We illustrate our methodology with two examples taken from the literature on archaeological seriation
A Bayesian method of sample size determination with practical applications
No full textThe problem motivating this article is the determination of sample size in clinical trials under normal likelihoods and at the substantive testing stage of a financial audit where normality is not an appropriate assumption. A combination of analytical and simulation based techniques within the Bayesian framework is proposed. The framework accommodates two different prior distributions: one is the general purpose fitting prior distribution used in Bayesian analysis and the other is the expert subjective prior distribution, the sampling prior which is believed to generate the parameter values which in turn generate the data. We obtain many theoretical results and one key result is that typical non-informative prior distributions lead to very small sample sizes. On the other hand, a very informative prior distribution may either lead to a very small or a very large sample
size depending on the location of the centre of the prior distribution and the hypothesized value of the parameter. The methods developed here are quite general and can be applied to other sample size determination (SSD) problems. A number of numerical illustrations which bring out many other aspects of the optimum sample size are given
Comment on "Bayesian Computation and Stochastic Systems"
No full textWe congratulate the authors on a magnificent paper, providing a nicely paced introduction to Markov chain Monte Carlo and its applications, together with several new ideas. In particular the class of pairwise difference priors is bound to have a substantial impact on future applied work. Other ideas given less prominence in the paper are also valuable, for example, the construction of simultaneous credible regions based on MCMC output. There are several issues which we wish to comment on in detail
Spatio-temporal modeling of fine particulate matter
No full textStudies indicate that even short-term exposure to high concentrations of fine atmospheric particulate matter (PM2.5) can lead to long-term health effects. In this paper, we propose a random effects model for PM2.5 concentrations. In particular, we anticipate urban/rural differences with regard to both mean levels and variability. Hence we introduce two random effects components, one for rural or background levels and the other as a supplement for urban areas. These are specified in the form of spatio-temporal processes. Weighting these processes through a population density surface results in nonstationarity in space. We analyze daily PM2.5 concentrations in three Midwestern U.S. states for the year 2001. A fully Bayesian model is implemented, using MCMC techniques, which enables full inference with regard to process unknowns as well as predictions in time and space
A new class of multivariate skew distributions with applications to Bayesian regression models
No full textThis article develops a new class of distributions by introducing skewness in the multivariate elliptically symmetric distributions. The class is obtained by using transformation and conditioning. The class contains many standard families including the multivariate skew normal and t distributions. Analytical forms of the densities are obtained and distributional properties are studied.
These developments are followed by practical examples in Bayesian regression models. Results on the existence of the posterior distributions and moments under improper priors for the regression
coefficients are obtained. The methods are illustrated using practical examples. <br/
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