Gibbs sampling requires a vector of parameters of interest that are initially unknown. These parameters will be denoted by the vectorΦ . Nuisance parameters, Θ , are also initially unknown. The goal of Gibbs sampling is to find estimates for the parameters of interest in order to determine how well the observable data fits the model of interest, and also whether or not data independent of the o...

This paper studies several di erent plans for selecting coordinates for updating via Gibbs sampling. It exploits the inherent features of the Gibbs sampling formulation, most notably its neighborhood structure, to characterize and compare the plans with regard to convergence to equilibrium and variance of the sample mean. Some of the plans rely on completely or almost completely random coordina...

We give families of examples where sharp rates of convergence to stationarity of the widely used Gibbs sampler are available. The examples involve standard exponential families and their conjugate priors. In each case, the transition operator is explicitly diagonalizable with classical orthogonal polynomials as eigenfunctions.

Recent advances in high throughput profiling of gene expression have catalyzed an explosive growth in functional genomics aimed at the elucidation of genes that are differentially expressed in various tissue or cell types across a range of experimental conditions. These studies can lead to the identification of diagnostic genes, classification of genes into functional categories, association of...

We propose a split-merge Markov chain algorithm to address the problem of inee-cient sampling for conjugate Dirichlet process mixture models. Traditional Markov chain Monte Carlo methods for Bayesian mixture models, such as Gibbs sampling, can become trapped in isolated modes corresponding to an inappropriate clustering of data points. This article describes a Metropolis-Hastings procedure that...

Wireless side monitoring employing distributed sniffers has been shown to complement wired side monitoring using Simple Network Management Protocol (SNMP) and base station logs, since it reveals detailed PHY and MAC behaviors, as well as timing information. Due to hardware limitations, wireless sniffers typically can only collect information on one channel at a time. Distributed algorithms are ...

A major limitation towards more widespread implementation of Bayesian approaches is that obtaining the posterior distribution often requires the integration of high-dimensional functions. This can be computationally very difficult, but several approaches short of direct integration have been proposed (reviewed by Smith 1991, Evans and Swartz 1995, Tanner 1996). We focus here on Markov Chain Mon...

We present a method for distributing collapsed Gibbs sampling over multiple processors that is simple, statistically correct, and memory efficient. The method uses blocked sampling, dividing the training data into relatively large sized blocks, and distributing the sampling of each block over multiple processors. At the end of each parallel run, MetropolisHastings rejection sampling is performe...