this paper we review several of these methods, and subsequently compare them in the context of two examples, the first a simple regression example, and the second a much more challenging hierarchical longitudinal model of the kind often encountered in biostatistical practice. We find that the joint model-parameter space search methods perform adequately but can be difficult to program and tune, while the marginal likelihood methods are often less troublesome and require less in the way of additional coding. Our results suggest that the latter methods may be most appropriate for practitioners working in many standard model choice settings, while the former remain important for comparing large numbers of models, or models whose parameters cannot be easily updated in relatively few blocks. We caution however that all of the methods we compare require significant human and computer effort, suggesting that less formal Bayesian model choice methods may offer a more realistic alternative in many cases.

This paper examines the problem of efficient Bayesian computation in the context of linear Gaussian Directed Acyclic Graph (DAG) models. Unobserved latent variables are grouped together in a block, and sparse matrix techniques for computation are explored. Conditional sampling and likelihood computations are shown to be straightforward using a sparse matrix approach, allowing MCMC algorithms with good mixing properties to be developed for problems with many thousands of latent variables. Keywords: Bayes linear models; block sampling; Gaussian models; linear systems; local computation; multivariate normal; precision matrix; sparse matrices; Markov Chain Monte Carlo (MCMC). # This is a University of Newcastle Statistics Preprint, STA01,2. Last updated: March 15, 2001. 1 Contents 1 Introduction 3 2 Model building 4 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Canonical parameterisation of the MVN . . . . . . . . . . . . . . . . . . ....

. In this paper we are concerned with estimating the fractional order of integration associated with a long-memory stochastic volatilitymodel. Wedevelop a new Bayesian estimator based on the Markov chain Monte Carlo sampler and the wavelet representation of the log-squared returns to drawvalues of the fractional order of integration and latentvolatilities from their joint posterior distribution. Unlike shortmemory stochastic volatility models, long-memory stochastic volatilitymodelsdonothave a state-space representation, and thus their sampler cannot employ the Kalman filters simulation smoother to update the chain of latentvolatilities. Instead, we design a simulator where the latent long-memory volatilities are drawn quickly and efficiently from the near independentmultivariate distribution of the long-memory volatility's wavelet coefficients. We find that sampling volatility in the wavelet domain, rather than in the time domain, leads to a fast and simulation-efficient sampler of the posterior distribution for the volatility's long-memory parameter and serves as a promising alternative estimator to the existing frequentist based estimators of long-memory volatility. Keywords: Long-memory# Markovchain Monte Carlo# Metropolis-Hastings# Semiparametric# Stochastic volatility# Wavelets JEL Classification: C11# C14# C22# 1

In the present paper we consider Bayesian estimation of a finite mixture of models with random effects which is also known as the heterogeneity model. First, we discuss the properties of various MCMC samplers that are obtained from full conditional Gibbs sampling by grouping and collapsing. Whereas

Abstract not found

Description This package contains functions for panel data modeling and inference using Bayesian methods. It is a realization of models described in Chib(2008): Panel Data Modeling and

While adaptive methods for MCMC are under active development, their utility has been under-recognized. We briefly review some theoretical results relevant to adaptive MCMC. We then suggest a very simple and effective algorithm to adapt proposal densities for random walk Metropolis and Metropolis adjusted Langevin algorithms. The benefits of this algorithm are immediate, and we demonstrate its power by comparing its performance to that of three commonly-used MCMC algorithms that are widely-believed to be extremely efficient. Compared to data augmentation for probit models, slice sampling for geostatistical models, and Gibbs sampling with adaptive rejection sampling, 1 the adaptive random walk Metropolis algorithm that we suggest is both more efficient and more flexible.