The key quantity needed for Bayesian hypothesis testing and model selection is the marginal likelihood for a model, also known as the integrated likelihood, or the marginal probability of the data. In this paper we describe a way to use posterior simulation output to estimate marginal likelihoods. vVe describe the basic LaplaceMetropolis estimator for models without random effects. For models w...

Importance Sampling (IS) is a well-known Monte Carlo technique that approximates integrals involving a posterior distribution by means of weighted samples. In this work, we study the assignation of a single weighted sample which compresses the information contained in a population of weighted samples. Part of the theory that we present as Group Importance Sampling (GIS) has been employed implic...

In this paper, we study a special case of the Metropolis algorithm, the Independence Metropolis Sampler (IMS), in the finite state space case. The IMS is often used in designing components of more complex Markov Chain Monte Carlo algorithms. We present new results related to the first hitting time of individual states for the IMS. These results are expressed mostly in terms of the eigenvalues o...

In this paper we study the ergodicity properties of some adaptive Markov chain Monte Carlo algorithms (MCMC) that have been recently proposed in the literature. We prove that under a set of verifiable conditions, ergodic averages calculated from the output of a so-called adaptive MCMC sampler converge to the required value and can even, under more stringent assumptions, satisfy a central limit ...

The Monte Carlo procedure of MetropOliS et al. 1,2 is widely used to determine the equilibrium structural and ther:modynamic properties of gases, liquids, solids, and mesophases. In a previous paper we introduced a modification of the usual Metropolis procedure that gives more rapid convergence and thereby much more efficient Monte Carlo runs. In this new procedure each particle move is chosen ...

Umacs (Universal Markov chain sampler) is an R software package that facilitates the construction of the Gibbs sampler and Metropolis algorithm for Bayesian inference. Umacs is a practical tool to write samplers in R. This is sometimes necessary for large problems that cannot be fit using programs like BUGS. The user supplies the data, parameter names, updating functions, and a procedure for ge...