Inference for Dirichlet process hierarchical models is typically performed using Markov chain Monte Carlo methods, which can be roughly categorised into marginal and conditional methods. The former integrate out analytically the infinite-dimensional component of the hierarchical model and sample from the marginal distribution of the remaining variables using the Gibbs sampler. Conditional metho...

This chapter reviews the recent developments in Markov chain Monte Carlo simulation methods These methods, which are concerned with the simulation of high dimensional probability distributions, have gained enormous prominence and revolutionized Bayesian statistics The chapter provides background on the relevant Markov chain theory and provides detailed information on the theory and practice of ...

We present some new results on incorporating quasi-Monte Carlo rules into Markov chain Monte Carlo. First, we present some new constructions of points, fully equidistributed LFSRs, which are small enough that the entire point set can be used in a Monte Carlo calculation. Second, we introduce some antithetic and round trip sampling constructions and show that they preserve the completely uniform...

We present several Markov chain Monte Carlo simulation methods that have been widely used in recent years in econometrics and statistics. Among these is the Gibbs sampler, which has been of particular interest to econometricians. Although the paper summarizes some of the relevant theoretical literature, its emphasis is on the presentation and explanation of applications to important models that...

In this report, we propose an original approach to solve Fredholm equations of the second kind. We interpret the standard von Neumann expansion of the solution as an expectation with respect to a probability distribution de…ned on an union of subspaces of variable dimension. Based on this representation, it is possible to use trans-dimensional Markov Chain Monte Carlo (MCMC) methods such as Rev...

As the world advances, statisticians/mathematicians are being involved into more and more complex surveys for the development of society and human beings. Consequently, these complex survey data requires complicated and high-dimensional models for final analysis. We need sophisticated and efficient statistical/mathematical tools for estimation and prediction of these models. Frequently, we simu...

The paper and presentation will focus on MCMC methods, implemented together in MC2Pack, an ox package which allows you to run a range of sampling algorithm (MH, Gibbs, Griddy Gibbs, Adaptive Polar Importance Sampling, Adaptive Polar Sampling, and Adaptive Rejection Metropolis Sampling) on a given posterior. Computation of the marginal likelihood for the model is also done automatically, allowin...

We derive a Markov chain to sample from the posterior distribution for a phylogenetic tree given sequence information from the corresponding set of organisms, a stochastic model for these data, and a prior distribution on the space of trees. A transformation of the tree into a canonical cophenetic matrix form suggests a simple and effective proposal distribution for selecting candidate trees cl...