Showing papers by "Walter R. Gilks published in 1998"
TL;DR: In this article, the authors describe a framework based on the concept of Markov chain regeneration, which allows adaptation to occur infinitely often but does not disturb the stationary distribution of the chain or the consistency of sample path averages.
Abstract: Markov chain Monte Carlo (MCMC) is used for evaluating expectations of functions of interest under a target distribution π. This is done by calculating averages over the sample path of a Markov chain having π as its stationary distribution. For computational efficiency, the Markov chain should be rapidly mixing. This sometimes can be achieved only by careful design of the transition kernel of the chain, on the basis of a detailed preliminary exploratory analysis of π. An alternative approach might be to allow the transition kernel to adapt whenever new features of π are encountered during the MCMC run. However, if such adaptation occurs infinitely often, then the stationary distribution of the chain may be disturbed. We describe a framework, based on the concept of Markov chain regeneration, which allows adaptation to occur infinitely often but does not disturb the stationary distribution of the chain or the consistency of sample path averages.
321 citations
Journal Article•
TL;DR: The results show a massive peak in HIV infections around 1983 and suggest that the incidence of AIDS has now reached a plateau, although there is still substantial uncertainty about the future.
Abstract: Short-term projections of the acquired immune deficiency syndrome (AIDS) epidemic in England and Wales have been regularly updated since the publication of the Cox report in 1988. The key approach for those updates has been the back-calculation method, which has been informally adapted to acknowledge various sources of uncertainty as well as to incorporate increasingly available information on the spread of the human immunodeficiency virus (HIV) in the population. We propose a Bayesian formulation of the back-calculation method which allows a formal treatment of uncertainty and the inclusion of extra information, within a single coherent composite model. Estimation of the variably dimensioned model is carried out by using reversible jump Markov chain Monte Carlo methods. Application of the model to data for homosexual and bisexual males in England and Wales is presented, and the role of the various sources of information and model assumptions is appraised. Our results show a massive peak in HIV infections around 1983 and suggest that the incidence of AIDS has now reached a plateau, although there is still substantial uncertainty about the future.
24 citations
26 Mar 1998
TL;DR: Gilks, Richardson and Spiegelhalter as discussed by the authors used Gibbs sampler for Bayesian graphical modeling and the most basic of MCMC techniques, the Gibbs sampling sampler, and introduced ideas that were developed more fully in other chapters.
Abstract: This chapter features a worked example using Bayesian graphical modelling and the most basic of MCMC techniques, the Gibbs sampler, and serves to introduce ideas that are developed more fully in other chapters This case study first appeared in Gilks, Richardson and Spiegelhalter (1996), and frequent reference is made to other chapters in that book
3 citations