Generic reversible jump MCMC using graphical models |
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Authors: | David J Lunn Nicky Best John C Whittaker |
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Institution: | 1. MRC Biostatistics Unit, Institute of Public Health, University Forvie Site, Robinson Way, Cambridge, CB2 0SR, UK 2. Department of Epidemiology and Public Health, Imperial College London, London, UK 3. Department of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, UK
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Abstract: | Markov chain Monte Carlo techniques have revolutionized the field of Bayesian statistics. Their power is so great that they
can even accommodate situations in which the structure of the statistical model itself is uncertain. However, the analysis
of such trans-dimensional (TD) models is not easy and available software may lack the flexibility required for dealing with the complexities of real
data, often because it does not allow the TD model to be simply part of some bigger model. In this paper we describe a class
of widely applicable TD models that can be represented by a generic graphical model, which may be incorporated into arbitrary
other graphical structures without significantly affecting the mechanism of inference. We also present a decomposition of
the reversible jump algorithm into abstract and problem-specific components, which provides infrastructure for applying the
method to all models in the class considered. These developments represent a first step towards a context-free method for implementing
TD models that will facilitate their use by applied scientists for the practical exploration of model uncertainty. Our approach
makes use of the popular WinBUGS framework as a sampling engine and we illustrate its use via two simple examples in which
model uncertainty is a key feature. |
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