Towards Automatic Reversible Jump Markov Chain Monte Carlo

Since its introduction by Green (1995), reversible jump MCMC has been recognised as a powerful tool for making posterior inference about a wide range of statistical problems. Despite enjoying considerable application across a variety of disciplines, the method’s popularity has been tempered by the common perception that reversible jump samplers can be difficult to implement. Beginning with a review of reversible jump methods and recent research in the area, this thesis introduces steps towards the design of an automatic reversible jump sampler with the aim of taking the method outside of the domain of the MCMC expert. The need for a sampler is discussed and motivated by an application of reversible jump to a recent problem in biology. We build upon recent developments in the area of adaptive sampling, analysing and extending existing methods for their inclusion in an automatic reversible jump sampler. The automatic sampler that we introduce in the penultimate chapter of the thesis builds upon the first steps taken by Green (2003). Requiring minimal user input, it uses adaptive techniques to perform self-tuning and calibration for many trans-dimensional statistical problems. The broad applicability of the sampler is detailed, as are typical results, indicating performance comparable to problemspecific samplers, designed and tuned by hand. The thesis ends with some suggestions for further work. 3