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Parallel Markov Chain Monte Carlo

By Jonathan M. R. Byrd


The increasing availability of multi-core and multi-processor architectures provides\ud new opportunities for improving the performance of many computer simulations.\ud Markov Chain Monte Carlo (MCMC) simulations are widely used for approximate\ud counting problems, Bayesian inference and as a means for estimating very highdimensional\ud integrals. As such MCMC has found a wide variety of applications in\ud fields including computational biology and physics,financial econometrics, machine\ud learning and image processing.\ud This thesis presents a number of new method for reducing the runtime of\ud Markov Chain Monte Carlo simulations by using SMP machines and/or clusters.\ud Two of the methods speculatively perform iterations in parallel, reducing the runtime\ud of MCMC programs whilst producing statistically identical results to conventional\ud sequential implementations. The other methods apply only to problem domains\ud that can be presented as an image, and involve using various means of dividing\ud the image into subimages that can be proceed with some degree of independence.\ud Where possible the thesis includes a theoretical analysis of the reduction in\ud runtime that may be achieved using our technique under perfect conditions, and\ud in all cases the methods are tested and compared on selection of multi-core and\ud multi-processor architectures. A framework is provided to allow easy construction\ud of MCMC application that implement these parallelisation methods

Topics: QA76
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