Active particles, Markov chain Monte Carlo and local adaptation

Anthony Lee (University of Warwick)

Friday 12th October, 2012 15:00-16:00 Maths 203


The use of auxiliary variables in various Monte Carlo methods has proliferated both explicitly and implicitly over the last two decades, as our understanding of how to devise effective algorithms has grown. In addition, massively parallel 'many-core' processors have become the focus of the high performance computing community for a variety of physical reasons, providing a strong incentive for algorithms in computational statistics to exhibit specific types of parallelism. Within the field of Monte Carlo methodology, population-based methods such as sequential Monte Carlo, parallel tempering and pseudo-marginal methods are promising auxiliary variable algorithms that can take advantage of available parallel resources while allowing the advantageous, principled interaction of simulated random variables. I will describe briefly a new perspective on auxiliary variables within reversible MCMC kernels that allows for the flexible construction of population-based MCMC kernels, including pseudo-marginal and particle MCMC kernels. One opportunity the methodology presents is "locally adaptive" MCMC kernels, which in contrast to adaptive MCMC does not forfeit time-homogeneity of the resulting Markov chain. I will describe methods that can be used to adapt kernels sensibly in realistic applications, where this adaptation can be both crucial to performing inference effectively.

(joint work with Christophe Andrieu (Bristol) and Arnaud Doucet (Oxford))

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