Plateau Proposal Distributions for Adaptive Component-wise Multiple-Try Metropolis
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Markov chain Monte Carlo (MCMC) methods are sampling methods that have become a commonly used tool in statistics, for example to perform Monte Carlo integration. As a consequence of the increase in computational power, many variations of MCMC methods exist for generating samples from arbitrary, possibly complex, target distributions. The performance of an MCMC method is predominately governed by the choice of the so-called proposal distribution used. In this paper, we introduce a new type of proposal distribution for the use in MCMC methods that operates component-wise and with multiple-tries per iteration. Specifically, the novel class of proposal distributions, called Plateau distributions, do not overlap, thus ensuring that the multiple-tries are drawn from different parts of the state space. We demonstrate in numerical simulations that this new type of proposals outperforms competitors and efficiently explores the state-space.
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