Moving Target Monte Carlo

03/10/2020

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by   Haoyun Ying, et al.

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The Markov Chain Monte Carlo (MCMC) methods are popular when considering sampling from a high-dimensional random variable 𝐱 with possibly unnormalised probability density p and observed data 𝐝. However, MCMC requires evaluating the posterior distribution p(𝐱|𝐝) of the proposed candidate 𝐱 at each iteration when constructing the acceptance rate. This is costly when such evaluations are intractable. In this paper, we introduce a new non-Markovian sampling algorithm called Moving Target Monte Carlo (MTMC). The acceptance rate at n-th iteration is constructed using an iteratively updated approximation of the posterior distribution a_n(𝐱) instead of p(𝐱|𝐝). The true value of the posterior p(𝐱|𝐝) is only calculated if the candidate 𝐱 is accepted. The approximation a_n utilises these evaluations and converges to p as n →∞. A proof of convergence and estimation of convergence rate in different situations are given.