Moving Target Monte Carlo

• URL: http://arxiv.org/abs/2003.04873v1
• Date: Tue, 10 Mar 2020 17:38:36 GMT
• Title: Moving Target Monte Carlo
• Authors: Haoyun Ying, Keheng Mao, Klaus Mosegaard
• Abstract summary: 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 $a_n(mathbfx)$. The true value of the posterior $p(mathbfx|mathbfd)$ is only calculated if the candidate $mathbfx$ is accepted.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Markov Chain Monte Carlo (MCMC) methods are popular when considering sampling from a high-dimensional random variable $\mathbf{x}$ with possibly unnormalised probability density $p$ and observed data $\mathbf{d}$. However, MCMC requires evaluating the posterior distribution $p(\mathbf{x}|\mathbf{d})$ of the proposed candidate $\mathbf{x}$ 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 $a_n(\mathbf{x})$ instead of $p(\mathbf{x}|\mathbf{d})$. The true value of the posterior $p(\mathbf{x}|\mathbf{d})$ is only calculated if the candidate $\mathbf{x}$ is accepted. The approximation $a_n$ utilises these evaluations and converges to $p$ as $n \rightarrow \infty$. A proof of convergence and estimation of convergence rate in different situations are given.

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