Moving Target Monte Carlo
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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Moving Target Monte Carlo. / Ying, Haoyun; Mao, Keheng; Mosegaard, Klaus.
I: arXiv, 10.03.2020.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Moving Target Monte Carlo
AU - Ying, Haoyun
AU - Mao, Keheng
AU - Mosegaard, Klaus
PY - 2020/3/10
Y1 - 2020/3/10
N2 - 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.
AB - 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.
KW - stat.CO
KW - cs.DS
KW - math.OC
KW - math.PR
KW - stat.ML
M3 - Journal article
JO - arXiv
JF - arXiv
ER -
ID: 261066167