### Abstract

Simulating from distributions with intractable normalizing constants has been a long-standing problem inmachine learning. In this letter, we propose a new algorithm, the Monte Carlo Metropolis-Hastings (MCMH) algorithm, for tackling this problem. The MCMH algorithm is a Monte Carlo version of the Metropolis-Hastings algorithm. It replaces the unknown normalizing constant ratio by a Monte Carlo estimate in simulations, while still converges, as shown in the letter, to the desired target distribution under mild conditions. The MCMH algorithm is illustrated with spatial autologistic models and exponential random graph models. Unlike other auxiliary variable Markov chain Monte Carlo (MCMC) algorithms, such as the Møller and exchange algorithms, the MCMH algorithm avoids the requirement for perfect sampling, and thus can be applied to many statistical models for which perfect sampling is not available or very expensive. TheMCMHalgorithm can also be applied to Bayesian inference for random effect models and missing data problems that involve simulations from a distribution with intractable integrals.

Original language | English |
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Pages (from-to) | 2199-2234 |

Number of pages | 36 |

Journal | Neural Computation |

Volume | 25 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2013 Aug 7 |

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### All Science Journal Classification (ASJC) codes

- Arts and Humanities (miscellaneous)
- Cognitive Neuroscience

### Cite this

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*Neural Computation*, vol. 25, no. 8, pp. 2199-2234. https://doi.org/10.1162/NECO_a_00466

**A Monte Carlo metropolis-hastings algorithm for sampling from distributions with intractable normalizing constants.** / Liang, Faming; Jin, Ick Hoon.

Research output: Contribution to journal › Letter

TY - JOUR

T1 - A Monte Carlo metropolis-hastings algorithm for sampling from distributions with intractable normalizing constants

AU - Liang, Faming

AU - Jin, Ick Hoon

PY - 2013/8/7

Y1 - 2013/8/7

N2 - Simulating from distributions with intractable normalizing constants has been a long-standing problem inmachine learning. In this letter, we propose a new algorithm, the Monte Carlo Metropolis-Hastings (MCMH) algorithm, for tackling this problem. The MCMH algorithm is a Monte Carlo version of the Metropolis-Hastings algorithm. It replaces the unknown normalizing constant ratio by a Monte Carlo estimate in simulations, while still converges, as shown in the letter, to the desired target distribution under mild conditions. The MCMH algorithm is illustrated with spatial autologistic models and exponential random graph models. Unlike other auxiliary variable Markov chain Monte Carlo (MCMC) algorithms, such as the Møller and exchange algorithms, the MCMH algorithm avoids the requirement for perfect sampling, and thus can be applied to many statistical models for which perfect sampling is not available or very expensive. TheMCMHalgorithm can also be applied to Bayesian inference for random effect models and missing data problems that involve simulations from a distribution with intractable integrals.

AB - Simulating from distributions with intractable normalizing constants has been a long-standing problem inmachine learning. In this letter, we propose a new algorithm, the Monte Carlo Metropolis-Hastings (MCMH) algorithm, for tackling this problem. The MCMH algorithm is a Monte Carlo version of the Metropolis-Hastings algorithm. It replaces the unknown normalizing constant ratio by a Monte Carlo estimate in simulations, while still converges, as shown in the letter, to the desired target distribution under mild conditions. The MCMH algorithm is illustrated with spatial autologistic models and exponential random graph models. Unlike other auxiliary variable Markov chain Monte Carlo (MCMC) algorithms, such as the Møller and exchange algorithms, the MCMH algorithm avoids the requirement for perfect sampling, and thus can be applied to many statistical models for which perfect sampling is not available or very expensive. TheMCMHalgorithm can also be applied to Bayesian inference for random effect models and missing data problems that involve simulations from a distribution with intractable integrals.

UR - http://www.scopus.com/inward/record.url?scp=84880992075&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880992075&partnerID=8YFLogxK

U2 - 10.1162/NECO_a_00466

DO - 10.1162/NECO_a_00466

M3 - Letter

C2 - 23607562

AN - SCOPUS:84880992075

VL - 25

SP - 2199

EP - 2234

JO - Neural Computation

JF - Neural Computation

SN - 0899-7667

IS - 8

ER -