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Accept–reject Metropolis–Hastings sampling and marginal likelihood estimation
Author(s) -
Chib Siddhartha,
Jeliazkov Ivan
Publication year - 2005
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2005.00277.x
Subject(s) - marginal likelihood , mathematics , conjugate prior , prior probability , metropolis–hastings algorithm , statistics , importance sampling , constant (computer programming) , sampling (signal processing) , block (permutation group theory) , marginal distribution , mathematical optimization , algorithm , computer science , maximum likelihood , markov chain monte carlo , bayesian probability , monte carlo method , random variable , geometry , filter (signal processing) , computer vision , programming language
We describe a method for estimating the marginal likelihood, based on Chib (1995) and C hib and Jeliazkov (2001), when simulation from the posterior distribution of the model parameters is by the accept–reject Metropolis–Hastings (ARMH) algorithm. The method is developed for one‐block and multiple‐block ARMH algorithms and does not require the (typically) unknown normalizing constant of the proposal density. The problem of calculating the numerical standard error of the estimates is also considered and a procedure based on batch means is developed. Two examples, dealing with a multinomial logit model and a Gaussian regression model with non‐conjugate priors, are provided to illustrate the efficiency and applicability of the method.