## Estimating Normalizing Constants and Reweighting Mixtures in Markov Chain Monte Carlo (1994)

Citations: | 40 - 0 self |

### BibTeX

@MISC{Geyer94estimatingnormalizing,

author = {Charles J. Geyer},

title = {Estimating Normalizing Constants and Reweighting Mixtures in Markov Chain Monte Carlo},

year = {1994}

}

### Years of Citing Articles

### OpenURL

### Abstract

Markov chain Monte Carlo (the Metropolis-Hastings algorithm and the Gibbs sampler) is a general multivariate simulation method that permits sampling from any stochastic process whose density is known up to a constant of proportionality. It has recently received much attention as a method of carrying out Bayesian, likelihood, and frequentist inference in analytically intractable problems. Although many applications of Markov chain Monte Carlo do not need estimation of normalizing constants, three do: calculation of Bayes factors, calculation of likelihoods in the presence of missing data, and importance sampling from mixtures. Here reverse logistic regression is proposed as a solution to the problem of estimating normalizing constants, and convergence and asymptotic normality of the estimates are proved under very weak regularity conditions. Markov chain Monte Carlo is most useful when combined with importance reweighting so that a Monte Carlo sample from one distribution can be used fo...