Importance sampling for families of distributions
Open Access
- 1 November 1999
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Applied Probability
- Vol. 9 (4) , 1202-1225
- https://doi.org/10.1214/aoap/1029962870
Abstract
This paper analyzes the performance of importance sampling distributions for computing expectations with respect to a whole family of probability laws in the context of Markov chain Monte Carlo simulation methods. Motivations for such a study arise in statistics as well as in statistical physics. Two choices of importance sampling distributions are considered in detail: mixtures of the distributions of interest and distributions that are "uniform over energy levels" (motivated by physical applications). We analyze two examples, a "witch's hat" distribution and the mean field Ising model, to illustrate the advantages that such simulation procedures are expected to offer in a greater generality. The connection with the recently proposed simulated tempering method is also examined.Keywords
This publication has 33 references indexed in Scilit:
- Markov chain decomposition for convergence rate analysisThe Annals of Applied Probability, 2002
- A note on Metropolis-Hastings kernels for general state spacesThe Annals of Applied Probability, 1998
- Annealing Markov Chain Monte Carlo with Applications to Ancestral InferenceJournal of the American Statistical Association, 1995
- Methods for Approximating Integrals in Statistics with Special Emphasis on Bayesian Integration ProblemsStatistical Science, 1995
- Markov Chains for Exploring Posterior DistributionsThe Annals of Statistics, 1994
- Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemesBiometrika, 1994
- Geometric Bounds for Eigenvalues of Markov ChainsThe Annals of Applied Probability, 1991
- Nonlocal Monte Carlo algorithm for self-avoiding walks with fixed endpointsJournal of Statistical Physics, 1990
- Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusionsCommunications in Mathematical Physics, 1986
- Optimum Monte-Carlo sampling using Markov chainsBiometrika, 1973