Exact sampling with coupled Markov chains and applications to statistical mechanics
Proceedings of the seventh international conference on Random structures and algorithms
Exact sampling and approximate counting techniques
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Stability of Stochastic Approximation under Verifiable Conditions
SIAM Journal on Control and Optimization
A method for bias-reduction of sample-based MLE of the autologistic model
Computational Statistics & Data Analysis
A Bayesian analysis of dual autoradiographic images
Computational Statistics & Data Analysis
Noncausal Gauss Markov random fields: parameter structure and estimation
IEEE Transactions on Information Theory
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Statistical inference for the models with intractable normalizing constants has attracted much attention. During the past two decades, various approximation- or simulation-based methods have been proposed for the problem, such as the Monte Carlo maximum likelihood method and the auxiliary variable Markov chain Monte Carlo methods. The Bayesian stochastic approximation Monte Carlo algorithm specifically addresses this problem: It works by sampling from a sequence of approximate distributions with their average converging to the target posterior distribution, where the approximate distributions can be achieved using the stochastic approximation Monte Carlo algorithm. A strong law of large numbers is established for the Bayesian stochastic approximation Monte Carlo estimator under mild conditions. Compared to the Monte Carlo maximum likelihood method, the Bayesian stochastic approximation Monte Carlo algorithm is more robust to the initial guess of model parameters. Compared to the auxiliary variable MCMC methods, the Bayesian stochastic approximation Monte Carlo algorithm avoids the requirement for perfect samples, and thus can be applied to many models for which perfect sampling is not available or very expensive. The Bayesian stochastic approximation Monte Carlo algorithm also provides a general framework for approximate Bayesian analysis.