Weak Convergence and Optimal Proposals for Monte Carlo Algorithms
نویسنده
چکیده
Metropolis-Hastings Markov chain Monte Carlo (MCMC) algorithms and other popular MCMC algorithms induce a Markov chain which has the target distribution as its stationary distribution. Optimal scaling refers to the need to tune the parameters of the proposal kernel in order to ensure the Markov chain obtained from the algorithm converges as fast as possible to stationarity. Theoretical results for optimal scaling are obtained by approximating high dimensional algorithm trajectories by diffusions, and then maximizing the speed measure of the corresponding diffusion with respect to a transformation of the scale parameter. These notes summarize most of the literature regarding the optimal tuning of Markov chain Monte Carlo algorithms, and discuss the applications of these findings in practice. We have added an extensive appendix which summarizes some needed background to understand the proofs and concepts presented in the various papers.
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