MARKOV CHAIN MONTE CARLO MIXING TIMES IN HIGH DIMENSIONS USING APPROXIMATE SPECTRAL GAPS
AGUÊMON YVES ATCHADÉ – BOSTON UNIVERSITY
Understanding the type of problems for which fast Markov Chain Monte Carlo (MCMC) sampling is possible is a question of fundamental interest. The study of the size of the spectral gap is a widely used approach. However this approach may be inappropriate when dealing with distributions with small isolated local modes. This talk introduces a concept of approximate spectral gap, a refinement that discounts the ill effects of small local modes, but still describes well the overall mixing behavior of the Markov chain. We use the idea to analyze several large scale MCMC algorithms and their simulated tempering versions. Applications to Bayesian computations on statistical models where the number of parameters and the number of data points are both very large are considered.