Limit theorems for some adaptive MCMC algorithms with subgeometric kernels: Part II

Details Limit theorems for some adaptive MCMC algorithms with subgeometric kernels: Part II Limit theorems for some adaptive MCMC algorithms with subgeometric kernels: Part II

2009-11-02

arxiv.org/abs/0911.0221v1

Mathematics

Probability

34 pages

Scientific paper

We prove a central limit theorem for a general class of adaptive Markov Chain
Monte Carlo algorithms driven by sub-geometrically ergodic Markov kernels. We
discuss in detail the special case of stochastic approximation. We use the
result to analyze the asymptotic behavior of an adaptive version of the
Metropolis Adjusted Langevin algorithm with a heavy tailed target density.

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