On the stability and ergodicity of adaptive scaling Metropolis algorithms

Details On the stability and ergodicity of adaptive scaling Metropolis algorithms On the stability and ergodicity of adaptive scaling Metropolis algorithms

2009-03-24

arxiv.org/abs/0903.4061v3

Stochastic Processes and their Applications 121(12):2839-2860, 2011

Mathematics

Probability

24 pages, 1 figure; major revision

Scientific paper

10.1016/j.spa.2011.08.006

The stability and ergodicity properties of two adaptive random walk Metropolis algorithms are considered. The both algorithms adjust the scaling of the proposal distribution continuously based on the observed acceptance probability. Unlike the previously proposed forms of the algorithms, the adapted scaling parameter is not constrained within a predefined compact interval. The first algorithm is based on scale adaptation only, while the second one incorporates also covariance adaptation. A strong law of large numbers is shown to hold assuming that the target density is smooth enough and has either compact support or super-exponentially decaying tails.

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