Robust adaptive Metropolis algorithm with coerced acceptance rate

摘要

The adaptive Metropolis (AM) algorithm of Haario, Saksman and Tamminen (Bernoulli 7(2):223-242, 2001) uses the estimated covariance of the target distribution in the proposal distribution. This paper introduces a new ro-bust adaptive Metropolis algorithm estimating the shape of the target distribution and simultaneously coercing the ac-ceptance rate. The adaptation rule is computationally simple adding no extra cost compared with the AM algorithm. The adaptation strategy can be seen as a multidimensional exten-sion of the previously proposed method adapting the scale of the proposal distribution in order to attain a given acceptance rate. The empirical results show promising behaviour of the new algorithm in an example with Student target distribution having no finite second moment, where the AM covariance estimate is unstable. In the examples with finite second mo-ments, the performance of the new approach seems to be competitive with the AM algorithm combined with scale adaptation.