Adaptive algorithms and stochastic approximations
Adaptive algorithms and stochastic approximations
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Stability of Stochastic Approximation under Verifiable Conditions
SIAM Journal on Control and Optimization
Statistics and Computing
Short communication: Grapham: Graphical models with adaptive random walk Metropolis algorithms
Computational Statistics & Data Analysis
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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 robust adaptive Metropolis algorithm estimating the shape of the target distribution and simultaneously coercing the acceptance 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 extension 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 moments, the performance of the new approach seems to be competitive with the AM algorithm combined with scale adaptation.