Robust adaptive Metropolis algorithm with coerced acceptance rate
- 947 Downloads
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.
KeywordsAcceptance rate Adaptive Markov chain Monte Carlo Ergodicity Metropolis algorithm Robustness
Unable to display preview. Download preview PDF.
- Andrieu, C., Robert, C.P.: Controlled MCMC for optimal sampling. Tech. Rep. Ceremade 0125, Université Paris Dauphine (2001) Google Scholar
- Andrieu, C., Moulines, É., Volkov, S.: Convergence of stochastic approximation for Lyapunov stable dynamics: a proof from first principles. Technical report (2004) Google Scholar
- Borkar, V.S.: Stochastic Approximation: A Dynamical Systems Viewpoint. Cambridge University Press, Cambridge (2008) Google Scholar
- Dongarra, J.J., Bunch, J.R., Moler, C.B., Stewart, G.W.: LINPACK Users’ Guide. Society for Industrial and Applied Mathematics (1979) Google Scholar
- Gelman, A., Roberts, G.O., Gilks, W.R.: Efficient Metropolis jumping rules. In: Bayesian Statistics 5, pp. 599–607. Oxford University Press, Oxford (1996) Google Scholar
- Gilks, W.R., Richardson, S., Spiegelhalter, D.J.: Markov Chain Monte Carlo in Practice. Chapman & Hall/CRC, Boca Raton (1998) Google Scholar
- Hastie, D.: Toward automatic reversible jump Markov chain Monte Carlo. PhD thesis, University of Bristol (2005) Google Scholar
- Vihola, M.: On the stability and ergodicity of adaptive scaling Metropolis algorithms. Preprint (2011b). arXiv:0903.4061v3