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Citation:

Vihola, M. (2011). Can the adaptive Metropolis algorithm collapse without the covariance lower bound?. Electronic Journal of Probability, 16, 45-75. DOI:10.1214/EJP.v16-840.

Title: | Can the adaptive Metropolis algorithm collapse without the covariance lower bound? |

Author: | Vihola, Matti |

Abstract: | The Adaptive Metropolis (AM) algorithm is based on the symmetric random-walk Metropolis algorithm. The proposal distribution has the following time-dependent covariance matrix at step $n+1$ \[ S_n = Cov(X_1,...,X_n) + \epsilon I, \] that is, the sample covariance matrix of the history of the chain plus a (small) constant $\epsilon>0$ multiple of the identity matrix $I$. The lower bound on the eigenvalues of $S_n$ induced by the factor $\epsilon I$ is theoretically convenient, but practically cumbersome, as a good value for the parameter $\epsilon$ may not always be easy to choose. This article considers variants of the AM algorithm that do not explicitly bound the eigenvalues of $S_n$ away from zero. The behaviour of $S_n$ is studied in detail, indicating that the eigenvalues of $S_n$ do not tend to collapse to zero in general. |

Publisher: | Institute of Mathematical Statistics |

Date: | 2011 |

Belongs to series: | Electronic Journal of Probability |

ISSN: | 1083-6489 |

Subjects: | adaptiivinen Markov chain Monte Carlo Metropolis-algoritmi stabiilius stokastinen approksimaatio Adaptive Markov chain Monte Carlo Metropolis algorithm stability stochastic approximation |

Rights: | This work is licensed under a Creative Commons Attribution 3.0 License. |

Rights: | http://creativecommons.org/licenses/by/3.0/ |

DOI: | 10.1214/EJP.v16-840 |

Original source: http://ejp.ejpecp.org/

Permanent link to this item: http://urn.fi/URN:NBN:fi:jyu-201210262789

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