Can the adaptive Metropolis algorithm collapse without the covariance lower bound?

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dc.contributor.author Vihola, Matti
dc.date.accessioned 2012-10-26T06:23:16Z
dc.date.available 2012-10-26T06:23:16Z
dc.date.issued 2011
dc.identifier.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.
dc.identifier.issn 1083-6489
dc.identifier.uri http://hdl.handle.net/123456789/40092
dc.description.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. fi
dc.language.iso eng
dc.publisher Institute of Mathematical Statistics
dc.relation.ispartofseries Electronic Journal of Probability
dc.relation.uri http://ejp.ejpecp.org/
dc.rights This work is licensed under a Creative Commons Attribution 3.0 License.
dc.rights.uri http://creativecommons.org/licenses/by/3.0/
dc.subject.other adaptiivinen Markov chain Monte Carlo fi
dc.subject.other Metropolis-algoritmi fi
dc.subject.other stabiilius fi
dc.subject.other stokastinen approksimaatio fi
dc.subject.other Adaptive Markov chain Monte Carlo en
dc.subject.other Metropolis algorithm en
dc.subject.other stability en
dc.subject.other stochastic approximation en
dc.title Can the adaptive Metropolis algorithm collapse without the covariance lower bound?
dc.type Article en
dc.identifier.urn URN:NBN:fi:jyu-201210262789
dc.subject.kota 111
dc.contributor.laitos Matematiikan ja tilastotieteen laitos fi
dc.contributor.laitos en
dc.type.uri http://purl.org/eprint/type/JournalArticle
dc.identifier.doi 10.1214/EJP.v16-840
dc.description.version Publisher's PDF
eprint.status http://purl.org/eprint/type/status/PeerReviewed

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