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.uri | https://jyx.jyu.fi/handle/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 | CC BY 3.0 | |
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.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.title | Can the adaptive Metropolis algorithm collapse without the covariance lower bound? | |
dc.type | Article | |
dc.identifier.urn | URN:NBN:fi:jyu-201210262789 | |
dc.contributor.laitos | Matematiikan ja tilastotieteen laitos | fi |
dc.contributor.laitos | | en |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | |
dc.type.coar | journal article | |
dc.description.reviewstatus | peerReviewed | |
dc.relation.issn | 1083-6489 | |
dc.type.version | publishedVersion | |
dc.rights.copyright | © Vihola, 2011. | |
dc.rights.accesslevel | openAccess | fi |
dc.rights.url | http://creativecommons.org/licenses/by/3.0/ | |
dc.relation.doi | 10.1214/EJP.v16-840 | |