 Rates of Convergence for a Bayesian Level Set EstimationGhislaine Gayraud and Judith Rousseau Scandinavian Journal of Statistics, 2005, vol. 32, issue 4, 639-660 Abstract: Abstract. We are interested in estimating level sets using a Bayesian non‐parametric approach, from an independent and identically distributed sample drawn from an unknown distribution. Under fairly general conditions on the prior, we provide an upper bound on the rate of convergence of the Bayesian level set estimate, via the rate at which the posterior distribution concentrates around the true level set. We then consider, as an application, the log‐spline prior in the two‐dimensional unit cube. Assuming that the true distribution belongs to a class of Hölder, we provide an upper bound on the rate of convergence of the Bayesian level set estimates. We compare our results with existing rates of convergence in the frequentist non‐parametric literature: the Bayesian level set estimator proves to be competitive and is also easy to compute, which is of no small importance. A simulation study is given as an illustration. Date: 2005 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:scjsta:v:32:y:2005:i:4:p:639-660 Ordering information: This journal article can be ordered from Access Statistics for this article Scandinavian Journal of Statistics is currently edited by ÿrnulf Borgan and Bo Lindqvist More articles in Scandinavian Journal of Statistics from Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association, Swedish Statistical Association |
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