Consistent semiparametric Bayesian inference about a location parameter

Ghosal, Subhashis ; Ghosh, Jayanta K. ; Ramamoorthi, R. V. (1999) Consistent semiparametric Bayesian inference about a location parameter Journal of Statistical Planning and Inference, 77 (2). pp. 181-193. ISSN 0378-3758

PDF - Publisher Version

Official URL:

Related URL:


We consider the problem of Bayesian inference about the centre of symmetry of a symmetric density on the real line based on independent identically distributed observations. A result of Diaconis and Freedman shows that the posterior distribution of the location parameter may be inconsistent if (symmetrized) Dirichlet process prior is used for the unknown distribution function. We choose a symmetrized Polya tree prior for the unknown density and independently choose θ according to a continuous and positive prior density on the real line. Suppose that the parameters of Polya tree depend only on the level m of the tree and the common values rm's are such that ∑m=1 rm-½ < ∞. Then it is shown that for a large class of true symmetric densities, including the trimodal distribution of Diaconis and Freedman, the marginal posterior of θ is consistent.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Consistency; Kullback-leibler Number; Location Parameter; Polya Tree; Dirichlet Process; Posterior Distribution
ID Code:22528
Deposited On:24 Nov 2010 08:24
Last Modified:17 May 2016 06:33

Repository Staff Only: item control page