Non parametric mixture priors based on an exponential random scheme

Petrone Sonia and Veronese Piero ()
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Petrone Sonia: Department of Economics, University of Insubria, Italy
Veronese Piero: University of Milan, Italy

Economics and Quantitative Methods from Department of Economics, University of Insubria

Abstract: We propose a general procedure for constructing nonparametric priors for Bayesian inference. Under very general assumptions,the proposed prior selects absolutely continuous distribution functions, hence it can be useful with continuous data. We use the notion of Feller-type approximation, with a random scheme based on the natural exponential family, in order to construct a large class of distribution functions. We show how one can assign a probability to such a class and discuss the main properties of the proposed prior, named Feller prior. Feller priors are related to mixture models with unknown number of components or, more generally,to mixtures with unknown weight distribution. Two illustrations relative to the estimation of a density and of a mixing distribution are carried out with respect to well known data-set in order to evaluate the performance ofour procedure. Computations are performed using a modified version of an MCMC algorithm which is briefly described.

Keywords: Bernstein Polynomials; density estimation; Feller operators; Hierarchical models; Mixture Models; Non-parametric Bayesian Inference (search for similar items in EconPapers)
Pages: 18 pages
Date: 2001-04
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Persistent link: https://EconPapers.repec.org/RePEc:ins:quaeco:qf0104

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