Statistical decision problems and Bayesian nonparametric methods

Gutierrez-Pena, Eduardo and Walker, Stephen G. (2005) Statistical decision problems and Bayesian nonparametric methods. International Statistical Review, 73 (3). pp. 309-330. ISSN 0306-7734. (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.1111/j.1751-5823.2005.tb00151...

Abstract

This paper considers parametric statistical decision problems conducted within a Bayesian nonparametric context. Our work was motivated by the realisation that typical parametric model selection procedures are essentially incoherent. We argue that one solution to this problem is to use a flexible enough model in the first place, a model that will not be checked no matter what data arrive. Ideally, one would use a nonparametric model to describe all the uncertainty about the density function generating the data. However, parametric models are the preferred choice for many statisticians, despite the incoherence involved in model checking, incoherence that is quite often ignored for pragmatic reasons. In this paper we show how coherent parametric inference can be carried out via decision theory and Bayesian nonparametrics. None of the ingredients discussed here are new, but our main point only becomes evident when one sees all priors-even parametric ones-as measures on sets of densities as opposed to measures on finite-dimensional parameter spaces.

Item Type: Article
Uncontrolled keywords: coherence; consistency; decision theory; divergence; expected utility; nonparametric prior; parametric predictive density distributions; inference; models; consistency; mixture
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Judith Broom
Date Deposited: 06 Sep 2008 09:17
Last Modified: 28 Apr 2014 12:41
Resource URI: http://kar.kent.ac.uk/id/eprint/10524 (The current URI for this page, for reference purposes)
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