## International Statistical Review

- Internat. Statist. Rev.
- Volume 73, Number 3 (2005), 309-330.

### Statistical Decision Problems and Bayesian Nonparametric Methods

Eduardo Gutiérrez-Peña and Stephen G. Walker

#### 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.

#### Article information

**Source**

Internat. Statist. Rev., Volume 73, Number 3 (2005), 309-330.

**Dates**

First available in Project Euclid: 5 December 2005

**Permanent link to this document**

https://projecteuclid.org/euclid.isr/1133819157

**Zentralblatt MATH identifier**

1105.62006

**Keywords**

Coherence Consistency Decision theory Divergence Expected utility Nonparametric prior Parametric predictive density

#### Citation

Gutiérrez-Peña, Eduardo; Walker, Stephen G. Statistical Decision Problems and Bayesian Nonparametric Methods. Internat. Statist. Rev. 73 (2005), no. 3, 309--330. https://projecteuclid.org/euclid.isr/1133819157