Gutierrez-Pena, Eduardo,
Walker, Stephen G.
(2005)
*
Statistical decision problems and Bayesian nonparametric methods.
*
International Statistical Review,
73
(3).
pp. 309-330.
ISSN 0306-7734.
(doi:10.1111/j.1751-5823.2005.tb00151.x)
(The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)
(KAR id:10524)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. | |

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 |
---|---|

DOI/Identification number: | 10.1111/j.1751-5823.2005.tb00151.x |

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: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |

Depositing User: | Judith Broom |

Date Deposited: | 06 Sep 2008 09:17 UTC |

Last Modified: | 16 Nov 2021 09:49 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/10524 (The current URI for this page, for reference purposes) |

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