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Posterior propriety in Bayesian extreme value analyses using reference priors

Northrop, PJ; Attalides, N; (2016) Posterior propriety in Bayesian extreme value analyses using reference priors. Statistica Sinica , 26 (2) pp. 721-743. 10.5705/ss.2014.034. Green open access

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Abstract

The Generalized Pareto (GP) and Generalized extreme value (GEV) distributions play an important role in extreme value analyses as models for threshold excesses and block maxima, respectively. For each of these distributions we consider Bayesian inference using “reference” prior distributions (in the general sense of priors constructed using formal rules) for the model parameters, specifically a Jeffreys prior, the maximal data information (MDI) prior and independent uniform priors on separate model parameters. We investigate whether these improper priors lead to proper posterior distributions. We show that, in the GP and GEV cases, the MDI prior, unless modified, never yields a proper posterior and that in the GEV case this also applies to the Jeffreys prior. We also show that a sample size of three (four) is sufficient for independent uniform priors to yield a proper posterior distribution in the GP (GEV) case.

Type: Article
Title: Posterior propriety in Bayesian extreme value analyses using reference priors
Open access status: An open access version is available from UCL Discovery
DOI: 10.5705/ss.2014.034
Publisher version: http://dx.doi.org/10.5705/ss.2014.034
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Extreme value theory, generalized extreme value distribution, generalized Pareto distribution, posterior propriety, reference prior
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/1469298
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