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A Poisson process reparameterisation for Bayesian inference for extremes

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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A Poisson process reparameterisation for Bayesian inference for extremes. / Sharkey, Paul; Tawn, Jonathan Angus.
In: Extremes, Vol. 20, No. 2, 06.2017, p. 239-263.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Sharkey, P & Tawn, JA 2017, 'A Poisson process reparameterisation for Bayesian inference for extremes', Extremes, vol. 20, no. 2, pp. 239-263. https://doi.org/10.1007/s10687-016-0280-2

APA

Sharkey, P., & Tawn, J. A. (2017). A Poisson process reparameterisation for Bayesian inference for extremes. Extremes, 20(2), 239-263. https://doi.org/10.1007/s10687-016-0280-2

Vancouver

Sharkey P, Tawn JA. A Poisson process reparameterisation for Bayesian inference for extremes. Extremes. 2017 Jun;20(2):239-263. Epub 2016 Dec 17. doi: 10.1007/s10687-016-0280-2

Author

Sharkey, Paul ; Tawn, Jonathan Angus. / A Poisson process reparameterisation for Bayesian inference for extremes. In: Extremes. 2017 ; Vol. 20, No. 2. pp. 239-263.

Bibtex

@article{4fbc8170580d4dc3b9a0278ae15fa478,
title = "A Poisson process reparameterisation for Bayesian inference for extremes",
abstract = "A common approach to modelling extreme values is to consider the excesses above a high threshold as realisations of a non-homogeneous Poisson process. While this method offers the advantage of modelling using threshold-invariant extreme value parameters, the dependence between these parameters makes estimation more dicult. We present a novel approach for Bayesian estimation of the Poisson process model parameters by reparameterising in terms of a tuning parameter m. This paper presents a method for choosing the optimal value of m that near-orthogonalises the parameters, which is achieved by minimising the correlation betweenthe asymptotic posterior distribution of the parameters. This choice of m ensures more rapid convergence and ecient sampling from the joint posterior distribution using Markov Chain Monte Carlo methods. Samples from the parameterisation of interest are then obtained by a simple transform. Results are presented in the cases of identically and non-identically distributed models for extreme rainfall in Cumbria, UK.",
keywords = "Poisson processes , Extreme value theory, Bayesian inference, Reparameterisation , Covariate modelling ",
author = "Paul Sharkey and Tawn, {Jonathan Angus}",
year = "2017",
month = jun,
doi = "10.1007/s10687-016-0280-2",
language = "English",
volume = "20",
pages = "239--263",
journal = "Extremes",
issn = "1386-1999",
publisher = "Springer Netherlands",
number = "2",

}

RIS

TY - JOUR

T1 - A Poisson process reparameterisation for Bayesian inference for extremes

AU - Sharkey, Paul

AU - Tawn, Jonathan Angus

PY - 2017/6

Y1 - 2017/6

N2 - A common approach to modelling extreme values is to consider the excesses above a high threshold as realisations of a non-homogeneous Poisson process. While this method offers the advantage of modelling using threshold-invariant extreme value parameters, the dependence between these parameters makes estimation more dicult. We present a novel approach for Bayesian estimation of the Poisson process model parameters by reparameterising in terms of a tuning parameter m. This paper presents a method for choosing the optimal value of m that near-orthogonalises the parameters, which is achieved by minimising the correlation betweenthe asymptotic posterior distribution of the parameters. This choice of m ensures more rapid convergence and ecient sampling from the joint posterior distribution using Markov Chain Monte Carlo methods. Samples from the parameterisation of interest are then obtained by a simple transform. Results are presented in the cases of identically and non-identically distributed models for extreme rainfall in Cumbria, UK.

AB - A common approach to modelling extreme values is to consider the excesses above a high threshold as realisations of a non-homogeneous Poisson process. While this method offers the advantage of modelling using threshold-invariant extreme value parameters, the dependence between these parameters makes estimation more dicult. We present a novel approach for Bayesian estimation of the Poisson process model parameters by reparameterising in terms of a tuning parameter m. This paper presents a method for choosing the optimal value of m that near-orthogonalises the parameters, which is achieved by minimising the correlation betweenthe asymptotic posterior distribution of the parameters. This choice of m ensures more rapid convergence and ecient sampling from the joint posterior distribution using Markov Chain Monte Carlo methods. Samples from the parameterisation of interest are then obtained by a simple transform. Results are presented in the cases of identically and non-identically distributed models for extreme rainfall in Cumbria, UK.

KW - Poisson processes

KW - Extreme value theory

KW - Bayesian inference

KW - Reparameterisation

KW - Covariate modelling

U2 - 10.1007/s10687-016-0280-2

DO - 10.1007/s10687-016-0280-2

M3 - Journal article

VL - 20

SP - 239

EP - 263

JO - Extremes

JF - Extremes

SN - 1386-1999

IS - 2

ER -