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Bayesian uncertainty management in temporal dependence of extremes

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Bayesian uncertainty management in temporal dependence of extremes. / Lugrin, T.; Davison, A. C.; Tawn, J. A.

In: Extremes, Vol. 19, No. 3, 09.2016, p. 491-515.

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Lugrin, T. ; Davison, A. C. ; Tawn, J. A. / Bayesian uncertainty management in temporal dependence of extremes. In: Extremes. 2016 ; Vol. 19, No. 3. pp. 491-515.

Bibtex

@article{62cfa95e97c345b79e4fe3a6285413c6,
title = "Bayesian uncertainty management in temporal dependence of extremes",
abstract = "Both marginal and dependence features must be described when modelling the extremes of a stationary time series. There are standard approaches to marginal modelling, but long- and short-range dependence of extremes may both appear. In applications, an assumption of long-range independence often seems reasonable, but short-range dependence, i.e., the clustering of extremes, needs attention. The extremal index 0 < ≤ 1 is a natural limiting measure of clustering, but for wide classes of dependent processes, including all stationary Gaussian processes, it cannot distinguish dependent processes from independent processes with = 1. Eastoe and Tawn (Biometrika 99, 43–55 2012) exploit methods from multivariate extremes to treat the subasymptotic extremal dependence structure of stationary time series, covering both 0 < <1 and = 1, through the introduction of a threshold-based extremal index. Inference for their dependence models uses an inefficient stepwise procedure that has various weaknesses and has no reliable assessment of uncertainty. We overcome these issues using a Bayesian semiparametric approach. Simulations and the analysis of a UK daily river flow time series show that the new approach provides improved efficiency for estimating properties of functionals of clusters.",
keywords = "Asymptotic independence, Bayesian semiparametrics, Conditional extremes, Dirichlet process, Extreme value theory, Extremogram, Risk analysis, Threshold-based extremal index",
author = "T. Lugrin and Davison, {A. C.} and Tawn, {J. A.}",
note = "The final publication is available at Springer via http://dx.doi.org/10.1007/s10687-016-0258-0",
year = "2016",
month = sep
doi = "10.1007/s10687-016-0258-0",
language = "English",
volume = "19",
pages = "491--515",
journal = "Extremes",
issn = "1386-1999",
publisher = "Springer Netherlands",
number = "3",

}

RIS

TY - JOUR

T1 - Bayesian uncertainty management in temporal dependence of extremes

AU - Lugrin, T.

AU - Davison, A. C.

AU - Tawn, J. A.

N1 - The final publication is available at Springer via http://dx.doi.org/10.1007/s10687-016-0258-0

PY - 2016/9

Y1 - 2016/9

N2 - Both marginal and dependence features must be described when modelling the extremes of a stationary time series. There are standard approaches to marginal modelling, but long- and short-range dependence of extremes may both appear. In applications, an assumption of long-range independence often seems reasonable, but short-range dependence, i.e., the clustering of extremes, needs attention. The extremal index 0 < ≤ 1 is a natural limiting measure of clustering, but for wide classes of dependent processes, including all stationary Gaussian processes, it cannot distinguish dependent processes from independent processes with = 1. Eastoe and Tawn (Biometrika 99, 43–55 2012) exploit methods from multivariate extremes to treat the subasymptotic extremal dependence structure of stationary time series, covering both 0 < <1 and = 1, through the introduction of a threshold-based extremal index. Inference for their dependence models uses an inefficient stepwise procedure that has various weaknesses and has no reliable assessment of uncertainty. We overcome these issues using a Bayesian semiparametric approach. Simulations and the analysis of a UK daily river flow time series show that the new approach provides improved efficiency for estimating properties of functionals of clusters.

AB - Both marginal and dependence features must be described when modelling the extremes of a stationary time series. There are standard approaches to marginal modelling, but long- and short-range dependence of extremes may both appear. In applications, an assumption of long-range independence often seems reasonable, but short-range dependence, i.e., the clustering of extremes, needs attention. The extremal index 0 < ≤ 1 is a natural limiting measure of clustering, but for wide classes of dependent processes, including all stationary Gaussian processes, it cannot distinguish dependent processes from independent processes with = 1. Eastoe and Tawn (Biometrika 99, 43–55 2012) exploit methods from multivariate extremes to treat the subasymptotic extremal dependence structure of stationary time series, covering both 0 < <1 and = 1, through the introduction of a threshold-based extremal index. Inference for their dependence models uses an inefficient stepwise procedure that has various weaknesses and has no reliable assessment of uncertainty. We overcome these issues using a Bayesian semiparametric approach. Simulations and the analysis of a UK daily river flow time series show that the new approach provides improved efficiency for estimating properties of functionals of clusters.

KW - Asymptotic independence

KW - Bayesian semiparametrics

KW - Conditional extremes

KW - Dirichlet process

KW - Extreme value theory

KW - Extremogram

KW - Risk analysis

KW - Threshold-based extremal index

U2 - 10.1007/s10687-016-0258-0

DO - 10.1007/s10687-016-0258-0

M3 - Journal article

VL - 19

SP - 491

EP - 515

JO - Extremes

JF - Extremes

SN - 1386-1999

IS - 3

ER -