High-Order Composite Likelihood Inference for Max-Stable Distributions and Processes

Castruccio, Stefano; Huser, Raphaël; Genton, Marc G.

doi:10.1080/10618600.2015.1086656

Cited by 85 publications

(118 citation statements)

References 44 publications

Supporting

Mentioning

118

Contrasting

Order By: Relevance

“…Assuming temporal independence of the y 's, but spatial dependence, the log‐likelihood of the model is written as

ℓ (λ, κ, b, ψ) = \sum_{t = 1}^{T} \log g (y_{1 t}, \dots, y_{Nt}),

where g is the multivariate density of Brown‐Resnick model. Wadsworth and Tawn () give a closed form expression for g ; however, its computation results in a combinatorial explosion (Castruccio et al, ; Davison & Gholamrezaee, ). It is possible to circumvent this issue by making estimation based on the pairwise log‐likelihood (Padoan et al, ; Varin et al, )

ℓ_{1} (λ, κ, b, ψ) = \sum_{t = 1}^{T} \sum_{i = 1}^{N - 1} \sum_{j = i + 1}^{N} \log g_{ij} (y_{it}, y_{jt}),

where g i j is the bivariate density of ( Y i , Y j ), that is, associated to , and N is the number of stations.…”

Section: Methodsmentioning

confidence: 99%

Trend in the Co‐Occurrence of Extreme Daily Rainfall in West Africa Since 1950

et al. 2018

View full text Add to dashboard Cite

We propose in this paper a statistical framework to study the evolution of the co‐occurrence of extreme daily rainfall in West Africa since 1950. We consider two regions subject to contrasted rainfall regimes: Senegal and the central Sahel. We study the likelihood of the 3% largest daily rainfall (considering all days) in each region to occur simultaneously and, in a 20 year moving window approach, how this likelihood has evolved with time. Our method uses an anisotropic max‐stable process allowing us to properly represent the co‐occurrence of daily extremes and including the possibility of a preferred direction of co‐occurrence. In Senegal, a change is found in the 1980s, with preferred co‐occurrence along the E‐50‐N direction (i.e., along azimuth 50°) before the 1980s and weaker isotropic co‐occurrence afterward. In central Sahel, a change is also found in the 1980s but surprisingly with contrasting results. Anisotropy along the E‐W direction is found over the whole period, with greater extension after the 1980s. The paper discusses how the co‐occurrence of extremes can provide a qualitative indicator on change in size and propagation of the strongest storms. This calls for further research to identify the atmospheric processes responsible for such contrasted changes in storm properties.

show abstract

“…Assuming temporal independence of the y 's, but spatial dependence, the log‐likelihood of the model is written as

ℓ (λ, κ, b, ψ) = \sum_{t = 1}^{T} \log g (y_{1 t}, \dots, y_{Nt}),

ℓ_{1} (λ, κ, b, ψ) = \sum_{t = 1}^{T} \sum_{i = 1}^{N - 1} \sum_{j = i + 1}^{N} \log g_{ij} (y_{it}, y_{jt}),

where g i j is the bivariate density of ( Y i , Y j ), that is, associated to , and N is the number of stations.…”

Section: Methodsmentioning

confidence: 99%

Trend in the Co‐Occurrence of Extreme Daily Rainfall in West Africa Since 1950

et al. 2018

View full text Add to dashboard Cite

show abstract

“…By differentiating the distribution with respect to the variables z 1 ,…, z D , we can deduce that the corresponding density, or the full likelihood for one replicate, may be expressed as

g_{Full} false(z_{1}, ⋯, z_{D} false) = \exp false{- V false(z_{1}, ⋯, z_{D} false) false} \sum_{π \in P_{D}} true \prod_{i = 1}^{| π |} false{- V_{τ_{i}} false(z_{1}, ⋯, z_{D} false) false},

where

V_{τ_{i}}

denotes the partial derivative of the function V with respect to the variables indexed by the set τ i ⊆{1,…, D } (Huser et al, ; Castruccio et al, ). The sum in Equation is taken over the set of all possible partitions π={τ 1 ,…,τ |π| } of {1,…, D }, denoted by

P_{D}

, the size of which equals the Bell number of order D .…”

Section: Likelihood Inferencementioning

confidence: 99%

“…As detailed in Section , likelihood evaluations require the computation of a sum indexed by all elements of a given set

P_{D}

, the cardinality of which grows more than exponentially with the dimension, D . In a thorough simulation study, Castruccio, Huser, and Genton () stated that current technologies are limiting full likelihood inference to dimension 12 or 13, and they concluded that without meaningful methodological advances, a direct full likelihood approach will not be feasible.…”

Section: Introductionmentioning

confidence: 99%

“…Although this method is computationally attractive and inherits many good properties from the maximum likelihood estimator, it also entails a loss in efficiency, which becomes more apparent in high dimensions (Huser, Davison, & Genton, ). More efficient triplewise and higher order composite likelihoods were investigated by Genton, Ma, and Sang (), Huser and Davison (), Sang and Genton (), and Castruccio et al (). However, they are still not fully efficient, and it is not clear how to optimally select the composite likelihood terms.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Full likelihood inference for max‐stable data

Huser

Dombry

Ribatet

et al. 2019

Stat

Self Cite

View full text Add to dashboard Cite

We show how to perform full likelihood inference for max‐stable multivariate distributions or processes based on a stochastic expectation–maximization algorithm, which combines statistical and computational efficiency in high dimensions. The good performance of this methodology is demonstrated by simulation based on the popular logistic and Brown–Resnick models, and it is shown to provide computational time improvements with respect to a direct computation of the likelihood. Strategies to further reduce the computational burden are also discussed.

show abstract

“…• As discussed by Castruccio et al (2015), realizations from the HKEVP are dependent on the choice of spatial knots that define the kernels in the dependence structure. When fitting data with the HKEVP, the choice of knots has to be done carefully and has to be seen as a tradeoff between efficient estimation and computational burden.…”

Section: More About the Hkevpmentioning

confidence: 99%

Modeling extreme rainfall A comparative study of spatial extreme value models

2017

View full text Add to dashboard Cite

In this paper, focus is done on spatial models for extreme events and on their respective efficiency regarding the estimation of two risk measures: one extrapolating marginal distributions and one summarizing the spatial bivariate dependence of extremes. A wide comparison is performed on an innovative simulation plan that has been specifically designed from a daily precipitation data set. The objective of this paper is twofold: firstly, pointing out the inherent properties of each model, and secondly, advising users on how to choose the model depending on the specific type of risk.

show abstract

High-Order Composite Likelihood Inference for Max-Stable Distributions and Processes

Cited by 85 publications

References 44 publications

Trend in the Co‐Occurrence of Extreme Daily Rainfall in West Africa Since 1950

Trend in the Co‐Occurrence of Extreme Daily Rainfall in West Africa Since 1950

Full likelihood inference for max‐stable data

Modeling extreme rainfall A comparative study of spatial extreme value models

Contact Info

Product

Resources

About