Latent Process Modelling of Threshold Exceedances in Hourly Rainfall Series

Bortot, Paola; Gaetan, Carlo

doi:10.1007/s13253-016-0254-5

Cited by 9 publications

(15 citation statements)

References 27 publications

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“…The constraint ξ > 0 is not restrictive for dealing with precipitation in the French Mediterranean area, which is known to be heavy-tailed. For general modeling purposes, we can relax this assumption by following Bortot and Gaetan (2016): we consider a marginal transformation within the class of GP distributions for threshold exceedances, for which we suppose that α = 1 and β = 1 for identifiability. By transforming Y (x) through the probability integral transform…”

Section: A Hierarchical Model For Spatio-temporal Exceedancesmentioning

confidence: 99%

Hierarchical Space-Time Modeling of Asymptotically Independent Exceedances With an Application to Precipitation Data

Bacro

Gaetan

Opitz

et al. 2019

Journal of the American Statistical Association

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The statistical modeling of space-time extremes in environmental applications is key to understanding complex dependence structures in original event data and to generating realistic scenarios for impact models. In this context of high-dimensional data, we propose a novel hierarchical model for high threshold exceedances defined over continuous space and time by embedding a space-time Gamma process convolution for the rate of an exponential variable, leading to asymptotic independence in space and time. Its physically motivated anisotropic dependence structure is based on geometric objects moving through space-time according to a velocity vector. We demonstrate that inference based on weighted pairwise likelihood is fast and accurate. The usefulness of our model is illustrated by an application to hourly precipitation data from a study region in Southern France, where it clearly improves on an alternative censored Gaussian space-time random field model. While classical limit models based on threshold-stability fail to appropriately capture relatively fast joint tail decay 1 arXiv:1708.02447v2 [stat.ME] 14 May 2019 rates between asymptotic dependence and classical independence, strong empirical evidence from our application and other recent case studies motivates the use of more realistic asymptotic independence models such as ours.

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Section: A Hierarchical Model For Spatio-temporal Exceedancesmentioning

confidence: 99%

Hierarchical Space-Time Modeling of Asymptotically Independent Exceedances With an Application to Precipitation Data

Bacro

Gaetan

Opitz

et al. 2019

Journal of the American Statistical Association

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“…The PL approach to inference on the frequentist interpretation of this model (i.e., up to the exclusion of the priors and interpretation of θ ; see Bortot & Gaetan, ) can also easily be modified to account for data quantization. Rather than integrating over the latent parameters, the PL approach replaces the full likelihood given in Equation by a PL, which is simpler to evaluate and still captures some of the dependence characteristics of the model.…”

Section: Bayesian Latent Temporal Model For Extremesmentioning

confidence: 99%

“…Because it is easily expressed conditionally as a hierarchical model, Bayesian estimation is a natural choice. The same modeling framework recently appeared in Bortot and Gaetan (, ), who, in contrast, estimated model parameters with composite likelihoods using bivariate densities of pairs of observations. Because our implementation is fully Bayesian, it is able to make use of the full data likelihood, constructed hierarchically.…”

Section: Introductionmentioning

confidence: 97%

“…Choosing a Markov chain structure for the latent process, together with the conditional independence in the observation model, makes inference for this model computationally tractable. Bortot and Gaetan () used a pairwise likelihood (PL) approach for inference by splitting the complete log likelihood into bivariate blocks and summing these blocks to form a composite likelihood objective function. In contrast, we perform inference based on the full likelihood, taking advantage of the hierarchical structure to construct our Markov chain Monte Carlo (MCMC) sampler.…”

Section: Introductionmentioning

confidence: 99%

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An exponential–gamma mixture model for extreme Santa Ana winds

Bopp

Shaby

2017

Environmetrics

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We analyze the behavior of extreme winds occurring in Southern California during the Santa Ana wind season using a latent mixture model. This mixture representation is formulated as a hierarchical Bayesian model and fit using Markov chain Monte Carlo. The two‐stage model results in generalized Pareto margins for exceedances and generates temporal dependence through a latent Markov process. This construction induces asymptotic independence in the response, while allowing for dependence at extreme, but subasymptotic, levels. We compare this model with a frequentist analogue where inference is performed via maximum pairwise likelihood. We use interval censoring to account for data quantization and estimate the extremal index and probabilities of multiday occurrences of extreme Santa Ana winds over a range of high thresholds.

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“…The GEV distribution is often used to model the maxima of regional precipitation, while the GP distribution is an asymptotic distribution of exceedances over a threshold, which should be high enough to justify the assumptions of the model but low enough to capture a reasonable number of observations (Dupuis, 1999). Recent studies on extreme precipitation using GEV/GP distribution models are summarized in Table 1, where thresholds are determined by different methods such as the mean annual number of peaks (e.g., Van Montfort and WITTER, 1986), weights (e.g., Dupuis, 1999), mean residual life plot (e.g., Begueria and Vicente-Serrano, 2006;Bortot and Gaetan, 2016), percentiles (e.g., 90th, 95th and 99th percentile) and average annual occurrence (e.g., Jiang et al, 2009). However, most of these studies are proposed in regional scale, the performance of GEV and GP distribution and diverse threshold are still unclear across the world.…”

Section: Introductionmentioning

confidence: 99%

Effects of different statistical distribution and threshold criteria in extreme precipitation modelling over global land areas

Wang

Wen

Lei

et al. 2019

Intl Journal of Climatology

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In statistical modelling of extreme precipitation, most of previous studies were proposed for some certain regions, the effects of diverse extreme distribution and threshold remain unclear on a global scale. In this study, we evaluated the performance of different extreme distribution and threshold across the global land areas, and proposed the optimal criteria in distribution and threshold determination for monthly extreme precipitation modelling. The performance of the generalized extreme value (GEV) distribution and generalized Pareto distribution (GPD) models were compared and the applicability of GPD models with thresholds determined by different percentiles in each grid was analysed. The results show that the GPD model is more suitable than the GEV model for monthly extreme precipitation, and the threshold over global land areas is likely to be associated with the spatial distribution of annual precipitation magnitude. The 97–99th percentile is most applicable to arid regions (e.g., the northern edge of North America, central Asia, North Africa, southwest Asia, central South America). The 93–96th percentile is most applicable to semi‐arid and semi‐humid regions (e.g., eastern North America, a strip region in northern Eurasia, and inland semi‐arid areas in Asia). The 90–92 percentile is most applicable to humid regions (e.g., central and southern North America, most areas in South America, Eurasia [except central Eurasia], southern and central Africa).

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Latent Process Modelling of Threshold Exceedances in Hourly Rainfall Series

Cited by 9 publications

References 27 publications

Hierarchical Space-Time Modeling of Asymptotically Independent Exceedances With an Application to Precipitation Data

Hierarchical Space-Time Modeling of Asymptotically Independent Exceedances With an Application to Precipitation Data

An exponential–gamma mixture model for extreme Santa Ana winds

Effects of different statistical distribution and threshold criteria in extreme precipitation modelling over global land areas

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