A flexible Bayesian hierarchical modeling framework for spatially dependent peaks-over-threshold data

Yadav, Rishikesh; Huser, Raphaël; Opitz, Thomas

doi:10.1016/j.spasta.2022.100672

Cited by 4 publications

(3 citation statements)

References 26 publications

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“…Posterior inference is obtained from the LGCP model (7) based on a stochastic gradient-based MCMC method (For more details refer to [42] and Algorithm 1 in [43]). In LGCP models of the form (7), the set of parameters, hyperparameters, and latent variables is given by…”

Section: Computational Details For Fitting the Lgcp Modelmentioning

confidence: 99%

“…We update them within MCMC using a M-H algorithm, similar to updating φ ε and r ε . For the latent vectors {Λ t } T t=1 , we do not have closed-from posteriors, and thus we update them jointly using the stochastic gradient Langevin dynamics, which is similar to Algorithm 1 in [43]. For the latent vectors {ζ * t } T t=1 , we have closed-form full posteriors, and thus they are updated using Gibbs sampling.…”

Section: Computational Details For Fitting the Lgcp Modelmentioning

confidence: 99%

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A combined statistical and machine learning approach for spatial prediction of extreme wildfire frequencies and sizes

et al. 2023

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Motivated by the Extreme Value Analysis 2021 (EVA 2021) data challenge we propose a method based on statistics and machine learning for the spatial prediction of extreme wildfire frequencies and sizes. This method is tailored to handle large datasets, including missing observations. Our approach relies on a four-stage high-dimensional bivariate sparse spatial model for zero-inflated data, which is developed using stochastic partial differential equations (SPDE). In Stage 1, the observations are categorized in zero/nonzero categories and are modeled using a two-layered hierarchical Bayesian sparse spatial model to estimate the probabilities of these two categories. In Stage 2, before modeling the positive observations using a spatially-varying coefficients, smoothed parameter surfaces are obtained from empirical estimates using fixed rank kriging. This approximate Bayesian method inference was employed to avoid the high computational burden of large spatial data modeling using spatially-varying coefficients. In Stage 3, the standardized log-transformed positive observations from the second stage are further modeled using a sparse bivariate spatial Gaussian process. The Gaussian distribution assumption for wildfire counts developed in the third stage, is computationally effective but erroneous. Thus in Stage 4, the predicted values are rectified using Random Forests. Posterior inference is drawn for Stages 1 and 3 using Markov chain Monte Carlo (MCMC) sampling. A cross-validation scheme is then created for the artificially Extreme wildfire frequency and size prediction generated gaps, and the EVA 2021 prediction scores of the proposed model are compared to those obtained using certain natural competitors.

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Section: Computational Details For Fitting the Lgcp Modelmentioning

confidence: 99%

Section: Computational Details For Fitting the Lgcp Modelmentioning

confidence: 99%

A combined statistical and machine learning approach for spatial prediction of extreme wildfire frequencies and sizes

et al. 2023

Self Cite

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show abstract

“…The use of an NN for this problem offers the following benefits: The NN architecture is well suited for inference, allowing for the efficient estimation of parameters. In particular, the network can be quickly evaluated once trained, resulting in significant speed gains of up to 170 times or even more compared to traditional methods. To address the issue of uncertainty in our parameter estimates, we adopt the bootstrapping approach, which has been widely supported by previous research (see, for example, Cooley et al (2007), Huang et al (2016), Gamet and Jalbert (2022), Yadav et al (2022), Lenzi et al (2023), and Sainsbury‐Dale, Zammit‐Mangion, and Huser (2023)). In particular, to generate confidence intervals, we utilized the parametric bootstrap, which is typically computationally intensive.…”

Section: Introductionmentioning

confidence: 99%

Fast parameter estimation of generalized extreme value distribution using neural networks

Rai,

Hoffman,

Lahiri

et al. 2024

Environmetrics

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The heavy‐tailed behavior of the generalized extreme‐value distribution makes it a popular choice for modeling extreme events such as floods, droughts, heatwaves, wildfires and so forth. However, estimating the distribution's parameters using conventional maximum likelihood methods can be computationally intensive, even for moderate‐sized datasets. To overcome this limitation, we propose a computationally efficient, likelihood‐free estimation method utilizing a neural network. Through an extensive simulation study, we demonstrate that the proposed neural network‐based method provides generalized extreme value distribution parameter estimates with comparable accuracy to the conventional maximum likelihood method but with a significant computational speedup. To account for estimation uncertainty, we utilize parametric bootstrapping, which is inherent in the trained network. Finally, we apply this method to 1000‐year annual maximum temperature data from the Community Climate System Model version 3 across North America for three atmospheric concentrations: 289 ppm (pre‐industrial), 700 ppm (future conditions), and 1400 ppm , and compare the results with those obtained using the maximum likelihood approach.

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Flexible modeling of multivariate spatial extremes

Gong¹,

Huser²

2022

Spatial Statistics

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A flexible Bayesian hierarchical modeling framework for spatially dependent peaks-over-threshold data

Cited by 4 publications

References 26 publications

A combined statistical and machine learning approach for spatial prediction of extreme wildfire frequencies and sizes

A combined statistical and machine learning approach for spatial prediction of extreme wildfire frequencies and sizes

Fast parameter estimation of generalized extreme value distribution using neural networks

Flexible modeling of multivariate spatial extremes

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