An official website of the United States government
Summary The three-parameter generalized extreme value distribution arises from classical univariate extreme value theory, and is in common use for analysing the far tail of observed phenomena, yet important asymptotic properties of likelihood-based estimation under this standard model have not been established. In this paper we prove that the maximum likelihood estimator is global and unique. An interesting secondary result entails the uniform consistency of a class of limit relations in a tight neighbourhood of the true shape parameter.
more »
« less
Fast parameter estimation of generalized extreme value distribution using neural networks
Abstract 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.
more »
« less
- Award ID(s):
- 2210840
- PAR ID:
- 10500413
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Environmetrics
- Volume:
- 35
- Issue:
- 3
- ISSN:
- 1180-4009
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Accurate forecasting of extreme values in time series is critical due to the significant impact of extreme events on human and natural systems. This paper presents DeepExtrema, a novel framework that combines a deep neural network (DNN) with generalized extreme value (GEV) distribution to forecast the block maximum value of a time series. Implementing such a network is a challenge as the framework must preserve the inter-dependent constraints among the GEV model parameters even when the DNN is initialized. We describe our approach to address this challenge and present an architecture that enables both conditional mean and quantile prediction of the block maxima. The extensive experiments performed on both real-world and synthetic data demonstrated the superiority of DeepExtrema compared to other baseline methods.more » « less
-
We consider the question of learning the natural parameters of a k parameter \textit{minimal} exponential family from i.i.d. samples in a computationally and statistically efficient manner. We focus on the setting where the support as well as the natural parameters are appropriately bounded. While the traditional maximum likelihood estimator for this class of exponential family is consistent, asymptotically normal, and asymptotically efficient, evaluating it is computationally hard. In this work, we propose a computationally efficient estimator that is consistent as well as asymptotically normal under mild conditions. We provide finite sample guarantees to achieve an l2 error of α in the parameter estimation with sample complexity O(poly(k/α)) and computational complexity O(poly(k/α)). To establish these results, we show that, at the population level, our method can be viewed as the maximum likelihood estimation of a re-parameterized distribution belonging to the same class of exponential family.more » « less
-
Abstract The estimation of exceedance probabilities for extreme climatic events is critical for infrastructure design and risk assessment. Climatic events occur over a greater space than they are measured with point‐scale in situ gauges. In extreme value theory, the block maxima approach for spatial analysis of extremes depends on properly modeling the spatially varying Generalized Extreme Value marginal parameters (i.e., trend surfaces). Fitting these trend surfaces can be challenging since there are numerous spatial and temporal covariates that are potentially relevant for any given event type and region. Traditionally, covariate selection is based on assumptions regarding the topmost relevant drivers of the event. This work demonstrates the benefit of utilizing elastic‐net regression to support automatic selection from a relatively large set of physically relevant covariates during trend surface estimation. The trend surfaces presented are based on 24‐hr annual maximum precipitation for northeastern Colorado and the Texas‐Louisiana Gulf Coast.more » « less
-
Abstract Analysis of phylogenetic trees has become an essential tool in epidemiology. Likelihood-based methods fit models to phylogenies to draw inferences about the phylodynamics and history of viral transmission. However, these methods are often computationally expensive, which limits the complexity and realism of phylodynamic models and makes them ill-suited for informing policy decisions in real-time during rapidly developing outbreaks. Likelihood-free methods using deep learning are pushing the boundaries of inference beyond these constraints. In this paper, we extend, compare, and contrast a recently developed deep learning method for likelihood-free inference from trees. We trained multiple deep neural networks using phylogenies from simulated outbreaks that spread among 5 locations and found they achieve close to the same levels of accuracy as Bayesian inference under the true simulation model. We compared robustness to model misspecification of a trained neural network to that of a Bayesian method. We found that both models had comparable performance, converging on similar biases. We also implemented a method of uncertainty quantification called conformalized quantile regression that we demonstrate has similar patterns of sensitivity to model misspecification as Bayesian highest posterior density (HPD) and greatly overlap with HPDs, but have lower precision (more conservative). Finally, we trained and tested a neural network against phylogeographic data from a recent study of the SARS-Cov-2 pandemic in Europe and obtained similar estimates of region-specific epidemiological parameters and the location of the common ancestor in Europe. Along with being as accurate and robust as likelihood-based methods, our trained neural networks are on average over 3 orders of magnitude faster after training. Our results support the notion that neural networks can be trained with simulated data to accurately mimic the good and bad statistical properties of the likelihood functions of generative phylogenetic models.more » « less
