arXiv subjects

Benjamin A. Shaby

Publications and source records attributed to Benjamin A. Shaby.

15 recordsLinked to original sources

arXiv2026

Bayesian model averaging of risk set probabilities using a geometric representation of multivariate extremes

Modeling multivariate extremes using a geometric perspective leverages the shape of the multivariate point cloud to make inference on joint tail probabilities. While the original statistical framework for geometric extremes was fully parametric, relying on a gauge function that uniquely defines the shape for a given density, newer methods have introduced semi- and non-parametric alternatives to increase flexibility. We propose a modeling approach that retains the simplicity of the parametric framework but adds flexibility by using Bayesian model averaging (BMA) to improve prediction of tail risk probabilities. In contrast to previous works that use a truncated radial likelihood, we propose using a censored likelihood, which we find has consistently better performance in terms of predictive mean squared error, particularly in small-sample settings, although at the expense of increased bias. To generate predictions, we use a simple importance sampling scheme that seems to match the accuracy of more bespoke methods. Finally, we apply our approach to two fire weather indices, which are designed to capture somewhat orthogonal aspects of fire risk, to illustrate our method's practical utility in environmental applications.

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arXiv2026

Log-Laplace Nuggets for Fully Bayesian Fitting of Spatial Extremes Models to Threshold Exceedances

Flexible random scale-mixture models provide a framework for capturing a broad range of extremal dependence structures. However, likelihood-based inference under the peaks-over-threshold setting is often computationally infeasible, due to the censored likelihood requiring repeated evaluation of high-dimensional Gaussian distribution functions. We propose a multiplicative log-Laplace nugget that yields conditional independence in the censored likelihood, resulting in a joint likelihood function that is the product of univariate densities which are available in closed form. This eliminates multivariate Gaussian distribution function evaluations and thereby enables inference for threshold exceedances in high dimensions, which represents a major shift for spatial extremes modelling as the total computational cost is now primarily driven by standard spatial statistics operations. We further show that a broad class of scale-mixture processes augmented with the proposed nugget preserves the extremal dependence structure of the underlying smooth process. The proposed methodology is illustrated through simulation studies and an application to precipitation extremes.

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arXiv2025

Spatial scale-aware tail dependence modeling for high-dimensional spatial extremes

Extreme events over large spatial domains may exhibit highly heterogeneous tail dependence characteristics, yet most existing spatial extremes models yield only one dependence class over the entire spatial domain. To accurately characterize "data-level dependence'' in analysis of extreme events, we propose a mixture model that achieves flexible dependence properties and allows high-dimensional inference for extremes of spatial processes. We modify the popular random scale construction that multiplies a Gaussian random field by a single radial variable; we allow the radial variable to vary smoothly across space and add non-stationarity to the Gaussian process. As the level of extremeness increases, this single model exhibits both asymptotic independence at long ranges and either asymptotic dependence or independence at short ranges. We make joint inference on the dependence model and a marginal model using a copula approach within a Bayesian hierarchical model. Three different simulation scenarios show close to nominal frequentist coverage rates. Lastly, we apply the model to a dataset of extreme summertime precipitation over the central United States. We find that the joint tail of precipitation exhibits non-stationary dependence structure that cannot be captured by limiting extreme value models or current state-of-the-art sub-asymptotic models.

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arXiv2025

Semiparametric Estimation of the Shape of the Limiting Bivariate Point Cloud

We propose a model to flexibly estimate joint tail properties by exploiting the convergence of an appropriately scaled point cloud onto a compact limit set. Characteristics of the shape of the limit set correspond to key tail dependence properties. We directly model the shape of the limit set using Bezier splines, which allow flexible and parsimonious specification of shapes in two dimensions. We fit the Bezier splines to data in pseudo-polar coordinates using Markov chain Monte Carlo sampling, utilizing a limiting approximation to the conditional likelihood of the radii given angles. We propose a novel prior on the shape of the limit set via constraints on the parameters of the Bezier splines. A direct advantage of our Bayesian approach is that the support of this prior guarantees that each posterior sample is a valid limit set boundary, allowing direct posterior analysis of any quantity derived from the shape of the curve. Furthermore, we obtain interpretable inference on the asymptotic dependence class by using mixture priors with point masses on the corner of the unit box. Finally, we apply our model to bivariate datasets of extremes of variables related to fire risk and air pollution.

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arXiv2024

A Three-groups Non-local Model for Combining Heterogeneous Data Sources to Identify Genes Associated with Parkinson's Disease

We seek to identify genes involved in Parkinson's Disease (PD) by combining information across different experiment types. Each experiment, taken individually, may contain too little information to distinguish some important genes from incidental ones. However, when experiments are combined using the proposed statistical framework, additional power emerges. The fundamental building block of the family of statistical models that we propose is a hierarchical three-group mixture of distributions. Each gene is modeled probabilistically as belonging to either a null group that is unassociated with PD, a deleterious group, or a beneficial group. This three-group formalism has two key features. By apportioning prior probability of group assignments with a Dirichlet distribution, the resultant posterior group probabilities automatically account for the multiplicity inherent in analyzing many genes simultaneously. By building models for experimental outcomes conditionally on the group labels, any number of data modalities may be combined in a single coherent probability model, allowing information sharing across experiment types. These two features result in parsimonious inference with few false positives, while simultaneously enhancing power to detect signals. Simulations show that our three-groups approach performs at least as well as commonly-used tools for GWAS and RNA-seq, and in some cases it performs better. We apply our proposed approach to publicly-available GWAS and RNA-seq datasets, discovering novel genes that are potential therapeutic targets.

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arXiv2023

Modeling Extremal Streamflow using Deep Learning Approximations and a Flexible Spatial Process

Quantifying changes in the probability and magnitude of extreme flooding events is key to mitigating their impacts. While hydrodynamic data are inherently spatially dependent, traditional spatial models such as Gaussian processes are poorly suited for modeling extreme events. Spatial extreme value models with more realistic tail dependence characteristics are under active development. They are theoretically justified, but give intractable likelihoods, making computation challenging for small datasets and prohibitive for continental-scale studies. We propose a process mixture model (PMM) which specifies spatial dependence in extreme values as a convex combination of a Gaussian process and a max-stable process, yielding desirable tail dependence properties but intractable likelihoods. To address this, we employ a unique computational strategy where a feed-forward neural network is embedded in a density regression model to approximate the conditional distribution at one spatial location given a set of neighbors. We then use this univariate density function to approximate the joint likelihood for all locations by way of a Vecchia approximation. The PMM is used to analyze changes in annual maximum streamflow within the US over the last 50 years, and is able to detect areas which show increases in extreme streamflow over time.

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arXiv2023

Asymptotic posterior normality of the generalized extreme value distribution

The univariate generalized extreme value (GEV) distribution is the most commonly used tool for analyzing the properties of rare events. The ever greater utilization of Bayesian methods for extreme value analysis warrants detailed theoretical investigation, which has thus far been underdeveloped. Even the most basic asymptotic results are difficult to obtain because the GEV fails to satisfy standard regularity conditions. Here, we prove that the posterior distribution of the GEV parameter vector, given $n$ independent and identically distributed samples, converges in distribution to a trivariate normal distribution. The proof necessitates analyzing integrals of the GEV likelihood function over the entire parameter space, which requires considerable care because the support of the GEV density depends on the parameters in complicated ways.

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arXiv2023

Modeling First Arrival of Migratory Birds using a Hierarchical Max-infinitely Divisible Process

Humans have recorded the arrival dates of migratory birds for millennia, searching for trends and patterns. As the first arrival among individuals in a species is the realized tail of the probability distribution of arrivals, the appropriate statistical framework with which to analyze such events is extreme value theory. Here, for the first time, we apply formal extreme value techniques to the dynamics of bird migrations. We study the annual first arrivals of Magnolia Warblers using modern tools from the statistical field of extreme value analysis. Using observations from the eBird database, we model the spatial distribution of Magnolia Warbler arrivals as a max-infinitely divisible process, which allows us to spatially interpolate observed annual arrivals in a probabilistically-coherent way, and to project arrival dynamics into the future by conditioning on climatic variables.

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arXiv2020

A semiparametric spatiotemporal Bayesian model for the bulk and extremes of the Fosberg Fire Weather Index

Large wildfires pose a major environmental concern, and precise maps of fire risk can improve disaster relief planning. Fosberg Fire Weather Index (FFWI) is often used to measure wildfire risk; FFWI exhibits non-Gaussian marginal distributions as well as strong spatiotemporal extremal dependence and thus, modeling FFWI using geostatistical models like Gaussian processes is questionable. Extreme value theory (EVT)-driven models like max-stable processes are theoretically appealing but are computationally demanding and applicable only for threshold exceedances or block maxima. Disaster management policies often consider moderate-to-extreme quantiles of climate parameters and hence, joint modeling of the bulk and the tail of the data is required. In this paper, we consider a Dirichlet process mixture of spatial skew-t processes that can flexibly model the bulk as well as the tail. The proposed model has nonstationary mean and covariance structure, and also nonzero spatiotemporal extremal dependence. A simulation study demonstrates that the proposed model has better spatial prediction performance compared to some competing models. We develop spatial maps of FFWI medians and extremes, and discuss the wildfire risk throughout the Santa Ana region of California.

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arXiv2020

A Vecchia Approximation for High-Dimensional Gaussian Cumulative Distribution Functions Arising from Spatial Data

We introduce an approach to quickly and accurately approximate the cumulative distribution function of multivariate Gaussian distributions arising from spatial Gaussian processes. This approximation is trivially parallelizable and simple to implement using standard software. We demonstrate its accuracy and computational efficiency in a series of simulation experiments and apply it to analyzing the joint tail of a large precipitation dataset using a recently-proposed scale mixture model for spatial extremes. This dataset is many times larger than what was previously considered possible to fit using preferred inferential techniques.

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arXiv2020

A Hierarchical Max-Infinitely Divisible Spatial Model for Extreme Precipitation

Understanding the spatial extent of extreme precipitation is necessary for determining flood risk and adequately designing infrastructure (e.g., stormwater pipes) to withstand such hazards. While environmental phenomena typically exhibit weakening spatial dependence at increasingly extreme levels, limiting max-stable process models for block maxima have a rigid dependence structure that does not capture this type of behavior. We propose a flexible Bayesian model from a broader family of (conditionally) max-infinitely divisible processes that allows for weakening spatial dependence at increasingly extreme levels, and due to a hierarchical representation of the likelihood in terms of random effects, our inference approach scales to large datasets. Therefore, our model not only has a flexible dependence structure, but it also allows for fast, fully Bayesian inference, prediction and conditional simulation in high dimensions. The proposed model is constructed using flexible random basis functions that are estimated from the data, allowing for straightforward inspection of the predominant spatial patterns of extremes. In addition, the described process possesses (conditional) max-stability as a special case, making inference on the tail dependence class possible. We apply our model to extreme precipitation in North-Eastern America, and show that the proposed model adequately captures the extremal behavior of the data. Interestingly, we find that the principal modes of spatial variation estimated from our model resemble observed patterns in extreme precipitation events occurring along the coast (e.g., with localized tropical cyclones and convective storms) and mountain range borders. Our model, which can easily be adapted to other types of environmental datasets, is therefore useful to identify extreme weather patterns and regions at risk.

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arXiv2019

Hierarchical Transformed Scale Mixtures for Flexible Modeling of Spatial Extremes on Datasets with Many Locations

Flexible spatial models that allow transitions between tail dependence classes have recently appeared in the literature. However, inference for these models is computationally prohibitive, even in moderate dimensions, due to the necessity of repeatedly evaluating the multivariate Gaussian distribution function. In this work, we attempt to achieve truly high-dimensional inference for extremes of spatial processes, while retaining the desirable flexibility in the tail dependence structure, by modifying an established class of models based on scale mixtures Gaussian processes. We show that the desired extremal dependence properties from the original models are preserved under the modification, and demonstrate that the corresponding Bayesian hierarchical model does not involve the expensive computation of the multivariate Gaussian distribution function. We fit our model to exceedances of a high threshold, and perform coverage analyses and cross-model checks to validate its ability to capture different types of tail characteristics. We use a standard adaptive Metropolis algorithm for model fitting, and further accelerate the computation via parallelization and Rcpp. Lastly, we apply the model to a dataset of a fire threat index on the Great Plains region of the US, which is vulnerable to massively destructive wildfires. We find that the joint tail of the fire threat index exhibits a decaying dependence structure that cannot be captured by limiting extreme value models.

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arXiv2019

Projecting Flood-Inducing Precipitation with a Bayesian Analogue Model

The hazard of pluvial flooding is largely influenced by the spatial and temporal dependence characteristics of precipitation. When extreme precipitation possesses strong spatial dependence, the risk of flooding is amplified due to catchment factors that cause runoff accumulation such as topography. Temporal dependence can also increase flood risk as storm water drainage systems operating at capacity can be overwhelmed by heavy precipitation occurring over multiple days. While transformed Gaussian processes are common choices for modeling precipitation, their weak tail dependence may lead to underestimation of flood risk. Extreme value models such as the generalized Pareto processes for threshold exceedances and max-stable models are attractive alternatives, but are difficult to fit when the number of observation sites is large, and are of little use for modeling the bulk of the distribution, which may also be of interest to water management planners. While the atmospheric dynamics governing precipitation are complex and difficult to fully incorporate into a parsimonious statistical model, non-mechanistic analogue methods that approximate those dynamics have proven to be promising approaches to capturing the temporal dependence of precipitation. In this paper, we present a Bayesian analogue method that leverages large, synoptic-scale atmospheric patterns to make precipitation forecasts. Changing spatial dependence across varying intensities is modeled as a mixture of spatial Student-t processes that can accommodate both strong and weak tail dependence. The proposed model demonstrates improved performance at capturing the distribution of extreme precipitation over Community Atmosphere Model (CAM) 5.2 forecasts.

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arXiv2016

A Markov-switching model for heat waves

Heat waves merit careful study because they inflict severe economic and societal damage. We use an intuitive, informal working definition of a heat wave-a persistent event in the tail of the temperature distribution-to motivate an interpretable latent state extreme value model. A latent variable with dependence in time indicates membership in the heat wave state. The strength of the temporal dependence of the latent variable controls the frequency and persistence of heat waves. Within each heat wave, temperatures are modeled using extreme value distributions, with extremal dependence across time accomplished through an extreme value Markov model. One important virtue of interpretability is that model parameters directly translate into quantities of interest for risk management, so that questions like whether heat waves are becoming longer, more severe or more frequent are easily answered by querying an appropriate fitted model. We demonstrate the latent state model on two recent, calamitous, examples: the European heat wave of 2003 and the Russian heat wave of 2010.

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arXiv2013

A hierarchical max-stable spatial model for extreme precipitation

Extreme environmental phenomena such as major precipitation events manifestly exhibit spatial dependence. Max-stable processes are a class of asymptotically-justified models that are capable of representing spatial dependence among extreme values. While these models satisfy modeling requirements, they are limited in their utility because their corresponding joint likelihoods are unknown for more than a trivial number of spatial locations, preventing, in particular, Bayesian analyses. In this paper, we propose a new random effects model to account for spatial dependence. We show that our specification of the random effect distribution leads to a max-stable process that has the popular Gaussian extreme value process (GEVP) as a limiting case. The proposed model is used to analyze the yearly maximum precipitation from a regional climate model.

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