Tuesday, Aug 4: 2:00 PM - 3:50 PM
6404
Contributed Papers
Thomas M. Menino Convention & Exhibition Center
Room: CC-107A
Main Sponsor
Section on Statistics and the Environment
Presentations
Understanding the hidden drivers of extreme spatio-temporal behavior requires information-theoretic
tools that move beyond linear dependence and Gaussian assumptions. We develop a
tail-emphasized approach for detecting directional interactions in complex environmental processes
using Rényi transfer entropy, a measure that highlights information flow arising from rare
but influential events. To estimate the required conditional densities, we use Mixture Density
Networks (MDNs), which can represent heavy-tailed and multimodal structures and therefore
capture both bulk behavior and extremes. Our current analysis applies this framework to daily
maximum temperature from Pacific Northwest stations, together with complementary drought
and circulation indices. The ultimate aim is to use the discovered nonlinear and tail-sensitive
relationships to inform parsimonious spatio–temporal models that better represent the mechanisms
underlying extreme environmental responses.
Keywords
Rényi Transfer Entropy
Mixture Density Networks (MDNs)
Extreme events
Nonlinear dependence
Spatio-temporal climate dynamics
Information-theoretic causality
A key objective in spatial statistics is to simulate from predictive distributions--the distributions of a spatial process at select unobserved locations conditional on observations--to enable spatial prediction and uncertainty quantification. However, exact conditional simulation from predictive distributions is intractable or inefficient for many spatial process models. In this talk, we present Neural Conditional Simulation (NCS)--a method which utilizes neural diffusion models for conditional simulation from predictive distributions of complex spatial processes. Using a masking approach, we train a score-based diffusion model within a stochastic differential equation (SDE) framework to learn the conditional reverse process--a process which reverse-diffuses Gaussian noise into samples from conditional distributions. Importantly, the diffusion model only requires unconditional samples from the spatial process during training and is amortized with respect to the mask, provided the mask pattern is similar to those used during training. We conclude with a data application in which we use NCS to model spatial extremes data with max-stable processes.
Keywords
approximate simulation
simulation-based inference
diffusion model
spatial extremes
likelihood-free inference
generative model
Structures in snow-prone areas must be designed to withstand the weight of snow that accumulates on the roof. The design calculations require probabilistic estimates of annual extreme snow water equivalent (SWE), which are then used in a structural reliability analysis to determine the appropriate strength of the structural members (i.e., beams, columns, etc.) to prevent collapse during seasons of extreme snow accumulation. This paper outlines a data analysis workflow, starting from downscaled future projections of annual maximum SWE, progressing through a non-stationary extreme value analysis, and ending with design snow load (i.e., weight of accumulated snow as derived from SWE) recommendations suitable for inclusion in engineering codes and standards. The results show that design snow loads are expected to fall across most of the country as compared to historical estimates, with notable exceptions in the Upper Midwest. Most importantly, this talk highlights the opportunities and challenges associated with blending data and expertise between the statistics, climate science, and structural engineering communities to improve United States' infrastructure design standards.
Keywords
Extreme Value Theory
Non-Stationarity
Climate Change
Structural Engineering
Applied Environmental Statistics
Generalized Extreme Value Distribution
Understanding and modeling the relationship between the extremes of multiple variables is crucial for mitigating the risk associated with high impact phenomena. The study of geometric extremes, where extremal dependence properties are inferred from the deterministic limiting shapes of scaled sample clouds, provides an exciting approach to modeling the tail behavior of multivariate data. These shapes, termed limit sets, link several popular extremal dependence modelling frameworks. We propose a novel Bayesian approach to model limit sets for bivariate data. 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. Two applications are presented to showcase the usefulness of limit sets for studying tail dependence in environmental data: extremal dependence for fire weather variables in Santa Ana, California, and for air pollution monitoring data in the US.
Keywords
Bayesian inference
Environmental modeling
Multivariate extremes
Source apportionment modeling to quantify contributors to water pollutant concentrations is crucial for targeted monitoring, remediation, and the evaluation of regulatory interventions. Per- and polyfluoroalkyl substances (PFAS) pose a unique challenge in this space due to highly skewed concentration distributions and the need to assess both background levels and consequential exceedances of health-based thresholds. To address this, we develop a Bayesian hierarchical model that utilizes the extended generalized Pareto distribution (EGPD) to flexibly characterize both the lower and upper tails of PFAS concentrations, enabling inference across the entire distribution. Spatial dependence between potential surface sources and groundwater receptors is modeled using river-network distances, accurately reflecting hydrologic connectivity and downstream transport pathways. We apply this modeling framework to groundwater monitoring data from California's GAMA program to demonstrate its utility in a complex, real-world regulatory environment. Ultimately, this approach allows for the identification of sparse, localized source contributions while accommodating the uncertainty in extreme concentrations that often drive compliance decisions.
Keywords
Bayesian modeling
Spatial statistics
Extreme value modeling
Environmental monitoring
Understanding spatial variation in extreme events is crucial for risk management, early warning systems, and policy-making. Datasets of spatial extremes exhibit complex dependencies across geographic regions. Examples include maximum temperatures and wind speeds that increase the risk of wildfires, peak river discharges that lead to floods, and low soil moisture affecting crop yields. While recent advances in spatial extremes models provide more realistic representations of joint tail dependencies, statistical inference remains computationally demanding, especially for large datasets over hundreds of locations. These challenges stem from costly matrix operations on precision matrices and numerical integration in marginal distributions. In this study, we investigate scalable alternatives to full likelihood inference, leveraging advances in spatial modeling, amortized learning, and density regression techniques. We evaluate these methods through simulation studies and apply them to a high-resolution surface skin temperature dataset from the North American Land Data Assimilation System. Our findings provide insights into efficient, data-driven approaches for modeling spatial extremes,
Keywords
Spatial Extremes
Random Scale Mixture Models
Neural Bayes Estimators
Spare matrix approximations
Low-rank spatial models
Subasymptotic models
The increasing frequency of environmental shocks is challenging traditional mean-based statistical inference in ecological monitoring. We present a comprehensive framework for detecting, linking, and modeling extremes in multivariate time series. We contrast unsupervised anomaly detection methods (isolation forest and DBSCAN) to objectively identify rare events in environmental and biological data. Beyond detection, we quantify the synchronization of these extremes using the Matthews correlation coefficient with bootstrap-based inference, offering a robust alternative to standard correlation measures. Furthermore, to model the conditional distribution of biological responses to environmental stressors, we benchmark quantile regression forests (QRF) against linear quantile regression. Our analysis demonstrates that non-parametric machine learning (QRF) improves the quantification of tail dependencies often missed by parametric approaches. This work provides a flexible statistical toolkit for analyzing non-stationary driver-response relationships in complex systems.
Keywords
Rare event detection
Quantile regression
Isolation forest
Extreme
Time series analysis
Ecological statistics