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A new mixture model for spatiotemporal exceedances with flexible tail dependence

Ryan Li, Emily C. Hector, Brian J. Reich, Reetam Majumder

TL;DR

This paper addresses the challenge of modeling extreme daily streamflow with flexible tail dependence across space and time. It introduces a four-component spatio-temporal mixture of max-stable and inverted max-stable processes, coupled with a censored peaks-over-threshold framework for marginal fitting and simulation-based inference using random forests on chi-based summaries for dependence parameters. The framework can represent all four tail regimes (space-time, space-only, time-only, and fully independent) and is validated through simulation studies and an analysis of USGS streamflow data, revealing asymptotic independence in space and time with measurable space-time dependence. The approach has practical implications for flood risk assessment and extrapolation to unobserved sites, offering a scalable and interpretable path to capturing complex extremal dependence in high-resolution spatiotemporal data.

Abstract

We propose a new model and estimation framework for spatiotemporal streamflow exceedances above a threshold that flexibly captures asymptotic dependence and independence in the tail of the distribution. We model streamflow using a mixture of processes with spatial, temporal and spatiotemporal asymptotic dependence regimes. A censoring mechanism allows us to use only observations above a threshold to estimate marginal and joint probabilities of extreme events. As the likelihood is intractable, we use simulation-based inference powered by random forests to estimate model parameters from summary statistics of the data. Simulations and modeling of streamflow data from the U.S. Geological Survey illustrate the feasibility and practicality of our approach.

A new mixture model for spatiotemporal exceedances with flexible tail dependence

TL;DR

This paper addresses the challenge of modeling extreme daily streamflow with flexible tail dependence across space and time. It introduces a four-component spatio-temporal mixture of max-stable and inverted max-stable processes, coupled with a censored peaks-over-threshold framework for marginal fitting and simulation-based inference using random forests on chi-based summaries for dependence parameters. The framework can represent all four tail regimes (space-time, space-only, time-only, and fully independent) and is validated through simulation studies and an analysis of USGS streamflow data, revealing asymptotic independence in space and time with measurable space-time dependence. The approach has practical implications for flood risk assessment and extrapolation to unobserved sites, offering a scalable and interpretable path to capturing complex extremal dependence in high-resolution spatiotemporal data.

Abstract

We propose a new model and estimation framework for spatiotemporal streamflow exceedances above a threshold that flexibly captures asymptotic dependence and independence in the tail of the distribution. We model streamflow using a mixture of processes with spatial, temporal and spatiotemporal asymptotic dependence regimes. A censoring mechanism allows us to use only observations above a threshold to estimate marginal and joint probabilities of extreme events. As the likelihood is intractable, we use simulation-based inference powered by random forests to estimate model parameters from summary statistics of the data. Simulations and modeling of streamflow data from the U.S. Geological Survey illustrate the feasibility and practicality of our approach.
Paper Structure (15 sections, 1 theorem, 22 equations, 4 figures, 2 tables)

This paper contains 15 sections, 1 theorem, 22 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Our contributions:
  3. Background
  4. $\chi$-coefficient
  5. Max-stable and inverted max-stable process
  6. Regression Trees and Random Forests
  7. Spatiotemporal mixture model
  8. Tail model
  9. Asymptotic tail dependence
  10. Parameter estimation
  11. Marginal parameter estimates
  12. Dependence parameter estimates
  13. Simulation experiments
  14. Analysis of extreme streamflow
  15. Discussion

Key Result

Theorem 1

Under the model in e:Xmixturesimple:

Figures (4)

  • Figure 1: Empirical $\chi$ plots for four $\lambda$ settings for $X(s,t), X(s^\prime,t)$ (left), $X(s,t), X(s^\prime,t^\prime)$ (middle) and $X(s,t), X(s,t^\prime)$ (right).
  • Figure 2: Scale parameter estimates across space
  • Figure 3: QQ plot of marginal fits of streamflow data at thresholds $\tau = 0.5, 0.8, 0.9, 0.95$.
  • Figure 4: Empirical $\chi$ statistics for pairs of stations plotted against distance for different temporal lags (right) for each station. The red line indicates $\chi$ statistics for fitted model.

Theorems & Definitions (1)

  • Theorem 1