arXiv subjects

Jordan Richards

Publications and source records attributed to Jordan Richards.

27 records · Page 2Linked to original sources

arXiv2024

Flexible Modeling of Nonstationary Extremal Dependence using Spatially-Fused LASSO and Ridge Penalties

Statistical modeling of a nonstationary spatial extremal dependence structure is challenging. Max-stable processes are common choices for modeling spatially-indexed block maxima, where an assumption of stationarity is usual to make inference feasible. However, this assumption is often unrealistic for data observed over a large or complex domain. We propose a computationally-efficient method for estimating extremal dependence using a globally nonstationary, but locally-stationary, max-stable process by exploiting nonstationary kernel convolutions. We divide the spatial domain into a fine grid of subregions, assign each of them its own dependence parameters, and use LASSO ($L_1$) or ridge ($L_2$) penalties to obtain spatially-smooth parameter estimates. We then develop a novel data-driven algorithm to merge homogeneous neighboring subregions. The algorithm facilitates model parsimony and interpretability. To make our model suitable for high-dimensional data, we exploit a pairwise likelihood to draw inferences and discuss computational and statistical efficiency. An extensive simulation study demonstrates the superior performance of our proposed model and the subregion-merging algorithm over the approaches that either do not model nonstationarity or do not update the domain partition. We apply our proposed method to model monthly maximum temperatures at over 1400 sites in Nepal and the surrounding Himalayan and sub-Himalayan regions; we again observe significant improvements in model fit compared to a stationary process and a nonstationary process without subregion-merging. Furthermore, we demonstrate that the estimated merged partition is interpretable from a geographic perspective and leads to better model diagnostics by adequately reducing the number of subregion-specific parameters.

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arXiv2024

Extreme quantile regression with deep learning

Estimation of extreme conditional quantiles is often required for risk assessment of natural hazards in climate and geo-environmental sciences and for quantitative risk management in statistical finance, econometrics, and actuarial sciences. Interest often lies in extrapolating to quantile levels that exceed any past observations. Therefore, it is crucial to use a statistical framework that is well-adapted and especially designed for this purpose, and here extreme-value theory plays a key role. This chapter reviews how extreme quantile regression may be performed using theoretically-justified models, and how modern deep learning approaches can be harnessed in this context to enhance the model's performance in complex high-dimensional settings. The power of deep learning combined with the rigor of theoretically-justified extreme-value methods opens the door to efficient extreme quantile regression, in cases where both the number of covariates and the quantile level of interest can be simultaneously ``extreme''.

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arXiv2024

Regression modelling of spatiotemporal extreme U.S. wildfires via partially-interpretable neural networks

Risk management in many environmental settings requires an understanding of the mechanisms that drive extreme events. Useful metrics for quantifying such risk are extreme quantiles of response variables conditioned on predictor variables that describe, e.g., climate, biosphere and environmental states. Typically these quantiles lie outside the range of observable data and so, for estimation, require specification of parametric extreme value models within a regression framework. Classical approaches in this context utilise linear or additive relationships between predictor and response variables and suffer in either their predictive capabilities or computational efficiency; moreover, their simplicity is unlikely to capture the truly complex structures that lead to the creation of extreme wildfires. In this paper, we propose a new methodological framework for performing extreme quantile regression using artificial neutral networks, which are able to capture complex non-linear relationships and scale well to high-dimensional data. The "black box" nature of neural networks means that they lack the desirable trait of interpretability often favoured by practitioners; thus, we unify linear, and additive, regression methodology with deep learning to create partially-interpretable neural networks that can be used for statistical inference but retain high prediction accuracy. To complement this methodology, we further propose a novel point process model for extreme values which overcomes the finite lower-endpoint problem associated with the generalised extreme value class of distributions. Efficacy of our unified framework is illustrated on U.S. wildfire data with a high-dimensional predictor set and we illustrate vast improvements in predictive performance over linear and spline-based regression techniques.

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arXiv2024

Deep graphical regression for jointly moderate and extreme Australian wildfires

Recent wildfires in Australia have led to considerable economic loss and property destruction, and there is increasing concern that climate change may exacerbate their intensity, duration, and frequency. Hazard quantification for extreme wildfires is an important component of wildfire management, as it facilitates efficient resource distribution, adverse effect mitigation, and recovery efforts. However, although extreme wildfires are typically the most impactful, both small and moderate fires can still be devastating to local communities and ecosystems. Therefore, it is imperative to develop robust statistical methods to reliably model the full distribution of wildfire spread. We do so for a novel dataset of Australian wildfires from 1999 to 2019, and analyse monthly spread over areas approximately corresponding to Statistical Areas Level~1 and~2 (SA1/SA2) regions. Given the complex nature of wildfire ignition and spread, we exploit recent advances in statistical deep learning and extreme value theory to construct a parametric regression model using graph convolutional neural networks and the extended generalized Pareto distribution, which allows us to model wildfire spread observed on an irregular spatial domain. We highlight the efficacy of our newly proposed model and perform a wildfire hazard assessment for Australia and population-dense communities, namely Tasmania, Sydney, Melbourne, and Perth.

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arXiv2023

Insights into the drivers and spatio-temporal trends of extreme Mediterranean wildfires with statistical deep-learning

Extreme wildfires are a significant cause of human death and biodiversity destruction within countries that encompass the Mediterranean Basin. Recent worrying trends in wildfire activity (i.e., occurrence and spread) suggest that wildfires are likely to be highly impacted by climate change. In order to facilitate appropriate risk mitigation, we must identify the main drivers of extreme wildfires and assess their spatio-temporal trends, with a view to understanding the impacts of global warming on fire activity. We analyse the monthly burnt area due to wildfires over a region encompassing most of Europe and the Mediterranean Basin from 2001 to 2020, and identify high fire activity during this period in Algeria, Italy and Portugal. We build an extreme quantile regression model with a high-dimensional predictor set describing meteorological conditions, land cover usage, and orography. To model the complex relationships between the predictor variables and wildfires, we use a hybrid statistical deep-learning framework that can disentangle the effects of vapour-pressure deficit (VPD), air temperature, and drought on wildfire activity. Our results highlight that whilst VPD, air temperature, and drought significantly affect wildfire occurrence, only VPD affects wildfire spread. To gain insights into the effect of climate trends on wildfires in the near future, we focus on August 2001 and perturb temperature according to its observed trends (median over Europe: +0.04K per year). We find that, on average over Europe, these trends lead to a relative increase of 17.1\% and 1.6\% in the expected frequency and severity, respectively, of wildfires in August 2001, with spatially non-uniform changes in both aspects.

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arXiv2023

Joint Estimation of Extreme Spatially Aggregated Precipitation at Different Scales through Mixture Modelling

Although most models for rainfall extremes focus on point-wise values, it is aggregated precipitation over areas up to river catchment scale that is of the most interest. To capture the joint behaviour of precipitation aggregates evaluated at different spatial scales, parsimonious and effective models must be built with knowledge of the underlying spatial process. Precipitation is driven by a mixture of processes acting at different scales and intensities, e.g., convective and frontal, with extremes of aggregates for typical catchment sizes arising from extremes of only one of these processes, rather than a combination of them. High-intensity convective events cause extreme spatial aggregates at small scales but the contribution of lower-intensity large-scale fronts is likely to increase as the area aggregated increases. Thus, to capture small to large scale spatial aggregates within a single approach requires a model that can accurately capture the extremal properties of both convective and frontal events. Previous extreme value methods have ignored this mixture structure; we propose a spatial extreme value model which is a mixture of two components with different marginal and dependence models that are able to capture the extremal behaviour of convective and frontal rainfall and more faithfully reproduces spatial aggregates for a wide range of scales. Modelling extremes of the frontal component raises new challenges due to it exhibiting strong long-range extremal spatial dependence. Our modelling approach is applied to fine-scale, high-dimensional, gridded precipitation data. We show that accounting for the mixture structure improves the joint inference on extremes of spatial aggregates over regions of different sizes.

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arXiv2022

Modelling Extremes of Spatial Aggregates of Precipitation using Conditional Methods

Inference on the extremal behaviour of spatial aggregates of precipitation is important for quantifying river flood risk. There are two classes of previous approach, with one failing to ensure self-consistency in inference across different regions of aggregation and the other imposing highly restrictive assumptions. To overcome these issues, we propose a model for high-resolution precipitation data, from which we can simulate realistic fields and explore the behaviour of spatial aggregates. Recent developments have seen spatial extensions of the Heffernan and Tawn (2004) model for conditional multivariate extremes, which can handle a wide range of dependence structures. Our contribution is twofold: extensions and improvements of this approach and its model inference for high-dimensional data; and a novel framework for deriving aggregates addressing edge effects and sub-regions without rain. We apply our modelling approach to gridded East-Anglia, UK precipitation data. Return-level curves for spatial aggregates over different regions of various sizes are estimated and shown to fit very well to the data.

stat.ME↗

arXiv2022

On the Tail Behaviour of Aggregated Random Variables

In many areas of interest, modern risk assessment requires estimation of the extremal behaviour of sums of random variables. We derive the first order upper-tail behaviour of the weighted sum of bivariate random variables under weak assumptions on their marginal distributions and their copula. The extremal behaviour of the marginal variables is characterised by the generalised Pareto distribution and their extremal dependence through subclasses of the limiting representations of Ledford and Tawn (1997) and Heffernan and Tawn (2004). We find that the upper tail behaviour of the aggregate is driven by different factors dependent on the signs of the marginal shape parameters; if they are both negative, the extremal behaviour of the aggregate is determined by both marginal shape parameters and the coefficient of asymptotic independence (Ledford and Tawn, 1996); if they are both positive or have different signs, the upper-tail behaviour of the aggregate is given solely by the largest marginal shape. We also derive the aggregate upper-tail behaviour for some well known copulae which reveals further insight into the tail structure when the copula falls outside the conditions for the subclasses of the limiting dependence representations.

math.ST↗

arXiv2021

Spatial deformation for non-stationary extremal dependence

Modelling the extremal dependence structure of spatial data is considerably easier if that structure is stationary. However, for data observed over large or complicated domains, non-stationarity will often prevail. Current methods for modelling non-stationarity in extremal dependence rely on models that are either computationally difficult to fit or require prior knowledge of covariates. Sampson and Guttorp (1992) proposed a simple technique for handling non-stationarity in spatial dependence by smoothly mapping the sampling locations of the process from the original geographical space to a latent space where stationarity can be reasonably assumed. We present an extension of this method to a spatial extremes framework by considering least squares minimisation of pairwise theoretical and empirical extremal dependence measures. Along with some practical advice on applying these deformations, we provide a detailed simulation study in which we propose three spatial processes with varying degrees of non-stationarity in their extremal and central dependence structures. The methodology is applied to Australian summer temperature extremes and UK precipitation to illustrate its efficacy compared to a naive modelling approach.

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