arXiv subjects

Reetam Majumder

Publications and source records attributed to Reetam Majumder.

14 recordsLinked to original sources

arXiv2026

Spatial Extremes at Scale: A Case Study of Surface Skin Temperature and Heat Risk in the United States

Understanding and mapping extreme heat is critical for risk management and public health planning, particularly in regions with complex terrain and heterogeneous climate. We present a case study of extreme heat in the Four Corners region of the United States, using high-resolution surface skin temperature data from the North American Land Data Assimilation System to characterize spatially heterogeneous and seasonally varying extremes across complex terrain, and to assess their implications for heat-related public health risks. Spatial extremes exhibit complex dependencies across geographic regions, which require sophisticated statistical models to capture. While recent advances in spatial extreme value modeling provide flexible representations of joint tail dependencies, statistical inference remains computationally demanding, especially for datasets with a large number of locations. To address this, we propose a random scale mixture process that facilitates Bayesian inference of spatial extremes, and develop scalable inference strategies that leverage advances in spatial modeling and amortized learning. We evaluate the proposed inference methods through large-scale simulation studies, representing the first such extensive study in spatial extremes, and a high-resolution surface skin temperature application in the Four Corners region. Surface skin temperature is particularly useful as a predictor for air temperature, for studying heatwaves and related environmental phenomena, and to calculate heat indices reflecting downstream health risks at any location. Our findings provide insights into efficient, data-driven approaches for modeling spatial extremes, and serve as guidelines for practitioners in the fields of climate science, environmental risk assessment, and beyond.

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arXiv2026

Semi-parametric bulk and tail regression using spline-based neural networks

Semi-parametric quantile regression (SPQR) is a flexible approach to density regression that learns a spline-based representation of conditional density functions using neural networks. As it makes no parametric assumptions about the underlying density, SPQR performs well for in-sample testing and interpolation. However, it can perform poorly when modelling heavy-tailed data or when asked to extrapolate beyond the range of observations, as it fails to satisfy any of the asymptotic guarantees provided by extreme value theory (EVT). To build semi-parametric density regression models that can be used for reliable tail extrapolation, we create the blended generalised Pareto (GP) distribution, which i) provides a model for the entire range of data and, via a smooth and continuous transition, ii) benefits from exact GP upper-tails without the need for intermediate threshold selection. We combine SPQR with our blended GP to create semi-parametric quantile regression for extremes (SPQRx), which provides a flexible semi-parametric approach to density regression that is compliant with traditional EVT. We handle interpretability of SPQRx through the use of model-agnostic variable importance scores, which provide the relative importance of a covariate for separately determining the bulk and tail of the conditional density. The efficacy of SPQRx is illustrated on simulated data, and an application to U.S. wildfire burnt areas from 1990-2020.

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arXiv2026

Density correction for multivariate spatial fields of global climate model output using deep learning

Global Climate Models (GCMs) are numerical models that simulate complex physical processes within the Earth's climate system and are essential for understanding and predicting climate change. However, GCMs suffer from systemic biases due to simplifications made to the underlying physical processes. GCM output therefore needs to be bias corrected before it can be used for future climate projections. Most common bias correction methods, however, cannot preserve spatial, temporal, or inter-variable dependencies. We propose a new semi-parametric estimation of conditional densities (SPECD) approach for density correction of the joint distribution of daily precipitation and maximum temperature data obtained from gridded GCM spatial fields. The Vecchia approximation is employed to preserve dependencies in the observed field during the density correction process, which is carried out using semi-parametric quantile regression. The ability to calibrate joint distributions of GCM projections has potential advantages not only in estimating extremes, but also in better estimating compound hazards, like heat waves and drought, under potential climate change. Illustration on historical data from 1951-2014 over two 5 x 5 spatial grids in the US indicate that SPECD can preserve key marginal and joint distribution properties of precipitation and maximum temperature, and predictions obtained using SPECD are better calibrated compared to predictions using asynchronous quantile mapping and canonical correlation analysis, two commonly used bias correction approaches.

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arXiv2026

A new mixture model for spatiotemporal exceedances with flexible tail dependence

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.

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arXiv2025

Causal Spatial Quantile Regression

Treatment effects in a wide range of economic, environmental, and epidemiological applications often vary across space, and understanding the heterogeneity of causal effects across space and outcome quantiles is a critical challenge in spatial causal inference. To effectively capture spatial heterogeneity in distributional treatment effects, we propose a novel semiparametric neural network-based causal framework leveraging deep spatial quantile regression and then construct a plug-in estimator for spatial quantile treatment effects (SQTE). This framework incorporates an efficient adjustment procedure to mitigate the impact of spatial hidden confounders. Extensive simulations across various scenarios demonstrate that our methodology can accurately estimate SQTE, even with the presence of spatial hidden confounders. Additionally, the spatial confounding adjustment procedure effectively reduces neighborhood spatial patterns in the residuals. We apply this method to assess the spatially varying quantile treatment effects of maternal smoking on newborn birth weight in North Carolina, United States. Our findings consistently show negative effects across all birth weight quantiles, with particularly severe impacts observed in the lower quantile regions.

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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

Amortized Bayesian Local Interpolation NetworK: Fast covariance parameter estimation for Gaussian Processes

Gaussian processes (GPs) are a ubiquitous tool for geostatistical modeling with high levels of flexibility and interpretability, and the ability to make predictions at unseen spatial locations through a process called Kriging. Estimation of Kriging weights relies on the inversion of the process' covariance matrix, creating a computational bottleneck for large spatial datasets. In this paper, we propose an Amortized Bayesian Local Interpolation NetworK (A-BLINK) for fast covariance parameter estimation, which uses two pre-trained deep neural networks to learn a mapping from spatial location coordinates and covariance function parameters to Kriging weights and the spatial variance, respectively. The fast prediction time of these networks allows us to bypass the matrix inversion step, creating large computational speedups over competing methods in both frequentist and Bayesian settings, and also provides full posterior inference and predictions using Markov chain Monte Carlo sampling methods. We show significant increases in computational efficiency over comparable scalable GP methodology in an extensive simulation study with lower parameter estimation error. The efficacy of our approach is also demonstrated using a temperature dataset of US climate normals for 1991--2020 based on over 7,000 weather stations.

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arXiv2024

Deep Learning of Multivariate Extremes via a Geometric Representation

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 modelling the extremes of multivariate data. These shapes, termed limit sets, link together several popular extremal dependence modelling frameworks. Although the geometric approach is becoming an increasingly popular modelling tool, current inference techniques are limited to a low dimensional setting (d < 5), and generally require rigid modelling assumptions. In this work, we propose a range of novel theoretical results to aid with the implementation of the geometric extremes framework and introduce the first approach to modelling limit sets using deep learning. By leveraging neural networks, we construct asymptotically-justified yet flexible semi-parametric models for extremal dependence of high-dimensional data. We showcase the efficacy of our deep approach by modelling the complex extremal dependencies between meteorological and oceanographic variables in the North Sea off the coast of the UK.

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arXiv2024

Optimal Stock Portfolio Selection with a Multivariate Hidden Markov Model

The underlying market trends that drive stock price fluctuations are often referred to in terms of bull and bear markets. Optimal stock portfolio selection methods need to take into account these market trends; however, the bull and bear market states tend to be unobserved and can only be assigned retrospectively. We fit a linked hidden Markov model (LHMM) to relative stock price changes for S&P 500 stocks from 2011--2016 based on weekly closing values. The LHMM consists of a multivariate state process whose individual components correspond to HMMs for each of the 12 sectors of the S\&P 500 stocks. The state processes are linked using a Gaussian copula so that the states of the component chains are correlated at any given time point. The LHMM allows us to capture more heterogeneity in the underlying market dynamics for each sector. In this study, stock performances are evaluated in terms of capital gains using the LHMM by utilizing historical stock price data. Based on the fitted LHMM, optimal stock portfolios are constructed to maximize capital gain while balancing reward and risk. Under out-of-sample testing, the annual capital gain for the portfolios for 2016--2017 are calculated. Portfolios constructed using the LHMM are able to generate returns comparable to the S&P 500 index.

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arXiv2024

Stochastic Gradient MCMC for Massive Geostatistical Data

Gaussian processes (GPs) are commonly used for prediction and inference for spatial data analyses. However, since estimation and prediction tasks have cubic time and quadratic memory complexity in number of locations, GPs are difficult to scale to large spatial datasets. The Vecchia approximation induces sparsity in the dependence structure and is one of several methods proposed to scale GP inference. Our work adds to the substantial research in this area by developing a stochastic gradient Markov chain Monte Carlo (SGMCMC) framework for efficient computation in GPs. At each step, the algorithm subsamples a minibatch of locations and subsequently updates process parameters through a Vecchia-approximated GP likelihood. Since the Vecchia-approximated GP has a time complexity that is linear in the number of locations, this results in scalable estimation in GPs. Through simulation studies, we demonstrate that SGMCMC is competitive with state-of-the-art scalable GP algorithms in terms of computational time and parameter estimation. An application of our method is also provided using the Argo dataset of ocean temperature measurements.

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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

A Deep Learning Synthetic Likelihood Approximation of a Non-stationary Spatial Model for Extreme Streamflow Forecasting

Extreme streamflow is a key indicator of flood risk, and quantifying the changes in its distribution under non-stationary climate conditions is key to mitigating the impact of flooding events. We propose a non-stationary process mixture model (NPMM) for annual streamflow maxima over the central US (CUS) which uses downscaled climate model precipitation projections to forecast extremal streamflow. Spatial dependence for the model is specified as a convex combination of transformed Gaussian and max-stable processes, indexed by a weight parameter which identifies the asymptotic regime of the process. The weight parameter is modeled as a function of the annual precipitation for each of the two hydrologic regions within the CUS, introducing spatio-temporal non-stationarity within the model. The NPMM is flexible with desirable tail dependence properties, but yields an intractable likelihood. To address this, we embed a neural network within a density regression model which is used to learn a synthetic likelihood function using simulations from the NPMM with different parameter settings. Our model is fitted using observational data for 1972--2021, and inference carried out in a Bayesian framework. The two regions within the CUS are estimated to be in different asymptotic regimes based on the posterior distribution of the weight parameter. Annual streamflow maxima estimates based on global climate models for two representative climate pathway scenarios suggest an overall increase in the frequency and magnitude of extreme streamflow for 2006-2035 compared to the historical period of 1972-2005.

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arXiv2022

Stochastic Precipitation Generation for the Chesapeake Bay Watershed using Hidden Markov Models with Variational Bayes Parameter Estimation

Stochastic precipitation generators (SPGs) are a class of statistical models which generate synthetic data that can simulate dry and wet rainfall stretches for long durations. Generated precipitation time series data are used in climate projections, impact assessment of extreme weather events, and water resource and agricultural management. We construct an SPG for daily precipitation data that is specified as a semi-continuous distribution at every location, with a point mass at zero for no precipitation and a mixture of two exponential distributions for positive precipitation. Our generators are obtained as hidden Markov models (HMMs) where the underlying climate conditions form the states. We fit a 3-state HMM to daily precipitation data for the Chesapeake Bay watershed in the Eastern coast of the USA for the wet season months of July to September from 2000--2019. Data is obtained from the GPM-IMERG remote sensing dataset, and existing work on variational HMMs is extended to incorporate semi-continuous emission distributions. In light of the high spatial dimension of the data, a stochastic optimization implementation allows for computational speedup. The most likely sequence of underlying states is estimated using the Viterbi algorithm, and we identify the differences in the weather regimes associated with the states of the proposed model. Synthetic data generated from the HMM can reproduce monthly precipitation statistics as well as spatial dependency present in the historical GPM-IMERG data.

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arXiv2022

SPQR: An R Package for Semi-Parametric Density and Quantile Regression

We develop an R package SPQR that implements the semi-parametric quantile regression (SPQR) method in Xu and Reich (2021). The method begins by fitting a flexible density regression model using monotonic splines whose weights are modeled as data-dependent functions using artificial neural networks. Subsequently, estimates of conditional density and quantile process can all be obtained. Unlike many approaches to quantile regression that assume a linear model, SPQR allows for virtually any relationship between the covariates and the response distribution including non-linear effects and different effects on different quantile levels. To increase the interpretability and transparency of SPQR, model-agnostic statistics developed by Apley and Zhu (2020) are used to estimate and visualize the covariate effects and their relative importance on the quantile function. In this article, we detail how this framework is implemented in SPQR and illustrate how this package should be used in practice through simulated and real data examples.

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