arXiv subjects

Douglas W. Nychka

Publications and source records attributed to Douglas W. Nychka.

11 recordsLinked to original sources

arXiv2026

Locally stationary Argo ocean heat content estimates: Modeling, validation and uncertainty quantification

Argo profiling floats measure seawater temperature and salinity in the upper 2000 meters of the ocean. These floats are uniquely capable of measuring the global Ocean Heat Content (OHC), a quantity that is of central importance for understanding Earth Energy Imbalance. Yet, producing Argo-based OHC estimates with reliable uncertainties is statistically challenging due to the complex structure and large size of the Argo dataset. Here we present an end-to-end mapping and uncertainty quantification framework for Argo-based OHC estimation using state-of-the-art methods from spatio-temporal statistics. The framework is based on modeling vertically integrated Argo temperature profiles as a locally stationary Gaussian process defined over space and time. This enables us to produce computationally tractable OHC anomaly maps based on data-driven decorrelation scales estimated from the Argo observations. Our modeling choices are validated using statistical cross-validation, which demonstrates the importance of including a climatological time trend in the mean field and accounting for time in the covariance function. We quantify the uncertainty of these maps using local conditional simulation ensembles, a novel approach that leads to principled spatially and temporally correlated uncertainty quantification. A new paired cross-validation technique is presented to validate these uncertainties. The mapping framework is implemented in an open-source codebase that is designed to be modular, reproducible and extensible. To demonstrate the mapping and uncertainty quantification capabilities of this approach, we present new Argo OHC maps with uncertainties for 2004-2022 and report on various downstream climatological estimates and their uncertainties.

stat.AP↗

arXiv2026

A Bayesian hierarchical model for methane emission source apportionment

Reducing methane emissions from the oil and gas sector is a key component of short-term climate action. Emission reduction efforts are often conducted at the individual site-level, where being able to apportion emissions between a finite number of potentially emitting equipment is necessary for leak detection and repair as well as regulatory reporting of annualized emissions. We present a hierarchical Bayesian model, referred to as the multisource detection, localization, and quantification (MDLQ) model, for performing source apportionment on oil and gas sites using methane measurements from point sensor networks. The MDLQ model accounts for autocorrelation in the sensor data and enforces sparsity in the emission rate estimates via a spike-and-slab prior, as oil and gas equipment often emit intermittently. We use the MDLQ model to apportion methane emissions on an experimental oil and gas site designed to release methane in known quantities, providing a means of model evaluation. Data from this experiment are unique in their size (i.e., the number of controlled releases) and in their close approximation of emission characteristics on real oil and gas sites. As such, this study provides a baseline level of apportionment accuracy that can be expected when using point sensor networks on operational sites.

stat.AP↗

arXiv2025

Modeling Spatial Extremes using Non-Gaussian Spatial Autoregressive Models via Convolutional Neural Networks

Data derived from remote sensing or numerical simulations often have a regular gridded structure and are large in volume, making it challenging to find accurate spatial models that can fill in missing grid cells or simulate the process effectively, especially in the presence of spatial heterogeneity and heavy-tailed marginal distributions. To overcome this issue, we present a spatial autoregressive modeling framework, which maps observations at a location and its neighbors to independent random variables. This is a highly flexible modeling approach and well-suited for non-Gaussian fields, providing simpler interpretability. In particular, we consider the SAR model with Generalized Extreme Value distribution innovations to combine the observation at a central grid location with its neighbors, capturing extreme spatial behavior based on the heavy-tailed innovations. While these models are fast to simulate by exploiting the sparsity of the key matrices in the computations, the maximum likelihood estimation of the parameters is prohibitive due to the intractability of the likelihood, making optimization challenging. To overcome this, we train a convolutional neural network on a large training set that covers a useful parameter space, and then use the trained network for fast parameter estimation. Finally, we apply this model to analyze annual maximum precipitation data from ERA-Interim-driven Weather Research and Forecasting (WRF) simulations, allowing us to explore its spatial extreme behavior across North America.

stat.ML↗

arXiv2024

Adapting Quantile Mapping to Bias Correct Solar Radiation Data

Bias correction is a common pre-processing step applied to climate model data before it is used for further analysis. This article introduces an efficient adaptation of a well-established bias-correction method - quantile mapping - for global horizontal irradiance (GHI) that ensures corrected data is physically plausible through incorporating measurements of clearsky GHI. The proposed quantile mapping method is fit on reanalysis data to first bias correct for regional climate models (RCMs) and is tested on RCMs forced by general circulation models (GCMs) to understand existing biases directly from GCMs. Additionally, we adapt a functional analysis of variance methodology that analyzes sources of remaining biases after implementing the proposed quantile mapping method and considered biases by climate region. This analysis is applied to four sets of climate model output from NA-CORDEX and compared against data from the National Solar Radiation Database produced by the National Renewable Energy Lab.

stat.AP↗

arXiv2023

Fast parameter estimation of Generalized Extreme Value distribution using Neural Networks

The heavy-tailed behavior of the generalized extreme-value distribution makes it a popular choice for modeling extreme events such as floods, droughts, heatwaves, wildfires, etc. However, estimating the distribution's parameters using conventional maximum likelihood methods can be computationally intensive, even for moderate-sized datasets. To overcome this limitation, we propose a computationally efficient, likelihood-free estimation method utilizing a neural network. Through an extensive simulation study, we demonstrate that the proposed neural network-based method provides Generalized Extreme Value (GEV) distribution parameter estimates with comparable accuracy to the conventional maximum likelihood method but with a significant computational speedup. To account for estimation uncertainty, we utilize parametric bootstrapping, which is inherent in the trained network. Finally, we apply this method to 1000-year annual maximum temperature data from the Community Climate System Model version 3 (CCSM3) across North America for three atmospheric concentrations: 289 ppm $\mathrm{CO}_2$ (pre-industrial), 700 ppm $\mathrm{CO}_2$ (future conditions), and 1400 ppm $\mathrm{CO}_2$, and compare the results with those obtained using the maximum likelihood approach.

stat.ML↗

arXiv2021

Adapting conditional simulation using circulant embedding for irregularly spaced spatial data

Computing an ensemble of random fields using conditional simulation is an ideal method for retrieving accurate estimates of a field conditioned on available data and for quantifying the uncertainty of these realizations. Methods for generating random realizations, however, are computationally demanding, especially when the estimates are conditioned on numerous observed data and for large domains. In this article, a \textit{new}, \textit{approximate} conditional simulation approach is applied that builds on \textit{circulant embedding} (CE), a fast method for simulating stationary Gaussian processes. The standard CE is restricted to simulating stationary Gaussian processes (possibly anisotropic) on regularly spaced grids. In this work we explore two possible algorithms, namely local Kriging and nearest neighbor Kriging, that extend CE for irregularly spaced data points. We establish the accuracy of these methods to be suitable for practical inference and the speedup in computation allows for generating conditional fields close to an interactive time frame. The methods are motivated by the U.S. Geological Survey's software \textit{ShakeMap}, which provides near real-time maps of shaking intensity after the occurrence of a significant earthquake. An example for the 2019 event in Ridgecrest, California is used to illustrate our method.

stat.ME↗

arXiv2020

Fast covariance parameter estimation of spatial Gaussian process models using neural networks

Gaussian processes (GPs) are a popular model for spatially referenced data and allow descriptive statements, predictions at new locations, and simulation of new fields. Often a few parameters are sufficient to parameterize the covariance function, and maximum likelihood (ML) methods can be used to estimate these parameters from data. ML methods, however, are computationally demanding. For example, in the case of local likelihood estimation, even fitting covariance models on modest size windows can overwhelm typical computational resources for data analysis. This limitation motivates the idea of using neural network (NN) methods to approximate ML estimates. We train NNs to take moderate size spatial fields or variograms as input and return the range and noise-to-signal covariance parameters. Once trained, the NNs provide estimates with a similar accuracy compared to ML estimation and at a speedup by a factor of 100 or more. Although we focus on a specific covariance estimation problem motivated by a climate science application, this work can be easily extended to other, more complex, spatial problems and provides a proof-of-concept for this use of machine learning in computational statistics.

stat.ML↗

arXiv2019

Parallel cross-validation: a scalable fitting method for Gaussian process models

Gaussian process (GP) models are widely used to analyze spatially referenced data and to predict values at locations without observations. In contrast to many algorithmic procedures, GP models are based on a statistical framework, which enables uncertainty quantification of the model structure and predictions. Both the evaluation of the likelihood and the prediction involve solving linear systems. Hence, the computational costs are large and limit the amount of data that can be handled. While there are many approximation strategies that lower the computational cost of GP models, they often provide only sub-optimal support for the parallel computing capabilities of current (high-performance) computing environments. We aim at bridging this gap with a parameter estimation and prediction method that is designed to be parallelizable. More precisely, we divide the spatial domain into overlapping subsets and use cross-validation (CV) to estimate the covariance parameters in parallel. We present simulation studies, which assess the accuracy of the parameter estimates and predictions. Moreover, we show that our implementation has good weak and strong parallel scaling properties. For illustration, we fit an exponential covariance model to a scientifically relevant canopy height dataset with 5 million observations. Using 512 processor cores in parallel brings the evaluation time of one covariance parameter configuration to less than 1.5 minutes. The parallel CV method can be easily extended to include approximate likelihood methods, multivariate and spatio-temporal data, as well as non-stationary covariance models.

stat.CO↗

arXiv2018

Estimating Precipitation Extremes using Log-Histospline

One of the commonly used approaches to modeling extremes is the peaks-over-threshold (POT) method. The POT method models exceedances over a threshold that is sufficiently high or low so that the exceedance has approximately a generalized Pareto distribution (GPD). This method requires the selection of a threshold that might affect the estimates. Here we propose an alternative method, the Log-Histospline (LHSpline), to explore modeling the tail behavior and the remainder of the density in one step using the full range of the data. LHSpline applies a smoothing spline model to a finely binned histogram of the log transformed data to estimate its log density. By construction, a LHSpline estimation is constrained to have polynomial tail behavior, a feature commonly observed in daily rainfall observations. We illustrate the LHSpline method by analyzing precipitation data collected in Houston, Texas.

stat.ME↗

arXiv2018

A Case Study Competition Among Methods for Analyzing Large Spatial Data

The Gaussian process is an indispensable tool for spatial data analysts. The onset of the "big data" era, however, has lead to the traditional Gaussian process being computationally infeasible for modern spatial data. As such, various alternatives to the full Gaussian process that are more amenable to handling big spatial data have been proposed. These modern methods often exploit low rank structures and/or multi-core and multi-threaded computing environments to facilitate computation. This study provides, first, an introductory overview of several methods for analyzing large spatial data. Second, this study describes the results of a predictive competition among the described methods as implemented by different groups with strong expertise in the methodology. Specifically, each research group was provided with two training datasets (one simulated and one observed) along with a set of prediction locations. Each group then wrote their own implementation of their method to produce predictions at the given location and each which was subsequently run on a common computing environment. The methods were then compared in terms of various predictive diagnostics. Supplementary materials regarding implementation details of the methods and code are available for this article online.

stat.ME↗

arXiv2007

A Multiresolution Census Algorithm for Calculating Vortex Statistics in Turbulent Flows

The fundamental equations that model turbulent flow do not provide much insight into the size and shape of observed turbulent structures. We investigate the efficient and accurate representation of structures in two-dimensional turbulence by applying statistical models directly to the simulated vorticity field. Rather than extract the coherent portion of the image from the background variation, as in the classical signal-plus-noise model, we present a model for individual vortices using the non-decimated discrete wavelet transform. A template image, supplied by the user, provides the features to be extracted from the vorticity field. By transforming the vortex template into the wavelet domain, specific characteristics present in the template, such as size and symmetry, are broken down into components associated with spatial frequencies. Multivariate multiple linear regression is used to fit the vortex template to the vorticity field in the wavelet domain. Since all levels of the template decomposition may be used to model each level in the field decomposition, the resulting model need not be identical to the template. Application to a vortex census algorithm that records quantities of interest (such as size, peak amplitude, circulation, etc.) as the vorticity field evolves is given. The multiresolution census algorithm extracts coherent structures of all shapes and sizes in simulated vorticity fields and is able to reproduce known physical scaling laws when processing a set of voriticity fields that evolve over time.

stat.AP↗