arXiv subjects

Christopher K. Wikle

Publications and source records attributed to Christopher K. Wikle.

At least 19 recordsLinked to original sources

arXiv2026

Accounting for variable detection functions in temporal abundance modeling via transfer learning

Relative abundance, measured as the number of animals caught per unit of sampling effort (CPUE), is commonly used to monitor fish and wildlife populations, largely because sampling methods are cost-effective to implement. Modeling relative abundance, however, requires the assumption that the detection probability is constant across sampling events. This assumption is likely not valid, as the probability of detection often varies as a function of several factors, including the characteristics of individual animals and environmental conditions at the time of sampling. In contrast, methods to estimate absolute abundance, such as capture-recapture (CR), account for variable detection, but are often infeasible to implement across large spatiotemporal scales. Despite this, CR data are sometimes available for species of interest, albeit at smaller spatiotemporal extents. Leveraging information on detection probabilities from CR data to help inform estimates of widely available CPUE data could strengthen inferences about the status of fish and wildlife populations. We propose an approach to (i) learn the effect of environmental covariates on detection probabilities from CR data and (ii) transfer these detection functions to CPUE models for improved inference. Shown empirically through a simulation study, this approach improves estimates of abundance and the ability to detect temporal trends. We apply our transfer learning method using CR and CPUE data to recreationally important smallmouth bass (\textit{Micropterus dolomieu}) fisheries in Pennsylvania, USA rivers.

stat.AP↗

arXiv2025

Modeling Spatio-temporal Extremes via Conditional Variational Autoencoders

Extreme weather events are widely studied in fields such as agriculture, ecology, and meteorology. The spatio-temporal co-occurrence of extreme events can strengthen or weaken under changing climate conditions. In this paper, we propose a novel approach to model spatio-temporal extremes by integrating climate indices via a conditional variational autoencoder (cXVAE). A convolutional neural network (CNN) is embedded in the decoder to convolve climatological indices with the spatial dependence within the latent space, thereby allowing the decoder to be dependent on the climate variables. There are three main contributions here. First, we demonstrate through extensive simulations that the proposed conditional XVAE accurately emulates spatial fields and recovers spatially and temporally varying extremal dependence with very low computational cost post training. Second, we provide a simple, scalable approach to detecting condition-driven shifts and whether the dependence structure is invariant to the conditioning variable. Third, when dependence is found to be condition-sensitive, the conditional XVAE supports counterfactual experiments allowing intervention on the climate covariate and propagating the associated change through the learned decoder to quantify differences in joint tail risk, co-occurrence ranges, and return metrics. To demonstrate the practical utility and performance of the model in real-world scenarios, we apply our method to analyze the monthly maximum Fire Weather Index (FWI) over eastern Australia from 2014 to 2024 conditioned on the El Ni\~{n}o/Southern Oscillation (ENSO) index.

stat.ML↗

arXiv2025

Modeling high and low extremes with a novel dynamic spatio-temporal model

Extreme environmental events such as severe storms, drought, heat waves, flash floods, and abrupt species collapse have become more prevalent in the earth-atmosphere dynamic system in recent years. In order to fully understand the underlying mechanisms and enhance informed decision-making, a flexible model capable of accommodating extremes is necessary. Existing dynamic spatio-temporal statistical models exhibit limitations in capturing extremes when assuming Gaussian error distributions, whereas the current models for spatial extremes mostly assume temporal independence and are focused on joint upper tails at two or more locations. Here, we introduce a new class of dynamic spatio-temporal models that capture both high and low extremes using a mixture of heavy- and light-tailed distributions with varying tail indices. Our framework flexibly identifies extremal dependence and independence in both space and time with uncertainty quantification and supports missing data prediction, as in other dynamic spatio-temporal models. We demonstrate its effectiveness using a large reanalysis dataset of hourly particulate matter in the Central United States.

stat.ME↗

arXiv2025

A Statistician's Overview of Physics-Informed Neural Networks for Spatio-Temporal Data

The recent success of deep neural network models with physical constraints (so-called, Physics-Informed Neural Networks, PINNs) has led to renewed interest in the incorporation of mechanistic information in predictive models. Statisticians and others have long been interested in this problem, which has led to several practical and innovative solutions dating back decades. In this overview, we focus on the problem of data-driven prediction and inference of dynamic spatio-temporal processes that include mechanistic information, such as would be available from partial differential equations, with a strong focus on the quantification of uncertainty associated with data, process, and parameters. We give a brief review of several paradigms and focus our attention on Bayesian implementations given they naturally accommodate uncertainty quantification. We then show that it is straight-forward to include the Bayesian PINN (B-PINN) within the Bayesian hierarchical model (BHM) framework that has long been considered for modeling dynamic spatio-temporal processes. Such a BHM-PINN is illustrated via a simulation study in which a latent nonlinear Burgers' equation PDE governs the dynamics of Poisson distributed spatio-temporal data.

stat.ME↗

arXiv2025

An Anytime Valid Test for Complete Spatial Randomness

A relevant question when analyzing spatial point patterns is that of spatial randomness. More specifically, before any model can be fit to a point pattern a first step is to test the data for departures from complete spatial randomness (CSR). Traditional techniques employ distance or quadrat counts based methods to test for CSR based on batched data. In this paper, we consider the practical scenario of testing for CSR when the data are available sequentially (i.e., online). We present a sequential testing methodology called as {\em PRe-process} that is based on e-values and is a fast, efficient and nonparametric method. Simulation experiments with the truth departing from CSR in two different scenarios show that the method is effective in capturing inhomogeneity over time. Two real data illustrations considering lung cancer cases in the Chorley-Ribble area, England from 1974 - 1983 and locations of earthquakes in the state of Oklahoma, USA from 2000 - 2011 demonstrate the utility of the PRe-process in sequential testing of CSR.

stat.OT↗

arXiv2025

Inference for Log-Gaussian Cox Point Processes using Bayesian Deep Learning: Application to Human Oral Microbiome Image Data

It is common in nature to see aggregation of objects in space. Exploring the mechanism associated with the locations of such clustered observations can be essential to understanding the phenomenon, such as the source of spatial heterogeneity, or comparison to other event generating processes in the same domain. Log-Gaussian Cox processes (LGCPs) represent an important class of models for quantifying aggregation in a spatial point pattern. However, implementing likelihood-based Bayesian inference for such models presents many computational challenges, particularly in high dimensions. In this paper, we propose a novel likelihood-free inference approach for LGCPs using the recently developed BayesFlow approach, where invertible neural networks are employed to approximate the posterior distribution of the parameters of interest. BayesFlow is a neural simulation-based method based on "amortized" posterior estimation. That is, after an initial training procedure, fast feed-forward operations allow rapid posterior inference for any data within the same model family. Comprehensive numerical studies validate the reliability of the framework and show that BayesFlow achieves substantial computational gain in repeated application, especially for two-dimensional LGCPs. We demonstrate the utility and robustness of the method by applying it to two distinct oral microbial biofilm images.

stat.ME↗

arXiv2025

Capturing Extreme Events in Turbulence using an Extreme Variational Autoencoder (xVAE)

Turbulent flow fields are characterized by extreme events that are statistically intermittent and carry a significant amount of energy and physical importance. To emulate these flows, we introduce the extreme variational Autoencoder (xVAE), which embeds a max-infinitely divisible process with heavy-tailed distributions into a standard VAE framework, enabling accurate modeling of extreme events. xVAEs are neural network models that reduce system dimensionality by learning non-linear latent representations of data. We demonstrate the effectiveness of xVAE in large-eddy simulation data of wildland fire plumes, where intense heat release and complex plume-atmosphere interactions generate extreme turbulence. Comparisons with the commonly used Proper Orthogonal Decomposition (POD) modes show that xVAE is more robust in capturing extreme values and provides a powerful uncertainty quantification framework using variational Bayes. Additionally, xVAE enables analysis of the so-called copulas of fields to assess risks associated with rare events while rigorously accounting for uncertainty, such as simultaneous exceedances of high thresholds across multiple locations. The proposed approach provides a new direction for studying realistic turbulent flows, such as high-speed aerodynamics, space propulsion, and atmospheric and oceanic systems that are characterized by extreme events.

physics.flu-dyn↗

arXiv2024

Echo State Networks for Spatio-Temporal Area-Level Data

Spatio-temporal area-level datasets play a critical role in official statistics, providing valuable insights for policy-making and regional planning. Accurate modeling and forecasting of these datasets can be extremely useful for policymakers to develop informed strategies for future planning. Echo State Networks (ESNs) are efficient methods for capturing nonlinear temporal dynamics and generating forecasts. However, ESNs lack a direct mechanism to account for the neighborhood structure inherent in area-level data. Ignoring these spatial relationships can significantly compromise the accuracy and utility of forecasts. In this paper, we incorporate approximate graph spectral filters at the input stage of the ESN, thereby improving forecast accuracy while preserving the model's computational efficiency during training. We demonstrate the effectiveness of our approach using Eurostat's tourism occupancy dataset and show how it can support more informed decision-making in policy and planning contexts.

cs.LG↗

arXiv2024

Incorporating Asymmetric Loss for Real Estate Prediction with Area-level Spatial Data

We investigate two asymmetric loss functions, namely LINEX loss and power divergence loss for optimal spatial prediction with area-level data. With our motivation arising from the real estate industry, namely in real estate valuation, we use the Zillow Home Value Index (ZHVI) for county-level values to show the change in prediction when the loss is different (asymmetric) from a traditional squared error loss (symmetric) function. Additionally, we discuss the importance of choosing the asymmetry parameter, and propose a solution to this choice for a general asymmetric loss function. Since the focus is on area-level data predictions, we propose the methodology in the context of conditionally autoregressive (CAR) models. We conclude that choice of the loss functions for spatial area-level predictions can play a crucial role, and is heavily driven by the choice of parameters in the respective loss.

stat.AP↗

arXiv2024

Emulation with uncertainty quantification of regional sea-level change caused by the Antarctic Ice Sheet

Projecting sea-level change in various climate-change scenarios typically involves running forward simulations of the Earth's gravitational, rotational and deformational (GRD) response to ice mass change, which requires high computational cost and time. Here we build neural-network emulators of sea-level change at 27 coastal locations, due to the GRD effects associated with future Antarctic Ice Sheet mass change over the 21st century. The emulators are based on datasets produced using a numerical solver for the static sea-level equation and published ISMIP6-2100 ice-sheet model simulations referenced in the IPCC AR6 report. We show that the neural-network emulators have an accuracy that is competitive with baseline machine learning emulators. In order to quantify uncertainty, we derive well-calibrated prediction intervals for simulated sea-level change via a linear regression postprocessing technique that uses (nonlinear) machine learning model outputs, a technique that has previously been applied to numerical climate models. We also demonstrate substantial gains in computational efficiency: a feedforward neural-network emulator exhibits on the order of 100 times speedup in comparison to the numerical sea-level equation solver that is used for training.

physics.ao-ph↗

arXiv2023

A Criterion for Aggregation Error for Multivariate Spatial Data

The criterion for aggregation error (CAGE) is an important metric that aims to measure errors that arise in multiscale (or multi-resolution) spatial data, referred to as the modifiable areal unit problem and the ecological fallacy. Specifically, CAGE is a measure of between scale variance of eigenvectors in a Karhunen-Lo\'{e}ve expansion (KLE), motivated by a theoretical result, referred to as the ``null-MAUP-theorem,'' that states that the MAUP/ecological fallacy are not present when this variance is zero. CAGE was originally developed for univariate spatial data, but its use has been applied to multivariate spatial data without the development of a null-MAUP-theorem in the multivariate spatial setting. To fill this gap, we provide theoretical justification for a multivariate CAGE (MVCAGE), which includes multiscale multivariate extensions of the KLE, Mercer's theorem, and the-null-MAUP theorem. Additionally, we provide technical results that demonstrate that the MVCAGE is preferable to spatial-only CAGE, and extend commonly used basis functions used to compute CAGE to the multivariate spatial setting. Empirical results are provided to demonstrate the use of MVCAGE for uncertainty quantification and regionalization.

stat.ME↗

arXiv2023

Calibrated Forecasts of Quasi-Periodic Climate Processes with Deep Echo State Networks and Penalized Quantile Regression

Among the most relevant processes in the Earth system for human habitability are quasi-periodic, ocean-driven multi-year events whose dynamics are currently incompletely characterized by physical models, and hence poorly predictable. This work aims at showing how 1) data-driven, stochastic machine learning approaches provide an affordable yet flexible means to forecast these processes; 2) the associated uncertainty can be properly calibrated with fast ensemble-based approaches. While the methodology introduced and discussed in this work pertains to synoptic scale events, the principle of augmenting incomplete or highly sensitive physical systems with data-driven models to improve predictability is far more general and can be extended to environmental problems of any scale in time or space.

physics.ao-ph↗

arXiv2023

Flexible and efficient emulation of spatial extremes processes via variational autoencoders

Many real-world processes have complex tail dependence structures that cannot be characterized using classical Gaussian processes. More flexible spatial extremes models exhibit appealing extremal dependence properties but are often exceedingly prohibitive to fit and simulate from in high dimensions. In this paper, we aim to push the boundaries on computation and modeling of high-dimensional spatial extremes via integrating a new spatial extremes model that has flexible and non-stationary dependence properties in the encoding-decoding structure of a variational autoencoder called the XVAE. The XVAE can emulate spatial observations and produce outputs that have the same statistical properties as the inputs, especially in the tail. Our approach also provides a novel way of making fast inference with complex extreme-value processes. Through extensive simulation studies, we show that our XVAE is substantially more time-efficient than traditional Bayesian inference while outperforming many spatial extremes models with a stationary dependence structure. Lastly, we analyze a high-resolution satellite-derived dataset of sea surface temperature in the Red Sea, which includes 30 years of daily measurements at 16703 grid cells. We demonstrate how to use XVAE to identify regions susceptible to marine heatwaves under climate change and examine the spatial and temporal variability of the extremal dependence structure.

stat.ML↗

arXiv2023

Bayesian Ensemble Echo State Networks for Enhancing Binary Stochastic Cellular Automata

Binary spatio-temporal data are common in many application areas. Such data can be considered from many perspectives, including via deterministic or stochastic cellular automata, where local rules govern the transition probabilities that describe the evolution of the 0 and 1 states across space and time. One implementation of a stochastic cellular automata for such data is with a spatio-temporal generalized linear model (or mixed model), with the local rule covariates being included in the transformed mean response. However, in real world applications, we seldom have a complete understanding of the local rules and it is helpful to augment the transformed linear predictor with a latent spatio-temporal dynamic process. Here, we demonstrate for the first time that an echo state network (ESN) latent process can be used to enhance the local rule covariates. We implement this in a hierarchical Bayesian framework with regularized horseshoe priors on the ESN output weight matrices, which extends the ESN literature as well. Finally, we gain added expressiveness from the ESNs by considering an ensemble of ESN reservoirs, which we accommodate through model averaging. This is also new to the ESN literature. We demonstrate our methodology on a simulated process in which we assume we do not know all of the local CA rules, as well as a fire evolution data set, and data describing the spread of raccoon rabies in Connecticut, USA.

stat.AP↗

arXiv2023

Data-Driven Modeling of Wildfire Spread with Stochastic Cellular Automata and Latent Spatio-Temporal Dynamics

We propose a Bayesian stochastic cellular automata modeling approach to model the spread of wildfires with uncertainty quantification. The model considers a dynamic neighborhood structure that allows neighbor states to inform transition probabilities in a multistate categorical model. Additional spatial information is captured by the use of a temporally evolving latent spatio-temporal dynamic process linked to the original spatial domain by spatial basis functions. The Bayesian construction allows for uncertainty quantification associated with each of the predicted fire states. The approach is applied to a heavily instrumented controlled burn.

stat.AP↗

arXiv2023

Using Echo State Networks to Inform Physical Models for Fire Front Propagation

Wildfires can be devastating, causing significant damage to property, ecosystem disruption, and loss of life. Forecasting the evolution of wildfire boundaries is essential to real-time wildfire management. To this end, substantial attention in the wildifre literature has focused on the level set method, which effectively represents complicated boundaries and their change over time. Nevertheless, most of these approaches rely on a heavily-parameterized formulas for spread and fail to account for the uncertainty in the forecast. The rapid evolution of large wildfires and inhomogeneous environmental conditions across the domain of interest (e.g., varying land cover, fire-induced winds) give rise to a need for a model that enables efficient data-driven learning of fire spread and allows uncertainty quantification. Here, we present a novel hybrid model that nests an echo state network to learn nonlinear spatio-temporal evolving velocities (speed in the normal direction) within a physically-based level set model framework. This model is computationally efficient and includes calibrated uncertainty quantification. We show the forecasting performance of our model with simulations and two real data sets - the Haybress and Thomas megafires that started in California (USA) in 2017.

stat.ME↗

arXiv2022

Bayesian Hierarchical Models For Multi-type Survey Data Using Spatially Correlated Covariates Measured With Error

We introduce Bayesian hierarchical models for predicting high-dimensional tabular survey data which can be distributed from one or multiple classes of distributions (e.g., Gaussian, Poisson, Binomial, etc.). We adopt a Bayesian implementation of a Hierarchical Generalized Transformation (HGT) model to deal with the non-conjugacy of non-Gaussian data models when estimated using a Latent Gaussian Process (LGP) model. Survey data are usually prone to a high degree of sampling error, and we use covariates that are prone to measurement error as well as those free of any such error. A classical measurement error component is defined to deal with the sampling error in the covariates. The proposed models can be high-dimensional and we employ the notion of basis function expansions to provide an effective approach to dimension reduction. The HGT component lends flexibility to our model to incorporate multi-type response datasets under a unified latent process model framework. To demonstrate the applicability of our methodology, we provide the results from simulation studies and data applications arising from a dataset consisting of the U.S. Census Bureau's American Community Survey (ACS) 5-year period estimates of the total population count under the poverty threshold and the ACS 5-year period estimates of median housing costs at the county level across multiple states in the USA.

stat.ME↗

arXiv2022

REDS: Random Ensemble Deep Spatial prediction

There has been a great deal of recent interest in the development of spatial prediction algorithms for very large datasets and/or prediction domains. These methods have primarily been developed in the spatial statistics community, but there has been growing interest in the machine learning community for such methods, primarily driven by the success of deep Gaussian process regression approaches and deep convolutional neural networks. These methods are often computationally expensive to train and implement and consequently, there has been a resurgence of interest in random projections and deep learning models based on random weights -- so called reservoir computing methods. Here, we combine several of these ideas to develop the Random Ensemble Deep Spatial (REDS) approach to predict spatial data. The procedure uses random Fourier features as inputs to an extreme learning machine (a deep neural model with random weights), and with calibrated ensembles of outputs from this model based on different random weights, it provides a simple uncertainty quantification. The REDS method is demonstrated on simulated data and on a classic large satellite data set.

stat.CO↗