arXiv subjects

Christopher K. Wikle

Publications and source records attributed to Christopher K. Wikle.

At least 37 records · Page 2Linked to original sources

arXiv2022

A Bayesian Spatio-Temporal Level Set Dynamic Model and Application to Fire Front Propagation

Intense wildfires impact nature, humans, and society, causing catastrophic damage to property and the ecosystem, as well as the loss of life. Forecasting wildfire front propagation is essential in order to support fire fighting efforts and plan evacuations. The level set method has been widely used to analyze the change in surfaces, shapes, and boundaries. In particular, a signed distance function used in level set methods can readily be interpreted to represent complicated boundaries and their changes in time. While there is substantial literature on the level set method in wildfire applications, these implementations have relied on a heavily-parameterized formula for the rate of spread. These implementations have not typically considered uncertainty quantification or incorporated data-driven learning. Here, we present a Bayesian spatio-temporal dynamic model based on level sets, which can be utilized for forecasting the boundary of interest in the presence of uncertain data and lack of knowledge about the boundary velocity. The methodology relies on both a mechanistically-motivated dynamic model for level sets and a stochastic spatio-temporal dynamic model for the front velocity. We show the effectiveness of our method via simulation and with forecasting the fire front boundary evolution of two classic California megafires - the 2017-2018 Thomas fire and the 2017 Haypress.

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arXiv2022

A Review of Data-Driven Discovery for Dynamic Systems

Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations driving these complex nonlinear dynamic system using data-driven approaches. In this paper we review the current literature on data-driven discovery for dynamic systems. We provide a categorization to the different approaches for data-driven discovery and a unified mathematical framework to show the relationship between the approaches. Importantly, we discuss the role of statistics in the data-driven discovery field, describe a possible approach by which the problem can be cast in a statistical framework, and provide avenues for future work.

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arXiv2022

A Bayesian Approach for Spatio-Temporal Data-Driven Dynamic Equation Discovery

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent real-world dynamics well. Since the true dynamics of these complex systems are generally unknown, learning the governing equations can improve our understanding of the mechanisms driving the systems. Here, we develop a Bayesian approach to data-driven discovery of non-linear spatio-temporal dynamic equations. Our approach can accommodate measurement noise and missing data, both of which are common in real-world data, and accounts for parameter uncertainty. The proposed framework is illustrated using three simulated systems with varying amounts of observational uncertainty and missing data and applied to a real-world system to infer the temporal evolution of the vorticity of the streamfunction.

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arXiv2022

Bayesian Inverse Reinforcement Learning for Collective Animal Movement

Agent-based methods allow for defining simple rules that generate complex group behaviors. The governing rules of such models are typically set a priori and parameters are tuned from observed behavior trajectories. Instead of making simplifying assumptions across all anticipated scenarios, inverse reinforcement learning provides inference on the short-term (local) rules governing long term behavior policies by using properties of a Markov decision process. We use the computationally efficient linearly-solvable Markov decision process to learn the local rules governing collective movement for a simulation of the self propelled-particle (SPP) model and a data application for a captive guppy population. The estimation of the behavioral decision costs is done in a Bayesian framework with basis function smoothing. We recover the true costs in the SPP simulation and find the guppies value collective movement more than targeted movement toward shelter.

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arXiv2022

Statistical Deep Learning for Spatial and Spatio-Temporal Data

Deep neural network models have become ubiquitous in recent years, and have been applied to nearly all areas of science, engineering, and industry. These models are particularly useful for data that have strong dependencies in space (e.g., images) and time (e.g., sequences). Indeed, deep models have also been extensively used by the statistical community to model spatial and spatio-temporal data through, for example, the use of multi-level Bayesian hierarchical models and deep Gaussian processes. In this review, we first present an overview of traditional statistical and machine learning perspectives for modeling spatial and spatio-temporal data, and then focus on a variety of hybrid models that have recently been developed for latent process, data, and parameter specifications. These hybrid models integrate statistical modeling ideas with deep neural network models in order to take advantage of the strengths of each modeling paradigm. We conclude by giving an overview of computational technologies that have proven useful for these hybrid models, and with a brief discussion on future research directions.

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arXiv2021

Interpolating Population Distributions using Public-use Data: An Application to Income Segregation using American Community Survey Data

Income segregation measures the extent to which households choose to live near other households with similar incomes. Sociologists theorize that income segregation can exacerbate the impacts of income inequality, and have developed indices to measure it at the metro area level, including the information theory index introduced in \citet{reardon2011income}, and the divergence index presented in \citet{roberto2015divergence}. To study their differences, we construct both indices using recent American Community Survey (ACS) estimates of features of the income distribution. Since the elimination of the decennial census long form, methods of computing these estimates must be updated to use ACS estimates and account for survey error. We propose a model-based method to interpolate estimates of features of the income distribution that accounts for this error. This method improves on previous approaches by allowing for the use of more types of estimates, and by providing uncertainty quantification. We apply this method to estimate U.S. census tract-level income distributions using ACS tabulations, and in turn use these to construct both income segregation indices. We find major differences between the two indices in the relative ranking of metro areas, as well as differences in how both indices correlate with the Gini index.

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arXiv2021

A Bayesian Hidden Semi-Markov Model with Covariate-Dependent State Duration Parameters for High-Frequency Environmental Data

Environmental time series data observed at high frequencies can be studied with approaches such as hidden Markov and semi-Markov models (HMM and HSMM). HSMMs extend the HMM by explicitly modeling the time spent in each state. In a discrete-time HSMM, the duration in each state can be modeled with a zero-truncated Poisson distribution, where the duration parameter may be state-specific but constant in time. We extend the HSMM by allowing the state-specific duration parameters to vary in time and model them as a function of known covariates observed over a period of time leading up to a state transition. In addition, we propose a data subsampling approach given that high-frequency data can violate the conditional independence assumption of the HSMM. We apply the model to high-frequency data collected by an instrumented buoy in Lake Mendota. We model the phycocyanin concentration, which is used in aquatic systems to estimate the relative abundance of blue-green algae, and identify important time-varying effects associated with the duration in each state.

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arXiv2021

Correcting spatial Gaussian process parameter and prediction variance estimation under informative sampling

Informative sampling designs can impact spatial prediction, or kriging, in two important ways. First, the sampling design can bias spatial covariance parameter estimation, which in turn can bias spatial kriging estimates. Second, even with unbiased estimates of the spatial covariance parameters, since the kriging variance is a function of the observation locations, these estimates will vary based on the sample and overestimate the population-based estimates. In this work, we develop a weighted composite likelihood approach to improve spatial covariance parameter estimation under informative sampling designs. Then, given these parameter estimates, we propose three approaches to quantify the effects of the sampling design on the variance estimates in spatial prediction. These results can be used to make informed decisions for population-based inference. We illustrate our approaches using a comprehensive simulation study. Then, we apply our methods to perform spatial prediction on nitrate concentration in wells located throughout central California.

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arXiv2021

A higher-order singular value decomposition tensor emulator for spatio-temporal simulators

We introduce methodology to construct an emulator for environmental and ecological spatio-temporal processes that uses the higher order singular value decomposition (HOSVD) as an extension of singular value decomposition (SVD) approaches to emulation. Some important advantages of the method are that it allows for the use of a combination of supervised learning methods (e.g., random forests and Gaussian process regression) and also allows for the prediction of process values at spatial locations and time points that were not used in the training sample. The method is demonstrated with two applications: the first is a periodic solution to a shallow ice approximation partial differential equation from glaciology, and second is an agent-based model of collective animal movement. In both cases, we demonstrate the value of combining different machine learning models for accurate emulation. In addition, in the agent-based model case we demonstrate the ability of the tensor emulator to successfully capture individual behavior in space and time. We demonstrate via a real data example the ability to perform Bayesian inference in order to learn parameters governing collective animal behavior.

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arXiv2020

A Bayesian Hidden Semi-Markov Model with Covariate-Dependent State Duration Parameters for High-Frequency Data from Wearable Devices

Data collected by wearable devices in sports provide valuable information about an athlete's behavior such as their activity, performance, and ability. These time series data can be studied with approaches such as hidden Markov and semi-Markov models (HMM and HSMM) for varied purposes including activity recognition and event detection. HSMMs extend the HMM by explicitly modeling the time spent in each state. In a discrete-time HSMM, the duration in each state can be modeled with a zero-truncated Poisson distribution, where the duration parameter may be state-specific but constant in time. We extend the HSMM by allowing the state-specific duration parameters to vary in time and model them as a function of known covariates derived from the wearable device and observed over a period of time leading up to a state transition. In addition, we propose a data subsampling approach given that high-frequency data from wearable devices can violate the conditional independence assumption of the HSMM. We apply the model to wearable device data collected on a soccer referee in a Major League Soccer game. We model the referee's physiological response to the game demands and identify important time-varying effects of these demands associated with the duration in each state.

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arXiv2020

Spatio-Temporal Change of Support Modeling with R

Spatio-temporal change of support methods are designed for statistical analysis on spatial and temporal domains which can differ from those of the observed data. Previous work introduced a parsimonious class of Bayesian hierarchical spatio-temporal models, which we refer to as STCOS, for the case of Gaussian outcomes. Application of STCOS methodology from this literature requires a level of proficiency with spatio-temporal methods and statistical computing which may be a hurdle for potential users. The present work seeks to bridge this gap by guiding readers through STCOS computations. We focus on the R computing environment because of its popularity, free availability, and high quality contributed packages. The stcos package is introduced to facilitate computations for the STCOS model. A motivating application is the American Community Survey (ACS), an ongoing survey administered by the U.S. Census Bureau that measures key socioeconomic and demographic variables for various populations in the United States. The STCOS methodology offers a principled approach to compute model-based estimates and associated measures of uncertainty for ACS variables on customized geographies and/or time periods. We present a detailed case study with ACS data as a guide for change of support analysis in R, and as a foundation which can be customized to other applications.

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arXiv2020

A Bayesian Markov model with Pólya-Gamma sampling for estimating individual behavior transition probabilities from accelerometer classifications

The use of accelerometers in wildlife tracking provides a fine-scale data source for understanding animal behavior and decision-making. Current methods in movement ecology focus on behavior as a driver of movement mechanisms. Our Markov model is a flexible and efficient method for inference related to effects on behavior that considers dependence between current and past behaviors. We applied this model to behavior data from six greater white-fronted geese (Anser albifrons frontalis) during spring migration in mid-continent North America and considered likely drivers of behavior, including habitat, weather and time of day effects. We modeled the transitions between flying, feeding, stationary and walking behavior states using a first-order Bayesian Markov model. We introduced Pólya-Gamma latent variables for automatic sampling of the covariate coefficients from the posterior distribution and we calculated the odds ratios from the posterior samples. Our model provides a unifying framework for including both acceleration and Global Positioning System data. We found significant differences in behavioral transition rates among habitat types, diurnal behavior and behavioral changes due to weather. Our model provides straightforward inference of behavioral time allocation across used habitats, which is not amenable in activity budget or resource selection frameworks.

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arXiv2020

On the spatial and temporal shift in the archetypal seasonal temperature cycle as driven by annual and semi-annual harmonics

Statistical methods are required to evaluate and quantify the uncertainty in environmental processes, such as land and sea surface temperature, in a changing climate. Typically, annual harmonics are used to characterize the variation in the seasonal temperature cycle. However, an often overlooked feature of the climate seasonal cycle is the semi-annual harmonic, which can account for a significant portion of the variance of the seasonal cycle and varies in amplitude and phase across space. Together, the spatial variation in the annual and semi-annual harmonics can play an important role in driving processes that are tied to seasonality (e.g., ecological and agricultural processes). We propose a multivariate spatio-temporal model to quantify the spatial and temporal change in minimum and maximum temperature seasonal cycles as a function of the annual and semi-annual harmonics. Our approach captures spatial dependence, temporal dynamics, and multivariate dependence of these harmonics through spatially and temporally-varying coefficients. We apply the model to minimum and maximum temperature over North American for the years 1979 to 2018. Formal model inference within the Bayesian paradigm enables the identification of regions experiencing significant changes in minimum and maximum temperature seasonal cycles due to the relative effects of changes in the two harmonics.

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arXiv2020

Deep Integro-Difference Equation Models for Spatio-Temporal Forecasting

Integro-difference equation (IDE) models describe the conditional dependence between the spatial process at a future time point and the process at the present time point through an integral operator. Nonlinearity or temporal dependence in the dynamics is often captured by allowing the operator parameters to vary temporally, or by re-fitting a model with a temporally-invariant linear operator in a sliding window. Both procedures tend to be excellent for prediction purposes over small time horizons, but are generally time-consuming and, crucially, do not provide a global prior model for the temporally-varying dynamics that is realistic. Here, we tackle these two issues by using a deep convolution neural network (CNN) in a hierarchical statistical IDE framework, where the CNN is designed to extract process dynamics from the process' most recent behaviour. Once the CNN is fitted, probabilistic forecasting can be done extremely quickly online using an ensemble Kalman filter with no requirement for repeated parameter estimation. We conduct an experiment where we train the model using 13 years of daily sea-surface temperature data in the North Atlantic Ocean. Forecasts are seen to be accurate and calibrated. A key advantage of our approach is that the CNN provides a global prior model for the dynamics that is realistic, interpretable, and computationally efficient. We show the versatility of the approach by successfully producing 10-minute nowcasts of weather radar reflectivities in Sydney using the same model that was trained on daily sea-surface temperature data in the North Atlantic Ocean.

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arXiv2019

A Hierarchical Spatio-Temporal Statistical Model Motivated by Glaciology

In this paper, we extend and analyze a Bayesian hierarchical spatio-temporal model for physical systems. A novelty is to model the discrepancy between the output of a computer simulator for a physical process and the actual process values with a multivariate random walk. For computational efficiency, linear algebra for bandwidth limited matrices is utilized, and first-order emulator inference allows for the fast emulation of a numerical partial differential equation (PDE) solver. A test scenario from a physical system motivated by glaciology is used to examine the speed and accuracy of the computational methods used, in addition to the viability of modeling assumptions. We conclude by discussing how the model and associated methodology can be applied in other physical contexts besides glaciology.

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arXiv2019

Bayesian Hierarchical Models with Conjugate Full-Conditional Distributions for Dependent Data from the Natural Exponential Family

We introduce a Bayesian approach for analyzing (possibly) high-dimensional dependent data that are distributed according to a member from the natural exponential family of distributions. This problem requires extensive methodological advancements, as jointly modeling high-dimensional dependent data leads to the so-called "big n problem." The computational complexity of the "big n problem" is further exacerbated when allowing for non-Gaussian data models, as is the case here. Thus, we develop new computationally efficient distribution theory for this setting. In particular, we introduce the "conjugate multivariate distribution," which is motivated by the univariate distribution introduced in Diaconis and Ylvisaker (1979). Furthermore, we provide substantial theoretical and methodological development including: results regarding conditional distributions, an asymptotic relationship with the multivariate normal distribution, conjugate prior distributions, and full-conditional distributions for a Gibbs sampler. To demonstrate the wide-applicability of the proposed methodology, we provide two simulation studies and three applications based on an epidemiology dataset, a federal statistics dataset, and an environmental dataset, respectively.

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arXiv2019

Comparison of Deep Neural Networks and Deep Hierarchical Models for Spatio-Temporal Data

Spatio-temporal data are ubiquitous in the agricultural, ecological, and environmental sciences, and their study is important for understanding and predicting a wide variety of processes. One of the difficulties with modeling spatial processes that change in time is the complexity of the dependence structures that must describe how such a process varies, and the presence of high-dimensional complex data sets and large prediction domains. It is particularly challenging to specify parameterizations for nonlinear dynamic spatio-temporal models (DSTMs) that are simultaneously useful scientifically and efficient computationally. Statisticians have developed deep hierarchical models that can accommodate process complexity as well as the uncertainties in the predictions and inference. However, these models can be expensive and are typically application specific. On the other hand, the machine learning community has developed alternative "deep learning" approaches for nonlinear spatio-temporal modeling. These models are flexible yet are typically not implemented in a probabilistic framework. The two paradigms have many things in common and suggest hybrid approaches that can benefit from elements of each framework. This overview paper presents a brief introduction to the deep hierarchical DSTM (DH-DSTM) framework, and deep models in machine learning, culminating with the deep neural DSTM (DN-DSTM). Recent approaches that combine elements from DH-DSTMs and echo state network DN-DSTMs are presented as illustrations.

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arXiv2018

Spatio-Temporal Models for Big Multinomial Data using the Conditional Multivariate Logit-Beta Distribution

We introduce a Bayesian approach for analyzing high-dimensional multinomial data that are referenced over space and time. In particular, the proportions associated with multinomial data are assumed to have a logit link to a latent spatio-temporal mixed effects model. This strategy allows for covariances that are nonstationarity in both space and time, asymmetric, and parsimonious. We also introduce the use of the conditional multivariate logit-beta distribution into the dependent multinomial data setting, which leads to conjugate full-conditional distributions for use in a collapsed Gibbs sampler. We refer to this model as the multinomial spatio-temporal mixed effects model (MN-STM). Additionally, we provide methodological developments including: the derivation of the associated full-conditional distributions, a relationship with a latent Gaussian process model, and the stability of the non-stationary vector autoregressive model. We illustrate the MN-STM through simulations and through a demonstration with public-use Quarterly Workforce Indicators (QWI) data from the Longitudinal Employer Household Dynamics (LEHD) program of the U.S. Census Bureau.

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