arXiv subjects

Ephraim M. Hanks

Publications and source records attributed to Ephraim M. Hanks.

14 recordsLinked to original sources

arXiv2026

An Integrated Time-Varying Ornstein-Uhlenbeck Process for Jointly Modeling Individual and Population-Level Movement of Golden Eagles

With technological advancements, the quantity and quality of animal movement data have increased greatly. Currently, no movement model can be used to describe full-year data from migratory species by leveraging both individual movement and species distribution data. Herein we propose a full-year stochastic differential equation model for jointly modeling both individual movement and species distribution data. We show that this joint model, under certain assumptions, results in efficient computation of the spatio-temporal dynamics of the entire population, and thus provides straightforward inference on the species distribution data. We illustrate this model by analyzing 215 bird-years of golden eagle movement in western North America jointly with relative abundance data from eBird. We use the results to estimate wind project risk for these eagles and predict where they came from earlier in the year based on a single telemetry observation from later in the year. Our joint model enables additional inference and greater predictive power than afforded by sole use of eBird relative abundance.

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arXiv2025

Multiscale modelling of animal movement with persistent dynamics

Wild animals are commonly fitted with trackers that record their position through time, and statistical models for tracking data broadly fall into two categories: models focused on small-scale movement decisions, and models for large-scale spatial distributions. Due to this dichotomy, it is challenging to describe mathematically how animals' distributions arise from their short-term movement patterns, and to combine data sets collected at different scales. We propose a multiscale model of animal movement and space use based on the underdamped Langevin process, widely used in statistical physics. The model is convenient to describe animal movement for three reasons: it is specified in continuous time (such that its parameters are not dependent on an arbitrary time scale), its speed and direction are autocorrelated (similarly to real animal trajectories), and it has a closed form stationary distribution that we can view as a model of long-term space use. We use the common form of a resource selection function for the stationary distribution, to model the environmental drivers behind the animal's movement decisions. We further increase flexibility by allowing movement parameters to be time-varying, and find conditions under which the stationary distribution is preserved. We derive an explicit mathematical link to step selection functions, commonly used in wildlife studies, providing new theoretical results about their scale-dependence. We formulate the underdamped Langevin model as a state-space model and present a computationally efficient method of inference based on the Kalman filter and a marginal likelihood approach for mixed effect extensions.

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arXiv2023

Modeling First Arrival of Migratory Birds using a Hierarchical Max-infinitely Divisible Process

Humans have recorded the arrival dates of migratory birds for millennia, searching for trends and patterns. As the first arrival among individuals in a species is the realized tail of the probability distribution of arrivals, the appropriate statistical framework with which to analyze such events is extreme value theory. Here, for the first time, we apply formal extreme value techniques to the dynamics of bird migrations. We study the annual first arrivals of Magnolia Warblers using modern tools from the statistical field of extreme value analysis. Using observations from the eBird database, we model the spatial distribution of Magnolia Warbler arrivals as a max-infinitely divisible process, which allows us to spatially interpolate observed annual arrivals in a probabilistically-coherent way, and to project arrival dynamics into the future by conditioning on climatic variables.

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arXiv2021

A New Framework for Inference on Markov Population Models

In this work we construct a joint Gaussian likelihood for approximate inference on Markov population models. We demonstrate that Markov population models can be approximated by a system of linear stochastic differential equations with time-varying coefficients. We show that the system of stochastic differential equations converges to a set of ordinary differential equations. We derive our proposed joint Gaussian deterministic limiting approximation (JGDLA) model from the limiting system of ordinary differential equations. The results is a method for inference on Markov population models that relies solely on the solution to a system deterministic equations. We show that our method requires no stochastic infill and exhibits improved predictive power in comparison to the Euler-Maruyama scheme on simulated susceptible-infected-recovered data sets. We use the JGDLA to fit a stochastic susceptible-exposed-infected-recovered system to the Princess Diamond COVID-19 cruise ship data set.

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arXiv2020

A Mechanistic Model of Annual Sulfate Concentrations in the United States

We develop a mechanistic model to analyze the impact of sulfur dioxide emissions from coal-fired power plants on average sulfate concentrations in the central United States. A multivariate Ornstein-Uhlenbeck (OU) process is used to approximate the dynamics of the underlying space-time chemical transport process, and its distributional properties are leveraged to specify novel probability models for spatial data (i.e., spatially-referenced data with no temporal replication) that are viewed as either a snapshot or a time-averaged observation of the OU process. Air pollution transport dynamics determine the mean and covariance structure of our atmospheric sulfate model, allowing us to infer which process dynamics are driving observed air pollution concentrations. We use these inferred dynamics to assess the regulatory impact of flue-gas desulfurization (FGD) technologies on human exposure to sulfate aerosols.

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arXiv2020

Privacy for Spatial Point Process Data

In this work we develop methods for privatizing spatial location data, such as spatial locations of individual disease cases. We propose two novel Bayesian methods for generating synthetic location data based on log-Gaussian Cox processes (LGCPs). We show that conditional predictive ordinate (CPO) estimates can easily be obtained for point process data. We construct a novel risk metric that utilizes CPO estimates to evaluate individual disclosure risks. We adapt the propensity mean square error (pMSE) data utility metric for LGCPs. We demonstrate that our synthesis methods offer an improved risk vs. utility balance in comparison to radial synthesis with a case study of Dr. John Snow's cholera outbreak data.

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arXiv2019

Bayesian Analysis of Spatial Generalized Linear Mixed Models with Laplace Random Fields

Gaussian random field (GRF) models are widely used in spatial statistics to capture spatially correlated error. We investigate the results of replacing Gaussian processes with Laplace moving averages (LMAs) in spatial generalized linear mixed models (SGLMMs). We demonstrate that LMAs offer improved predictive power when the data exhibits localized spikes in the response. SGLMMs with LMAs are shown to maintain analogous parameter inference and similar computing to Gaussian SGLMMs. We propose a novel discrete space LMA model for irregular lattices and construct conjugate samplers for LMAs with georeferenced and areal support. We provide a Bayesian analysis of SGLMMs with LMAs and GRFs over multiple data support and response types.

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arXiv2017

On the Relationship between Conditional (CAR) and Simultaneous (SAR) Autoregressive Models

We clarify relationships between conditional (CAR) and simultaneous (SAR) autoregressive models. We review the literature on this topic and find that it is mostly incomplete. Our main result is that a SAR model can be written as a unique CAR model, and while a CAR model can be written as a SAR model, it is not unique. In fact, we show how any multivariate Gaussian distribution on a finite set of points with a positive-definite covariance matrix can be written as either a CAR or a SAR model. We illustrate how to obtain any number of SAR covariance matrices from a single CAR covariance matrix by using Givens rotation matrices on a simulated example. We also discuss sparseness in the original CAR construction, and for the resulting SAR weights matrix. For a real example, we use crime data in 49 neighborhoods from Columbus, Ohio, and show that a geostatistical model optimizes the likelihood much better than typical first-order CAR models. We then use the implied weights from the geostatistical model to estimate CAR model parameters that provides the best overall optimization.

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arXiv2017

A Spatially-Varying Stochastic Differential Equation Model for Animal Movement

Animal movement exhibits complex behavior which can be influenced by unobserved environmental conditions. We propose a model which allows for a spatially-varying movement rate and spatially-varying drift through a semiparametric potential surface and a separate motility surface. These surfaces are embedded in a stochastic differential equation framework which allows for complex animal movement patterns in space. The resulting model is used to analyze the spatially-varying behavior of ants to provide insight into the spatial structure of ant movement in the nest.

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arXiv2016

Hierarchical animal movement models for population-level inference

New methods for modeling animal movement based on telemetry data are developed regularly. With advances in telemetry capabilities, animal movement models are becoming increasingly sophisticated. Despite a need for population-level inference, animal movement models are still predominantly developed for individual-level inference. Most efforts to upscale the inference to the population-level are either post hoc or complicated enough that only the developer can implement the model. Hierarchical Bayesian models provide an ideal platform for the development of population-level animal movement models but can be challenging to fit due to computational limitations or extensive tuning required. We propose a two-stage procedure for fitting hierarchical animal movement models to telemetry data. The two-stage approach is statistically rigorous and allows one to fit individual-level movement models separately, then resample them using a secondary MCMC algorithm. The primary advantages of the two-stage approach are that the first stage is easily parallelizable and the second stage is completely unsupervised, allowing for a completely automated fitting procedure in many cases. We demonstrate the two-stage procedure with two applications of animal movement models. The first application involves a spatial point process approach to modeling telemetry data and the second involves a more complicated continuous-time discrete-space animal movement model. We fit these models to simulated data and real telemetry data arising from a population of monitored Canada lynx in Colorado, USA.

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arXiv2016

Flexible discrete space models of animal movement

Movement drives the spread of infectious disease, gene flow, and other critical ecological processes. To study these processes we need models for movement that capture complex behavior that changes over time and space in response to biotic and abiotic factors. Penalized likelihood approaches, such as penalized semiparametric spline expansions and LASSO regression, allow inference on complex models without overfitting. Continuous-time Markov chains (CTMCs) have been recently introduced as a flexible discrete-space model for animal movement. Modeling with CTMCs involves discretizing an animal's path to the resolution of a raster grid. The resulting stochastic process model can easily incorporate environmental and other covariates, represented as raster layers, that affect directional bias and overall movement rate. We introduce a weighted likelihood approach that allows for modeling movement using CTMCs, with path uncertainty due to missing data modeled by imputing continuous-time paths between telemetry locations. The framework we introduce allows for inference on CTMC movement models using existing software for fitting Poisson regression models, including penalized versions of Poisson regression. The result is a flexible, powerful, and accessible framework for modeling a wide range of animal movement behavior.

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arXiv2015

Dynamic Models of Animal Movement with Spatial Point Process Interactions

When analyzing animal movement, it is important to account for interactions between individuals. However, statistical models for incorporating interaction behavior in movement models are limited. We propose an approach that models dependent movement by augmenting a dynamic marginal movement model with a spatial point process interaction function within a weighted distribution framework. The approach is flexible, as marginal movement behavior and interaction behavior can be modeled independently. Inference for model parameters is complicated by intractable normalizing constants. We develop a double Metropolis-Hastings algorithm to perform Bayesian inference. We illustrate our approach through the analysis of movement tracks of guppies (Poecilia reticulata)

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arXiv2015

A Constructive Spatio-Temporal Approach to Modeling Spatial Covariance

I present an approach for modeling areal spatial covariance by considering the stationary distribution of a spatio-temporal Markov random walk. In the areal data case, this stationary distribution corresponds to an intrinsic simultaneous autoregressive (SAR) model for spatial correlation, and provides a principled approach to specifying areal spatial models when a spatio-temporal generating process can be assumed. I apply the approach to a study of spatial genetic variation of trout in a stream network in Connecticut, USA, and a study of crime rates in neighborhoods of Columbus, OH, USA.

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arXiv2015

Continuous-time discrete-space models for animal movement

The processes influencing animal movement and resource selection are complex and varied. Past efforts to model behavioral changes over time used Bayesian statistical models with variable parameter space, such as reversible-jump Markov chain Monte Carlo approaches, which are computationally demanding and inaccessible to many practitioners. We present a continuous-time discrete-space (CTDS) model of animal movement that can be fit using standard generalized linear modeling (GLM) methods. This CTDS approach allows for the joint modeling of location-based as well as directional drivers of movement. Changing behavior over time is modeled using a varying-coefficient framework which maintains the computational simplicity of a GLM approach, and variable selection is accomplished using a group lasso penalty. We apply our approach to a study of two mountain lions (Puma concolor) in Colorado, USA.

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