Indexing and partitioning the spatial linear model for large data sets.

We consider four main goals when fitting spatial linear models: 1) estimating covariance parameters, 2) estimating fixed effects, 3) kriging (making point predictions), and 4) block-kriging (predicting the average value over a region). Each of these goals can present different challenges when analyzing large spatial data sets. Current research uses a variety of methods, including spatial basis functions (reduced rank), covariance tapering, etc, to achieve these goals.

Marginal inference for hierarchical generalized linear mixed models with patterned covariance matrices using the Laplace approximation.

We develop hierarchical models and methods in a fully parametric approach to generalized linear mixed models for any patterned covariance matrix. The Laplace approximation is used to marginally estimate covariance parameters by integrating over all fixed and latent random effects. The Laplace approximation relies on Newton-Raphson updates, which also leads to predictions for the latent random effects.

Integrated animal movement and spatial capture-recapture models: Simulation, implementation, and inference.

Over the last decade, spatial capture-recapture (SCR) models have become widespread for estimating demographic parameters in ecological studies. However, the underlying assumptions about animal movement and space use are often not realistic. This is a missed opportunity because interesting ecological questions related to animal space use, habitat selection, and behavior cannot be addressed with most SCR models, despite the fact that the data collected in SCR studies - individual animals observed at specific locations and times - can provide a rich source of information about these processes and how they relate to demographic rates.

Evaluation of camera trap-based abundance estimators for unmarked populations.

Estimates of species abundance are critical to understand population processes and to assess and select management actions. However, capturing and marking individuals for abundance estimation, while providing robust information, can be economically and logistically prohibitive, particularly for species with cryptic behavior. Camera traps can be used to collect data at temporal and spatial scales necessary for estimating abundance, but the use of camera traps comes with limitations when target species are not uniquely identifiable (i.

When to be discrete: the importance of time formulation in understanding animal movement.

Animal movement is essential to our understanding of population dynamics, animal behavior, and the impacts of global change. Coupled with high-resolution biotelemetry data, exciting new inferences about animal movement have been facilitated by various specifications of contemporary models. These approaches differ, but most share common themes.