Andrew E. Seaton | Searcharxiv

arXiv2026

Spatial Capture-Recapture With Penalized Regression Splines to Flexibly Model Wildlife Density and Distribution

Spatial capture-recapture models are routinely used to estimate the abundance and distribution of wild animal populations and involve a latent spatial point process of animal activity centres that describes the spatial distribution of individuals. While traditional spatial capture-recapture models use a Poisson process, the assumption of conditional independence between points is often violated in practice due to factors not included in the point process, such as social clustering, territoriality, or preferential selection of habitat due to unobserved covariates. Log-Gaussian Cox processes are commonly used in spatial statistics to overcome weaknesses of Poisson processes, but methods to fit them within spatial capture-recapture do not currently exist. Here, we present a spatial capture-recapture framework that allows for the use of penalized regression splines to describe the activity centre distribution, with model fitting via a Laplace-approximate penalized marginal maximum likelihood approach. Our method approximates using a log-Gaussian Cox process for activity centres, and allows flexible modelling of nonlinear effect of covariates on density. We illustrate the use of our method with a simulation study and two case-studies. We demonstrate that, while population size estimates of traditional approaches are robust to density model misspecification, our approach substantially improves the estimation of spatial animal distributions.

stat.ME↗

arXiv2024

inlabru: software for fitting latent Gaussian models with non-linear predictors

The integrated nested Laplace approximation (INLA) method has become a popular approach for computationally efficient approximate Bayesian computation. In particular, by leveraging sparsity in random effect precision matrices, INLA is commonly used in spatial and spatio-temporal applications. However, the speed of INLA comes at the cost of restricting the user to the family of latent Gaussian models and the likelihoods currently implemented in {INLA}, the main software implementation of the INLA methodology. {inlabru} is a software package that extends the types of models that can be fitted using INLA by allowing the latent predictor to be non-linear in its parameters, moving beyond the additive linear predictor framework to allow more complex functional relationships. For inference it uses an approximate iterative method based on the first-order Taylor expansion of the non-linear predictor, fitting the model using INLA for each linearised model configuration. {inlabru} automates much of the workflow required to fit models using {R-INLA}, simplifying the process for users to specify, fit and predict from models. There is additional support for fitting joint likelihood models by building each likelihood individually. {inlabru} also supports the direct use of spatial data structures, such as those implemented in the {sf} and {terra} packages. In this paper we outline the statistical theory, model structure and basic syntax required for users to understand and develop their own models using {inlabru}. We evaluate the approximate inference method using a Bayesian method checking approach. We provide three examples modelling simulated spatial data that demonstrate the benefits of the additional flexibility provided by {inlabru}.

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