Flexible spatial modelling with inlabru – a distance sampling case study

Speaker: Andy Seaton (University of St.Andrews)

Abstract

I will present a chapter of my thesis on fitting a spatial point process model with a point transect distance sampling observation process.  I’ll present distance sampling from a spatial point process perspective and draw links with the classical distance sampling literature.  The point process model is assumed to be a log-Gaussian Cox process, which allows the use of spatially structured random effects to describe the density of birds.  Here I use a Gaussian Markov random field approach based on a stochastic partial differential equation representation of the random field.  Both the spatial model and the observation model are fitted jointly using integrated nested Laplace approximations (INLA).  I will introduce a novel approach to dealing with model components which are non-linear in their parameters – in this case the distance sampling detection function.  This is based on a linearisation approach that optimises over “non-linear” parameters, fitting the model with INLA for each estimate of the non-linear model component.  This linearisation scheme is implemented in the R package inlabru – which extends the functionality of R-INLA and provides useful wrappers that simplify the INLA code required specify, fit, and interrogate models fitted using INLA.  I will show results from a case study applied to a single-year of a point transect distance sampling survey of a tropical bird endemic to Hawai’i.  The model is readily extendible to multiple years.  I will also briefly discuss some issues with summarising and visualising results from spatial models with random fields.  To end I will mention some general ideas where I think this linearisation approach could be useful to fitting models in statistical ecology more generally – this is not completed work, just some ideas for the future.