Flexible spatial modelling with inlabru – a distance sampling case study
Speaker: Andy Seaton (University of St.Andrews)
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.