01 A Non-Stationary Bayesian Species Distribution Model, and its Application in Marine Megafauna.

Oregon Convention Center 

Let us start with a simple illustration of some fish that lives in shallow sea waters. An impermeable barrier for this fish would be a set of islands where there is no scenario in which fishes go over it. However, there might be sand patches with varying water coverage depending on the tide. These sand patches cannot be considered permanently impermeable barriers as fishes will be present, but will do so less often than in the normal non barrier area. This is a rather common set up, however there is no solution as we have no models for this case. We propose a Transparent barrier model that can deal with complex barrier scenarios. Moreover, it relies on a Matérn field making it as efficient as the classic stationary models in spatial statistics. The Transparent Barrier model is based on interpreting the Matérn correlation as a collection of paths through a Simultaneous Autoregressive (SAR) model, manipulating local dependencies to cut off paths crossing physical barriers and formulated as a stochastic partial differential equation (SPDE) for well-behaved discretization. Then, we include a transparency parameter to explicitly add barriers with different levels of permeability.

Spatial distribution model

Non stationary Gaussian random field

Barrier model

Coastline and island problem

Stochastic Partial Differential Equations (SPDE)

INLA 

Section on Bayesian Statistical Science