Spatial point processes — theory and practice

Dr Janine Illian – 21 August, 2017

Overview

In statistical ecology a specific data structure, e.g. resulting from a common survey method, often motivates both statistical methodology and software development. The specific survey method as well as the statistical methodology adapt to the practicality of data collection but do not directly reflect the underlying ecological process of interest. This results in highly specialised modelling approaches and, at the same time, little exchange among the developers of the different strands of methodology.

In this talk we discuss how thinking in terms of the processes that we would like to model rather than thinking in terms of the survey method can yield a flexible class of models. Specifically, the ecological processes of interest here are the structures formed by individuals in space and time, reflecting the individuals’ interaction among each other and with the environment.

Spatial point processes are stochastic processes that model the location of individuals in space and time. However, classical point process methodology assumes the entire spatial area of interest has been surveyed and that individuals have been detected uniformly in space. Treating surveying plot sampling or distance sampling as a thinning of a spatial point process allows us to use methodology developed for spatial point processes and to operate in a general spatial modelling context. As a result, general and computationally efficient model fitting software such as R-INLA, based on computationally efficient integrated nested Laplace approximation become relevant.

In this talk we illustrate how the software package inlabru, which has been designed to fit thinned point process models and is based on R-INLA may be used to fit flexible spatial modes to a wide range of ecological data structures. In addition, we show how this developments has in turn contributed to widening the class of models that may be fitted with R-INLA.