Spatial Modelling in a Marine Environment When Sampling with Unknown Inclusion Probabilities
Janine B. Illian, David L. Borchers
University of St Andrews

In studies on the spatial distribution of marine mammals it is rarely the case that all individuals present in a survey area can be sampled. This is partly due to survey areas in marine environments typically being very large and partly due to the difficulty of detecting many marine species even within searched areas. The probability of inclusion in the sample is central to inference and there is a spatial component to inclusion probability: it depends on the observers' and individuals' location. In most applications this must be estimated from observed data.

Methods for modelling inclusion probability and spatial distribution from such surveys exist, using strip transect surveys, distance sampling surveys and capture-recapture surveys for example. However, they tend to assume simplistic spatial models to estimate inclusion probability and then separately estimate spatial distribution over the survey area conditional on the estimated inclusion probabilities. When inclusion probabilities are non-zero over large spatial ranges, simultaneous estimation of inclusion probability and spatial distribution is a more satisfactory approach.

Until recently, it has been difficult to conduct inference with realistically complex models of object distribution due to an absence of methods able to deal with noisy observations of location on ecological surveys as well as computational complexity. Here we discuss methods for drawing inference using more realistic models based on spatial point process methodology, in particular log Gaussian Cox processes. Recent work by Rue et al. (2009) and Illian et al. (2010) has provided approaches to fitting these point process models to complex point pattern data sets, based on integrated nested Laplace approximation (INLA). We discuss here how these approaches may be exploited in the context of models of the distribution of marine animals.

Keywords: Spatial sampling; Spatial point processes

Biography: Dr Illian is a faculty member at the School of Mathematics and Statistics at the University of St Andrews. She is based at the Centre for Research into Ecological and Environmental Modelling (CREEM). Dr Illian's research operates on the interface between ecology and statistics, in particular on the analysis and modelling of complex spatial data. Interdisciplinary collaboration forms an integral part of her research and continuing exchange with the ecological community is essential for all of her work. She is lead author of a recently published, extensive textbook on spatial point processes, which summarises the state of the art of the subject area but also makes the methodology available to non-specialists and applied researchers, in particular ecologists.