Charlotte Boyd and Mathieu Woillez
UW School of Aquatic & Fishery Sciences
February 28, 2011

Geostatistical conditional simulations are a useful tool for capturing the full range of variability in spatial data. The distribution of schooling fish is inherently patchy – this patchiness may be lost in kriging which presents a best local estimate at each point and tends to smooth over local variability. In contrast, stochastic geostatistical simulations reproduce the variability of a variogram model. Simulations can be conditioned on the observed data values, and, on average, reproduce the statistical properties and spatial pattern of the sample data. Multiple simulations can therefore be used as the basis for estimating uncertainty at given locations. Geostatistical simulation is thus relevant to analyses of spatial sample data in which measurement error, local variability, or sampling uncertainty are important (such as risk assessment and decision analysis). In the Gaussian case, geostatistical conditional simulation can be achieved relatively easily by adding a simulated error term to the kriging. However, in the case of acoustic surveys of schooling fish, where the acoustic backscatter is often characterized by a high proportion of zeroes and skewed positive values, some transformations are necessary. Here, we present and discuss two contrasting approaches to perform geostatistical conditional simulation in this context – one based on transformed Gaussian simulations and on a Gibbs sampler to handle the numerous zero acoustic values within a classical geostatistical framework, and the other based on a binomial/ lognormal hurdle model within a generalized linear mixed modeling framework.