Spatial and Temporal Modelling of Hoki Distribution using Gaussian Markov Random Fields

In order to carry out assessment of marine stock levels, an accurate estimate of the current year's population abundance must be formulated. Standardized catch per unit of effort (CPUE) values are, in theory, proportional to population abundance. However, this only holds if the species catchability is constant over time. In almost all cases it is not, due to the existence of spatial and temporal variation. In this thesis, we fit various models to test different combinations and structures of spatial and temporal autocorrelation within hoki (Macruronus novaezelandiae) CPUE. A Bayesian approach was taken, and the spatial and temporal components were modelled using Gaussian Markov random fields. The data was collected from summer research trawl surveys carried out by the National Institute of Water and Atmospheric Research (NIWA) and the Ministry for Primary Industries (MPI). It allowed us to model spatial distribution using both areal and point reference approaches. To fit the models, we used the software Stan (Gelman et al., 2015) which implements Hamiltonian Monte Carlo. Model comparison was carried out using the Watanabe-Akaike information criterion (WAIC, (Watanabe, 2010)). We found that trawl year was the most important factor to explain variation in research survey hoki CPUE. Furthermore, the areal approach provided better indices of abundance than the point reference approach