Model selection and sensitivity analysis in a class of Bayesian spatial distribution models

This work is focused on Bayesian hierarchical modeling of geographical distribution of marine species Coregonus lavaretus L. s.l. along the Gulf of Bothnia. Spatial dependences are modeled by Gaussian processes. The main modeling objective is to predict whitefish larvae distribution for previously unobserved spatial locations along the Gulf of Bothnia. In order to achieve this objective, we have to solve two main tasks: to investigate the sensitivity of posterior parameters estimates with respect to different parameter priors, and to solve model selection task. In model selection, among all candidate models, we have to choose the model with best predictive performance. The candidate models were divided into two main groups: models that describe spatial effects, and models without such description. The candidates in each group involved different number (6 or 8) and expressions of environmental variables. In the group describing spatial effects, we analyzed four different models of Gaussian mean, and for every mean model we used four different prior parameters combinations. The same four models of latent function were used in the candidates where spatial dependences were not described. For every such model we assigned four different priors of overdispersion parameter. Thus, all at all, 32 candidate models were analyzed. All candidate models were estimated with Hamiltonian Monte Carlo MCMC algorithm. Model checks were conducted using the posterior predictive distributions. The predictive distributions were evaluated using the logarithmic score with 10 fold cross validation. The analysis of posterior estimates in models describing spatial effects revealed, that these estimates were very sensitive to prior parameters choices. The provided sensitivity analysis helped us to choose the most suitable priors combination. The results from model selection showed that the model, which showed best predictive performance, does not need to be very complicated and to involve description of spatial effects when the data are not informative enough to detect well the spatial effects. Although the selected model was simpler, the corresponding predictive maps of log larvae intensity correctly predicted the larvae distribution along the Gulf of Bothnia