Highly structured spatial models as a tool for analyzing the spread of diseases and species distributions

In the last years, the use of complex statistical models has increased to improve our knowledge on the spread of diseases and the distribution of species, being of great interest in Ecology and Epidemiology. Complexity in these models arises for instance when including the use of beta likelihoods and spatial e ects. This complexity makes the inferential and predictive processes challenging to perform. Bayesian statistics represent a good alternative to deal with these models, because it is based on the idea that the information and uncertainty can be expressed in terms of probability distributions. Moreover, this complexity can be readily handled with hierarchical Bayesian models without much di culty. However, despite the di erent advantages of the Bayesian inference, the main challenge is to nd an analytic expression for posterior distributions of the parameters and hyperparameters. Several numeric approaches have been proposed such as Markov chain Monte Carlo methods (MCMC) or integrated nested Laplace approximation (INLA). Here, we present three di erent complex real problems which can be approached with hierarchical Bayesian models using INLA. In particular, a beta regression model with random e ects to study a persimmon disease caused by the fungus Mycosphaerella nawae in the Comunitat Valenciana region in Spain, and a beta spatial regression to study the spatial distribution of the genetic diversity of the plant Arabidopsis thaliana in the Iberian Peninsula. In addition, we show a preliminary analysis of an emerging plant disease, known as the olive quick decline syndrome and caused by the bacterium Xylella fastidiosa, which is expanding rapidly in the southern region of Apulia in Italy, Corsica, continental France, as well as outbreaks in Balearic Islands in Spain.