Evaluating Spatio-temporal models for crop yield forecasting using INLA: implications to pricing area yield crop insurance contracts

In an area yield crop insurance farmers collect an indemnity whenever the county average yield falls beneath a yield guarantee, regardless of the farmers actual yields. The pricing methodology for this kind of insurance requires the estimation of the expected crop yield at the county level. This can be done in a hierarchical Bayesian framework via spatio-temporal modelling of areal crop yield data. Inference in this kind of models is typically based on Markov chain
Monte Carlo methods. However, these methods suffer from several problems: Computational time is long, parameter samples can be highly correlated and estimates may have a large Monte Carlo error. Additionally, a huge number of models with different components resulting from the combination of regional effects, time trends and time-space interactions, as well as of several covariates entering in the models in different ways, need to be fitted and compared in order to identify the more suitable one to be used in the calculation
of the premium rates of the areal crop yield insurance contract. This task becomes very time consuming when the number of areas increases.

A recent alternative to MCMC methods to perform inference in latent Gaussian
models are the integrated nested Laplace approximations (INLA). In this paper, using the INLA approach, was possible to fit and compare in an efficient way several spatio-temporal crop yield models in order to identify the most suitable ones to calculate the premium rate of an areal crop yield insurance contract for maize in Paraná state (Brazil). Further we propose an extension of the INLA approach that enable the application of the same methodology using a complex dynamic spatio-temporal model for areal data within reasonable computational time and in a user friendly way with INLA.