Functional ANOVA for Modelling Temperature Profiles in Ecuador

The experiments obtained from global and regional climate models have recently become popular and are widely used in the Statistical literature to analyze and understand the evolution of natural phenomena such as climate change in a limited area, using discretized versions of physical processes that they are modeled by systems of differential equations. This methodology is appropriate for the analysis of time series of climatic variables; therefore, the present work is motivated by the need to compare sources of variability in the projections made by the computational models used to model the climate. We propose to use a functional data modeling through an ANOVA, assigning prior distributions of Gaussian processes in each batch of the functional effects. Some alternatives to specify the model will be discussed, and computationally efficient strategies will be considered for the simulation of the samples and estimation of the posterior distribution using a Markov Chain Monte Carlo algorithm for the first case and a Laplace approximation for the second case. The methodology will be illustrated through two cases: the effect of the geographical region on the temperature profiles in the meteorological stations of Ecuador and the sources of variability in the output of regional climate models.