The deductive phase of statistical analysis via predictive simulations: test, validation and control of a linear model with autocorrelated errors representing a food process

Abstract

Statistical analysis consists of two phases: induction for model parameter estimation and deduction to make decisions on the basis of the statistical model. In the Bayesian context, predictive analysis is the key concept to perform the deductive phase. In that context, Monte-Carlo posterior simulations are shown to be extremely valuable tools to achieve for instance model selection and model checking. Example of predictive analysis by simulation is detailed for the linear model with Autocorrelated Errors which has been beforehand estimated by Gibbs sampling. Numerical illustrations are then given for a food process with data collected on line. Special attention is cast on the control of its anticipated behavior under uncertainty within Bayesian decision theory.