Estimating variable association in contingency tables through probabilistic expert systems when samples are drawn according to stratified sampling designs

This article focuses on the learning algorithms of a PES structure, given a sample of observations from a finite population, drawn according to a stratified sample design. The structural learning algorithms can be of two typologies: the score+search and the constraint based algorithms. Here we focus on the score+search case, for which the most likely structure, given the observed data, will be identified optimizing an objective function (typically a penalized likelihood), by means of optimization methods that, in this case, will be given by the greedy search and the genetic algorithms ones. Structural learning will be tackled considering the necessary networks for one class of estimators (named E-PES estimator) built over a PES that includes the variables of interest and the design variable.