Modeling and simulating complexity for discrete graphic Markov models: an experimental study
Elva Dı́az, Eunice Ponce de León · 2004
Abstract. In this paper the problem studied is how the complexity of the model structure affects the performance of an algorithm constructed to simulate random samples from the model structure S of a discrete graphic Markov model. A definition of the complexity of the structure S of a discrete Markov model is given proportional to the sum of the number of edges of the maximal cliques, minus the number of edges that are in the intersections of the maximal cliques. The constructed algorithm is a hybrid consisting of a modified IPF and a Gibbs-Sampler. The model structure of the family is encoded as a list of strings, each string correspond to a maximal clique GM of the graph of the model. This graph represents the conditional independence restrictions defining the structure of the model. As results, the departure model fits each sample generated by the modified IPF algorithm the performance of the Gibbs-Sampler algorithm depends on the complexity of the model: the percent of Gibbs-Sampler samples not significant different from the corresponding probability distributions of departure decreases with the growing complexity of the models and is the least with dense models, this means that the performance of the Gibbs-Sampler depends on the complexity of the models.