Several statistical techniques have been recently developed for the inference of cancer progression models from the increasingly available NGS cross sectional mutational profiles. A particular algorithm, CAPRI, was proven to be the most efficient with respect to sample size and level of noise in the data. The algorithm combines structural constraints based on Suppes' theory of probabilistic causation and maximum likelihood fit with regularization,and defines constrained Bayesian networks, named Suppes-Bayes Causal Networks(SBCNs), which account for the selective advantage relations among genomic events. In general, SBCNs are effective in modeling any phenomenon driven by cumulative dynamics, as long as the modeled events are persistent. We here discuss on the effectiveness of the SBCN theoretical framework and we investigate the inference of: (i) the priors based on Suppes' theory and (ii) different maximum likelihood regularization parameters on the inference performance estimated on large synthetically generated datasets.