Bayesian nonparametric models for count data with applications to customer base management
Antonio Carlos Canale · Padua Research Archive (University of Padova) · 2012
Motivated by the analysis of telecommunications marketing data, which are multidimensional, longitudinal and mostly consisting in counts, this thesis introduces novel Bayesian nonparametric techniques for the estimation of probability mass functions and count stochastic processes. In addition, the theoretical basis of nonparametric mixture models for mixed-scale density estimation are provided. Mixed-scale data consists in joint continuous, count and categorical variables. Although Bayesian nonparametric models for continuous variables are well developed, the literature on related approaches for counts is limited and that for mixed-scale variables is close to none. The leading idea of this work is to induce prior distributions on the spaces of interest via priors on suitable latent spaces and mapping functions. Precisely a class of priors on the space of the probability mass functions and of the mixed-scale densities is induced through priors on the space of continuous densities and another class of priors on count stochastic process is induced through priors on the space of continuous stochastic processes. Asymptotic properties of these procedures are studied and results in terms of large support and posterior consistency are obtained under suitable assumptions. Efficient Gibbs samplers are developed for posterior computation, and the performance of the proposed methods is assessed in simulation studies and real data applications.