Dynamic Bayesian models: extensions and new proposals

• Autor(a) principal: Victor Schmidt Comitti
• Data de Publicação: 2019
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/33546
• topic: zero inflated/overdispersed distribution; Negative Binomial distribution; Parameter driven model; Dynamic Generalized Linear Model; Bayesian inference; change-point detection; Product Partition Models; Estatística. - Teses.; Séries temporais.; Modelos dinâmicos Bayesianos.; Modelos de partição produto.; Dados de contagem

Even though many time series presents problems such as overdispersion, zero inflation and change-points, these features, usually, are not incorporated into the most common dynamic Bayesian models available in the literature. To address these problems, we worked on two strands in this dissertation. In the first strand, the objective is to introduce new Bayesian dynamic models for time series of counts that allow for observations in distributions that can more adequately adjust to some common features related to the modeling of discrete data. We present a new framework for uniparametric Dynamic Bayesian Models of counts whose particular cases include Bell, Poisson-Lindley, Yule-Simon and Borel models. Furthermore, a biparametric Negative binomial model with unknown shape parameter is provided. The inferential procedure preserves the sequential nature of the Bayesian analysis and is similar to the Dynamic Generalized Linear Models (DGLM) with a novel of incorporating Monte Carlo integration to the recursive algorithm in order to deal with the intractability of the updating distributions and an ARMS step to sample from the posterior distribution of the shape parameter. We also consider a conjugate Beta Prime of the second kind distribution prior for the mean of the process. The simulation results show a good performance of the estimators considered for the static parameter, which can be reasonably estimated. The application results also highlights a better performance of the proposed uni/biparametric models over the Poisson model. In the second strand of this work we incorporate the Product Partition Models class into the DGLM. This new formulation, that we call DGLM-PPM, retains the flexibility and generality of the DGLM class and also provides a framework for Bayesian multiple change-point detection in time series. To sample from the partition and the discount factor we use a Gibbs Sampler with an ARMS step appended. A simulation study is conducted and the results show that the proposed model is able to detect the points of regime switch in the simulated data. The superiority of our proposal over the conventional DGLM is further confirmed in two real data applications in which the DGLM-PPM outperforms the conventional DGLM in-sample and out-of-sample.