2008/02/01 by Kostas Triantafyllopoulos, K. Triantafyllopoulos, Triantafyllopoulos, K.
Computer Science · Mathematics · #Applications (stat.AP) #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #stat.AP #stat.ME
paper · pdf · doi:10.48550/arxiv.0802.0219
38 pages, 12 figures, 4 tables
arxiv created 2008/02/01 · openalex publication_date 2008/02/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this paper is to provide a discussion, with illustrating examples, on Bayesian forecasting for dynamic generalized linear models (DGLMs). Adopting approximate Bayesian analysis, based on conjugate forms and on Bayes linear estimation, we describe the theoretical framework and then we provide detailed examples of response distributions, including binomial, Poisson, negative binomial, geometric, normal, log-normal, gamma, exponential, Weibull, Pareto, beta, and inverse Gaussian. We give numerical illustrations for all distributions (except for the normal). Putting together all the above distributions, we give a unified Bayesian approach to non-Gaussian time series analysis, with applications from finance and medicine to biology and the behavioural sciences. Throughout the models we discuss Bayesian forecasting and, for each model, we derive the multi-step forecast mean. Finally, we describe model assessment using the likelihood function, and Bayesian model monitoring.