Identifiability, Improper Priors and Gibbs Sampling for Generalized Linear Models

Markov chain Monte Carlo algorithms are widely used in the fitting of generalized linear models (GLM). Such model fitting is somewhat of an art form requiring suitable trickery and tuning to obtain results one can have confidence in. A wide range of practical issues arise. The focus here is on parameter identifiability and posterior propriety. In particular, we clarify that non-identifiability arises for usual GLM's and discuss its implications for simulation based model fitting. Since often, some part of the prior specification is vague we consider whether the resulting posterior is proper, providing rather general and easy to check results for GLM's. We also show that if a Gibbs sampler is run with an improper posterior, it may be possible to use the output to obtain meaningful inference for certain model unknowns. Key words and phrases: Convergence; Embedded Posterior; Estimability; Integrability; Non-full rank models. 1 Introduction Currently, simulation-based methods offer the be..

Meta-analysis of observational studies

Observational studies such as those used to investigate lifecourse epidemiology present particular challenges for meta-analysis. This chapter discusses the differences between meta-analysis of randomised controlled trials and observational studies, introduces methods for meta-analysis in this unique setting, and illustrates the issues involved using a real example from a meta-analysis in the field of diet and cancer. Emphasis is placed on practicalities of how to conduct meta-analyses of observational studies where the information presented in the articles reviewed may be limited