Hyper-$g$ priors for generalized linear models

Mixtures of g-Priors in Generalized Linear Models

Mixtures of Zellner’s g-priors have been studied extensively in linear models and have been shown to have numerous desirable properties for Bayesian variable selection and model averaging. Several extensions of g-priors to Generalized Linear Models (GLMs) have been proposed in the literature; however, the choice of prior distribution of g and resulting properties for inference have received con...

g - priors for Linear Regression

where X is the design matrix, ∼ N (0, σI), and β ∼ N (β0, gσ(XTX)−1). The prior on σ is the Jeffreys prior, π(σ) ∝ 1 σ2 , and usually, β0 is taken to be 0 for simplification purposes. The appeal of the method is that there is only one free parameter g for all linear regression. Furthermore, the simplicity of the g-prior model generally leads to easily obtained analytical results. However, we st...

Bayesian Inference for Spatial Beta Generalized Linear Mixed Models

In some applications, the response variable assumes values in the unit interval. The standard linear regression model is not appropriate for modelling this type of data because the normality assumption is not met. Alternatively, the beta regression model has been introduced to analyze such observations. A beta distribution represents a flexible density family on (0, 1) interval that covers symm...

Extended Linear Models with Gaussian Priors Extended Linear Models with Gaussian Priors

Identi ability, Improper Priors and Gibbs Sampling for Generalized Linear Models

Markov chain Monte Carlo algorithms are widely used in the tting of generalized linear models (GLM). Such model tting is somewhat of an art form requiring suitable trickery and tuning to obtain results one can have conndence in. A wide range of practical issues arise. The focus here is on parameter identiiability and posterior propriety. In particular, we clarify that non-identiiability arises ...