  The recently developed semi-parametric generalized linear model (SPGLM)
offers more flexibility as compared to the classical GLM by including the
baseline or reference distribution of the response as an additional parameter
in the model. However, some inference summaries are not easily generated under
existing maximum-likelihood based inference (ML-SPGLM). This includes
uncertainty in estimation for model-derived functionals such as exceedance
probabilities. The latter are critical in a clinical diagnostic or
decision-making setting. In this article, by placing a Dirichlet prior on the
baseline distribution, we propose a Bayesian model-based approach for inference
to address these important gaps. We establish consistency and asymptotic
normality results for the implied canonical parameter. Simulation studies and
an illustration with data from an aging research study confirm that the
proposed method performs comparably or better in comparison with ML-SPGLM. The
proposed Bayesian framework is most attractive for inference with small sample
training data or in sparse-data scenarios.
