Gamma Belief Functions

This paper proves that the combination of gamma distributions via Dempster’s rule is also a gamma and therefore establishes the notion of gamma belief functions or gamma evidence, extending the scope of continuous belief functions from Gaussian belief functions to three additional members of the exponential family of distributions: gamma, exponential, and Erlang. It applies the result to the combination of generalized gamma regressions for evidence-based ensemble learning. Using simulated data and thousands of replications, the paper shows that the predictions by the combined model is very close to that made by regression models built by merging partial data sets but surprisingly outperforms in predicting actual responses.