Comparison of the Frequentist MATA Confidence Interval with Bayesian Model-Averaged Confidence Intervals

Model averaging is a technique used to account for model uncertainty, in both Bayesian and frequentist multimodel inferences. In this paper, we compare the performance of model-averaged Bayesian credible intervals and frequentist confidence intervals. Frequentist intervals are constructed according to the model-averaged tail area (MATA) methodology. Differences between the Bayesian and frequentist methods are illustrated through an example involving cloud seeding. The coverage performance and interval width of each technique are then studied using simulation. A frequentist MATA interval performs best in the normal linear setting, while Bayesian credible intervals yield the best coverage performance in a lognormal setting. The use of a data-dependent prior probability for models improved the coverage of the model-averaged Bayesian interval, relative to that using uniform model prior probabilities. Data-dependent model prior probabilities are philosophically controversial in Bayesian statistics, and our results suggest that their use is beneficial when model averaging.