A note on fiducial model averaging as an alternative to checking Bayesian and frequentist models

作者：Bickel David R.^*

来源：Communications in Statistics - Theory and Methods, 2018, 47(13): 3125-3137.

DOI：10.1080/03610926.2017.1348522

• Bayesian model averaging
• coherent fiducial distribution
• confidence distribution
• distributional inference
• fiducial inference
• frequentist model averaging
• model assessment
• model checking
• model criticism
• posterior predictive check
• prior predictive check
• prior-data conflict

Just as frequentist hypothesis tests have been developed to check model assumptions, prior predictive p-values and other Bayesian p-values check prior distributions as well as other model assumptions. These model checks not only suffer from the usual threshold dependence of p-values, but also from the suppression of model uncertainty in subsequent inference. One solution is to transform Bayesian and frequentist p-values for model assessment into a fiducial distribution across the models. Averaging the Bayesian or frequentist posterior distributions with respect to the fiducial distribution can reproduce results from Bayesian model averaging or classical fiducial inference.

• 出版日期2018