Frequentist and Bayesian inference unified and generalized by evidential support distributions

What is it about?

Frequentist inference in the form of p-values and confidence intervals is simply represented by posterior distributions called confidence distributions. They, unlike Bayesian posterior distributions, do not require prior distributions. The laws of probably enable combining confidence distributions with Bayesian posterior distributions. The resulting posterior probability of a hypothesis is interpreted as the amount of support for that hypothesis from the evidence. More generally, the Bayes-frequentist posterior distribution of a parameter of interest is a distribution of evidential support that is suitable for interval estimation and point estimation as well as hypothesis testing.

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Why is it important?

Applications of evidential support distributions include solutions to restricted parameter problems and propagating the uncertainty about which model to use. The main application addressed is that of using a confidence distribution to propagate the uncertainty in estimating a prior by empirical Bayes methods.

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