Abstract
Probability matching priors for Bayesian prediction in non-regular case are considered. For one-parameter family of distributions, the resulting priors match the posterior predictive quantile with the frequentist one up to the order of o(n−2), and they are solutions of a certain differential equation (denoted by matching equation). Although predictive probability matching priors depend on a nominal rate α in general, we provide a prior which satisfy the matching equation for every nominal rate α in non-regular location and scale models. A multi-parameter extension including location-scale model is also discussed.
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