A Note on the Probability Difference Between Matching Priors Based on Posterior Quantiles and on Inversion of Conditional Likelihood Ratio Statistics

Abstract

A necessary and sufficient condition is given so that the second order probability matching priors based on posterior quantiles will be the priors under which the Bayesian and frequentist Bartlett corrected conditional likelihood ratio statistics differ by 0(l). Several examples are given to illustrate the idea.

Keywords

Second order matching prior Bartlett correction Conditional likelihood ratio statistic Likelihood ratio statistic Parametric orthogonality Posterior quantile Posterior credible region.

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