In recent years, extensive work has been done concerning the derivation of noninformative prior distributions assuring approximate frequentist validity of Bayesian inferences.This paper provides a review of matching priors obtained via quantiles and via the distribution function. Various matching criteria are described and discussed. Emphasis is laid on a proposal of designing priors matching the true coverage probability as well as the false coverage probabilities of contiguous alternatives with the respective Bayesian counterparts.The review is not primarily meant to be a comprehensive account on the area, but, rather, to convey the main underlying ideas and point out the relationships between matching priors and other noninformative priors, such as the Jeffreys' and the reference priors.
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