Probability matching priors are a standard tool used to ensure that Bayes credible sets have the correct unconditional frequentist interpretation as confidence regions up to higher-order magnitudes of error.

We extend the analysis to ancillary statistic models, where the correct inference to be performed is a conditional one. Our results suggest that the method developed by DiCiccio and Young (2010) based on Barndorff-Nielsen's (1986) adjustment to the signed root likelihood ratio statistic is particularly useful in identifying priors which ensure higher-order matching. In some transformation models, the matching is exact in the sense that, if we choose a prior identified by our matching method, then the Bayesian limits have exactly the correct conditional frequentist interpretation. Comparisons are also made to the unconditional matching methods and priors of Datta and Mukerjee (2004).