  Bayesian properties of the signed root likelihood ratio statistic are
analysed. Conditions for first-order probability matching are derived by the
examination of the Bayesian posterior and frequentist means of this statistic.
Second-order matching conditions are shown to arise from matching of the
Bayesian posterior and frequentist variances of a mean-adjusted version of the
signed root statistic. Conditions for conditional probability matching in
ancillary statistic models are derived and discussed.
