TY - UNPB
T1 - On the uniqueness of probability matching priors
AU - Staicu, A-M
AU - Reid, Nancy
N1 - Sponsorship: NSERC
PY - 2007
Y1 - 2007
N2 - Probability matching priors are priors for which Bayesian and frequentist inference,
in the form of posterior quantiles, or confidence intervals, agree to some order of approximation. These priors are constructed by solving a first order partial differential equation, that may be difficult to solve. However, Peers (1965) and Tibshirani (1989) showed that under parameter orthogonality a family of matching priors can be obtained. The present work shows that, when used in a third order approximation to the
posterior marginal density, the Peers-Tibshirani class of matching priors is essentially unique.
AB - Probability matching priors are priors for which Bayesian and frequentist inference,
in the form of posterior quantiles, or confidence intervals, agree to some order of approximation. These priors are constructed by solving a first order partial differential equation, that may be difficult to solve. However, Peers (1965) and Tibshirani (1989) showed that under parameter orthogonality a family of matching priors can be obtained. The present work shows that, when used in a third order approximation to the
posterior marginal density, the Peers-Tibshirani class of matching priors is essentially unique.
KW - orthogonal parameters
KW - approximate Bayesian inference
KW - Laplace approximation
KW - tail probability approximation
M3 - Working paper
BT - On the uniqueness of probability matching priors
ER -