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On the construction of Bayes–confidence regions
Author(s) -
Sweeting T. J.
Publication year - 1999
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00206
Subject(s) - bayes' theorem , confidence interval , mathematics , statistics , bayes' rule , posterior probability , scalar (mathematics) , bayes factor , bayesian probability , geometry
We obtain approximate Bayes–confidence intervals for a scalar parameter based on directed likelihood. The posterior probabilities of these intervals agree with their unconditional coverage probabilities to fourth order, and with their conditional coverage probabilities to third order. These intervals are constructed for arbitrary smooth prior distributions. A key feature of the construction is that log‐likelihood derivatives beyond second order are not required, unlike the asymptotic expansions of Severini.