RELATIONSHIPS BETWEEN POST-DATA ACCURACY MEASURES

CONSTANTINOS GOUTIS^{1} AND GEORGE CASELLA^{2}

1Department of Statistical Science, University College London, Gower St., London, WC1E 6BT, U.K. and

Departamento de Estadistica y Econometria, Universidad Carlos III de Madrid,

Calle Madrid 126, 28903 Getafe, Madrid, Spain

2Biometrics Unit, Cornell University, 434 Warren Hall, Ithaca, NY 14853, U.S.A.

(Received March 27, 1995; revised April 3, 1996)

Abstract. In the usual frequentist formulation of testing and interval estimation there is a strong relationship between α-level tests and 1 − α confidence intervals. Such strong relationships do not always persist for post-data, or Bayesian, measures of accuracy of these procedures. We explore the relationship between post-data measures of accuracy of both tests and interval estimates, measures that are derived under a decision-theoretic structure. We find that, in general, there are strong post-data relationships in the one-sided case, and some relationships in the two-sided case.

Key words and phrases: Posterior probability, coverage probability, null hypothesis, Bayes, p-value.