Exponential Models: Approximations for Probabilities
D. A. S. Fraser, Ali Asghar Naderi, Kexin Ji, Wei Lin, Jie Susie Su · Journal of the Iranian Statistical Society · 2011
Welch & Peers (1963) used a root-information prior to ob- tain posterior probabilities for a scalar parameter exponential model and showed that these Bayes probabilities had the confidence property to second order asymptotically. An important undercurrent of this in- dicates that the constant information reparameterization provides loca- tion model structure, for which the confidence property was and is well known. This paper examines the role of the scalar-parameter exponen- tial model for obtaining approximate probabilities and approximate con- fidence levels, and then addresses the extension for the vector-parameter exponential model.