Abstract
A prior for statistical inference can be one of three basic types: a mathematical prior originally proposed in Bayes [Philos. Trans. R. Soc. Lond. 53 (1763) 370–418; 54 (1764) 269–325], a subjective prior presenting an opinion, or a truly objective prior based on an identified frequency reference. In this note we consider a method for deriving a mathematical prior based on approximate location models. This produces a mathematical posterior, and any practical interpretation of such a posterior is in terms of exact or approximate confidence under the postulated model. We describe how a proposed prior can be simply checked for consistency with confidence methods, using expansions about the maximum likelihood estimator.
Citation
D. A. S. Fraser. N. Reid. "On default priors and approximate location models." Braz. J. Probab. Stat. 25 (3) 353 - 361, November 2011. https://doi.org/10.1214/11-BJPS147
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