statistical information a bayesian perspective贝叶斯的角度的统计信息.pdf

Entropy 2012, 14, 2254-2264; doi:10.3390/ OPEN ACCESS entropy ISSN 1099-4300 /journal/entropy Article Statistical Information: A Bayesian Perspective Rafael B. Stern * and Carlos A. de B. Pereira Department of Statistics, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213, USA ´ ´ ˜ ˜ Instituto de Matematica e Estatıstica, Universidade de Sao Paulo, Rua do Matao 1010, 05508-900, ˜ Sao Paulo, Brazil; E-Mail: cpereira@ime.usp.br (C.A.B.P.) * Author to whom correspondence should be addressed; E-Mail: rbstern@. Received: 15 August 2012; in revised form: 28 September 2012 / Accepted: 1 November 2012 / Published: 7 November 2012 Abstract: We explore the meaning of information about quantities of interest. Our approach is divided in two scenarios: the analysis of observations and the planning of an experiment. First, we review the Sufficiency, Conditionality and Likelihood principles and how they relate to trivial experiments. Next, we review Blackwell Sufficiency and show that sampling without replacement is Blackwell Sufficient for sampling with replacement. Finally, we unify the two scenarios presenting an extension of the relationship between Blackwell Equivalence and the Likelihood Principle. Keywords: statistical information; Blackwell sufficiency; likelihood principle 1. Introduction One of the goals of statistics is to extract information about unknown q