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Statistical Information: A Bayesian Perspective
Department of Statistics, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213, USA
Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-900, São Paulo, Brazil
* Author to whom correspondence should be addressed.
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
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Stern, R.B.; Pereira, C.A.B. Statistical Information: A Bayesian Perspective. Entropy 2012, 14, 2254-2264.
Stern RB, Pereira CAB. Statistical Information: A Bayesian Perspective. Entropy. 2012; 14(11):2254-2264.
Stern, Rafael B.; Pereira, Carlos A. de B. 2012. "Statistical Information: A Bayesian Perspective." Entropy 14, no. 11: 2254-2264.