Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2009.tde-03082009-135643
Document
Author
Full name
Rafael Bassi Stern
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2009
Supervisor
Committee
Pereira, Carlos Alberto de Braganca (President)
Cozman, Fabio Gagliardi
Wechsler, Sergio
Title in Portuguese
Diagramas de influência e teoria estatística
Keywords in Portuguese
Análise Pré-Posteriori
Diagramas de Influência
Estatística Bayesiana
Informação
Suficiência de Blackwell
Abstract in Portuguese
Title in English
Influence Diagrams and Statistical Theory
Keywords in English
Bayesian Statistics
Blackwell Sufficiency
Influence Diagrams
Information
Pre-Posterior Analysis.
Abstract in English
The main objective of this work is to analyze the controversial concept of information in Statistics. To do so, firstly the concept of information according to Basu is presented. Next, the analysis is divided in three parts: information in a data set, information in an experiment and influence diagrams. In the first two parts, we always tried to define properties an information function should satisfy in order to be in accordance to the concept of Basu. In the first part, it was studied how the likelihood principle is an equivalence class which follows from believing that trivial experiments do not bring information. Metrics which satisfy the likelihood principle were also presented and used to analyze an intuitive example. In the second part, the problem became that of determining information of a particular experiment. The relation between Blackwell's suciency, trivial experiments and classical suciency was presented. Blackwell's equivalence was also analyzed and its relationship with the Likelihood Principle was exposed. The metrics presented to evaluate the information in a data set were also adapted to do so with experiments. Finally, in the first parts a number of symmetries were shown as essencial elements of the concept of information. To gain more intuition about these elements, we tried to rewrite them using the graphic tool of influence diagrams. Therefore, definitions as sufficiency, Blackwell's sufficiency, minimal sufficiency and completeness were shown again, only using influence diagrams.