Title of article :
An algebraic theory for statistical information based on the theory of hints Original Research Article
Author/Authors :
Jürg Kohlas، نويسنده , , Paul-André Monney، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2008
Pages :
21
From page :
378
To page :
398
Abstract :
Statistical problems were at the origin of the mathematical theory of evidence, or Dempster–Shafer theory. It was also one of the major concerns of Philippe Smets, starting with his PhD dissertation. This subject is reconsidered here, starting with functional models, describing how data is generated in statistical experiments. Inference is based on these models, using probabilistic assumption-based reasoning. It results in posterior belief functions on the unknown parameters. Formally, the information used in the process of inference can be represented by hints. Basic operations on hints are combination, corresponding to Dempster’s rule, and focussing. This leads to an algebra of hints. Applied to functional models, this introduces an algebraic flavor into statistical inference. It emphasizes the view that in statistical inference different pieces of information have to be combined and then focussed onto the question of interest. This theory covers Bayesian and Fisher type inference as two extreme cases of a more general theory of inference.
Keywords :
Statistical inference , Belief functions , Probabilistic assumption-based reasoning , Bayesian analysis , Fiducial probabilities , Functional models , Hints
Journal title :
International Journal of Approximate Reasoning
Serial Year :
2008
Journal title :
International Journal of Approximate Reasoning
Record number :
1182497
Link To Document :
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