Deciding with Judgment

 

Simone Manganelli

European Central Bank

 

Abstract:

Non sample information is hidden in frequentist statistics in the choice of the hypothesis to be tested and of the confidence level. Explicit treatment of these elements provides the connection between Bayesian and frequentist statistics. A frequentist decision maker starts from a judgmental decision and moves to the closest boundary of the confidence interval of the first order conditions, for a given loss function. This statistical decision rule does not perform worse than the judgmental decision with a probability equal to the confidence level. For any given prior, there is a mapping from the sample realization to the confidence level which makes Bayesian and frequentist decision rules equivalent. Frequentist decision rules can also be interpreted as decisions under ambiguity.

 

 

 

 

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Emanuela Rosazza Gianin
Dipartimento di Statistica e Metodi Quantitativi
Università di Milano-Bicocca
Edificio U7 – 4° Piano
Via Bicocca degli Arcimboldi, 8
20126 Milano

Tel. 02 64483208
Fax. 02 64483105
e-mail: emanuela.rosazza1@unimib.it

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