Εμπειρική Μπεϋζιανή εκτίμηση με εφαρμογές στην ασφαλιστική επιστήμη και τον αναλογισμό
Empirical Bayes estimation with applications in actuarial science
SubjectΚατανομή (Οικονομική θεωρία)
In this thesis, we focus on the study and presentation of the empirical Bayes estimation methods, which borrows elements, both form classical and Bayesian statistics. These methods allow the modelling of complicated problems using Bayesian techniques, but employ classical statistics methods for obtaining parameter estimates. The main difference between classical and Bayesian statistics, is the definition of the statistical model's unknown parameters. In the first case, the parameters are considered to be unknown fixed quantities, whereas in the second one, they are random variables. It is that difference that has led to the dispute between classical and Bayesian supporting statisticians. On one hand, the classical statistics supporters, do not agree with the lack of objectivity in the results obtain using Bayesian methods and on the other hand, the Bayesian statistics supporters believe that if there is any further information regarding the parameter beforehand, it must be utilized. Initially, the Bayes approach is presented, which makes use of the same basic methodology and hypotheses as the empirical Bayes approach. Then the parametric and non-parametric empirical Bayes is also presented, ending with the credibility theory and its connection with the Bayes and empirical Bayes approach.