Bayesian Statistics in Actuarial Science

1. Front Matter

   Pages i-xiii

   PDF

2. Introduction

   • Stuart A. Klugman

   Pages 1-3

3. Bayesian Statistical Analysis

   • Stuart A. Klugman

   Pages 5-16

4. Computational Aspects of Bayesian Analysis

   • Stuart A. Klugman

   Pages 17-35

5. Prediction with Parameter Uncertainty

   • Stuart A. Klugman

   Pages 37-55

6. The Credibility Problem

   • Stuart A. Klugman

   Pages 57-64

7. The Hierarchical Bayesian Approach

   • Stuart A. Klugman

   Pages 65-79

8. The Hierarchical Normal Linear Model

   • Stuart A. Klugman

   Pages 81-113

9. Examples

   • Stuart A. Klugman

   Pages 115-149

10. Modifications to the Hierarchical Normal Linear Model

    • Stuart A. Klugman

    Pages 151-157

11. Back Matter

    Pages 159-237

    PDF

The debate between the proponents of "classical" and "Bayesian" statistica} methods continues unabated. It is not the purpose of the text to resolve those issues but rather to demonstrate that within the realm of actuarial science there are a number of problems that are particularly suited for Bayesian analysis. This has been apparent to actuaries for a long time, but the lack of adequate computing power and appropriate algorithms had led to the use of various approximations. The two greatest advantages to the actuary of the Bayesian approach are that the method is independent of the model and that interval estimates are as easy to obtain as point estimates. The former attribute means that once one learns how to analyze one problem, the solution to similar, but more complex, problems will be no more difficult. The second one takes on added significance as the actuary of today is expected to provide evidence concerning the quality of any estimates. While the examples are all actuarial in nature, the methods discussed are applicable to any structured estimation problem. In particular, statisticians will recognize that the basic credibility problem has the same setting as the random effects model from analysis of variance.

• actuarial science
• algorithm
• bayesian statistics
• calculus
• rating
• statistical analysis
• statistics

• Drake University, USA

  Stuart A. Klugman

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