Bayesian Statistics in Actuarial Science : with Emphasis on Credibility

1. Introduction -- 2. Bayesian Statistical Analysis -- 3. Computational Aspects of Bayesian Analysis -- 4. Prediction with Parameter Uncertainty -- 5. The Credibility Problem -- 6. The Hierarchical Bayesian Approach -- 7. The Hierarchical Normal Linear Model -- 8. Examples -- 9. Modifications to the Hierarchical Normal Linear Model -- Appendix. Algorithms, Programs, and Data Sets -- A. The Simplex Method of Function Maximization -- B. Adaptive Gaussian Integration -- C. Gauss-Hermite Integration -- D. Polar Method for Generating Normal Deviates -- E. GAUSS Programs -- 1. Simplex Maximization -- 2. Adaptive Gaussian Integration -- 3. Gauss-Hermite Integration -- 4. Monte Carlo Integration -- 5. Tierney-Kadane Integration -- F. Data Sets -- 1. Data Set 1 -- 2. Data Sets 2–4.