A Course in Computational Probability and Statistics

1. Randomness. - 1. 1 Fundamentals. - 1. 2 Random Number Generation. - Appendix 1: Figures. - 2. Simulation. - 2. 1 Simple Monte Carlo. - 2. 2 Assignments. - 2. 3 Randomness and Monte Carlo. - 2. 4 Improved Monte Carlo. - 2. 5 Quadrature. - 2. 6 Conclusions. - 3. Limit Theorems. - 3. 1 Limits of Convolutions. - 3. 2 An Insurance Model. - 3. 3 Approximation. - Appendix 3: Figures. - 4. Stochastic Processes. - 4. 1 General Properties. - 4. 2 An Investment Example. - 4. 3 Stationary Stochastic Processes. - 4. 4 Markov Chains. - Appendix 4: Figures. - 5. Particular Stochastic Processes. - 5. 1 A Growth Model. - 5. 2 The Random Phase Model. - 5. 3 Renewal Processes. - Appendix 5: Figures. - 6. Decision Problems. - 6. 1 Generalities. - 6. 2 A Stochastic Approximation Problem. - 6. 3 An Insurance Game. - 6. 4 Design of Experiments. - 6. 5 A Search Problem. - Appendix 6: Figures. - 7. A Computational Approach to Statistics. - 7. 1 Statistical Computing. - 7. 2 Analysis of Variance. - 7. 3 Non-Standard Situations. - 7. 4 Bayesian Estimation. - Appendix 7: Figures. - 8. Time-Series Analysis. - 8. 1 Estimation of the Spectral Density. - 8. 2 The Fast Fourier Transform. - 8. 3 Regression Analysis of Time Series. - 8. 4 Signal Detection. - Appendix 8: Figures. - References. Language: English