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.