Statistical Computing

  1. Simulation and Resampling Methods
    1. Random Number Generation
      1. Pseudo-Random Number Generators
        1. Linear Congruential Generators
          1. Mersenne Twister
            1. Cryptographically Secure Generators
              1. Seed Setting and Reproducibility
                1. Testing Random Number Quality
                2. Uniform Random Variables
                  1. Properties of Uniform Distribution
                    1. Generating Uniform Variates
                    2. Non-Uniform Random Variables
                      1. Inverse Transform Method
                        1. Acceptance-Rejection Sampling
                          1. Composition Methods
                            1. Ratio-of-Uniforms Method
                            2. Specific Distributions
                              1. Normal Distribution
                                1. Box-Muller Transform
                                  1. Polar Method
                                    1. Ziggurat Algorithm
                                    2. Exponential Distribution
                                      1. Gamma Distribution
                                        1. Beta Distribution
                                          1. Discrete Distributions
                                            1. Bernoulli and Binomial
                                              1. Poisson Distribution
                                                1. Multinomial Distribution
                                            2. Monte Carlo Methods
                                              1. Basic Monte Carlo Simulation
                                                1. Monte Carlo Integration
                                                  1. Estimating Probabilities
                                                    1. Confidence Intervals for Estimates
                                                    2. Variance Reduction Techniques
                                                      1. Antithetic Variables
                                                        1. Control Variates
                                                          1. Importance Sampling
                                                            1. Stratified Sampling
                                                            2. Applications in Statistics
                                                              1. Estimating Sampling Distributions
                                                                1. Power Analysis
                                                                  1. Sensitivity Analysis
                                                                    1. Model Validation
                                                                  2. Bootstrap Methods
                                                                    1. Non-parametric Bootstrap
                                                                      1. Bootstrap Sampling
                                                                        1. Bootstrap Distribution
                                                                          1. Bootstrap Bias Estimation
                                                                            1. Bootstrap Variance Estimation
                                                                            2. Bootstrap Confidence Intervals
                                                                              1. Percentile Method
                                                                                1. Bias-Corrected and Accelerated (BCa)
                                                                                  1. Bootstrap-t Method
                                                                                  2. Parametric Bootstrap
                                                                                    1. Model-Based Resampling
                                                                                      1. Residual Bootstrap
                                                                                      2. Bootstrap Applications
                                                                                        1. Regression Diagnostics
                                                                                          1. Model Selection
                                                                                            1. Hypothesis Testing
                                                                                          2. Other Resampling Methods
                                                                                            1. Jackknife Methods
                                                                                              1. Leave-One-Out Jackknife
                                                                                                1. Delete-d Jackknife
                                                                                                  1. Jackknife Bias Correction
                                                                                                  2. Permutation Tests
                                                                                                    1. Exact Permutation Tests
                                                                                                      1. Approximate Permutation Tests
                                                                                                        1. Two-Sample Tests
                                                                                                          1. Correlation Tests
                                                                                                          2. Cross-Validation
                                                                                                            1. k-Fold Cross-Validation
                                                                                                              1. Leave-One-Out Cross-Validation
                                                                                                                1. Stratified Cross-Validation
                                                                                                                  1. Time Series Cross-Validation
                                                                                                                    1. Model Assessment and Selection

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                                                                                                                4. Numerical Methods for Statistics

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                                                                                                                6. Advanced Computational Methods