1. Computational statistics, course introduction Course contents  Monte Carlo Methods  Random number generation  Simulation methodology  Bootstrap  Markov Chain Monte Carlo  Sensitivity analysis  Screening methods  Variance-based methods  Numerical linear algebra  Systems of linear equations  Optimization methods

2. Computational statistics, course introduction Random number generation  Generating pseudo random numbers with a uniform distribution on the unit interval (0,1)  Generating random numbers with a given cumulative distribution function F(x)

3. Computational statistics, course introduction Simulation methodology  Crude Monte Carlo simulations  Antithetic sampling  Simulations using quasi random numbers

4. Computational statistics, course introduction The Bootstrap  Substituting un unknown distribution function for an empirical distribution function  Resampling techniques  Bootstrap intervals

5. Computational statistics, course introduction Markov Chain Monte Carlo  Metropolis-Hastings algorithm  Gibbs sampling

6. Computational statistics, course introduction Sensitivity analysis – screening methods  One-at-time designs  Fractional factorial designs

7. Computational statistics, course introduction Sensitivity analysis – variance-based methods  Measures of variation  Designs of computer experiments

8. Computational statistics, course introduction Systems of linear equations  Choleski decomposition  QR decomposition  Singular-value decomposition

9. Computational statistics, course introduction Systems of linear equations  Choleski decomposition  QR decomposition  Singular-value decomposition

10. Computational statistics, course introduction Optimization  Steepest decent methods