STATISTICAL COMPUTING

Topics:

1. Monte Carlo Methods -- 3 weeks
   • Basic principles
   • Simulating random numbers from various distributions
     • The inverse CDF and its use
     • The accept/reject method
     • The normal distribution and its relatives
   • Integration and estimation by Monte Carlo and other rules
     • Basic principles
     • Trapezoid rule and Simpson's rule
     • Variance reduction
     • Importance sampling
     • Stratified sampling
2. Computations in Multivariate Linear Regression -- 3 weeks
   • Least squares estimators
   • The QR decomposition
   • Gram-Schmidt orthogonalization
   • The Cholesky factorization
3. Bootstrap and Cross-validation -- 3 weeks
   • Introduction to bootstrap
   • Bootstrap variance and bias estimation
   • Bootstrap confidence intervals
   • Better bootstrap confidence intervals (if time permits)
   • Cross-validation
4. Numerical Methods for Optimization and Estimation -- 3 weeks
   • Maximum likelihood estimation
   • Newton-Raphson and Fisher scoring methods
   • Application to logistic regression
   • The EM-algorithm
   • Nonlinear regression and the Gauss-Newton method