| Lecturer | Prof. Felix Abramovich (felix@post.tau.ac.il) | ||
| Teaching Assistant | Yelena Stuklin (grei@mscc.huji.ac.il) | ||
| Lecture Hours | Monday 12-14, Orenshtein 102 | ||
| Exercises | Thursday 16-18, Schreiber 8 |
| Prerequisites: | Probability, Introduction to Statistics, Introduction to Computers |
| Course Requirements: | each student has to submit all projects required during the term. |
Topics:
- Monte Carlo Methods
- basic principles
- random number generator
- simulating random numbers from various distributions
- inverse CDF
- acceptance/rejection
- normal distribution
- multivariate distributions
- Monte Carlo estimation
- basic principles
- variance reduction
- Bootstrap & jackknife
- introduction to bootstrap
- bootstrap variance and bias estimation
- bootstrap confidence intervals
- jackknife: introduction, variance and bias estimation
- Computaions in multivariate linear regression
- least squares estimators
- QR decomposition
- Gram-Schmidt orthogonalization
- Numerical methods for optimization and estimation
- maximum likelihood estimation
- Newton-Raphson and Fisher scoring methods
- logistic regression
- nonlinear regression, Gauss-Newton method
Literature
- Gentle, J.E. Random Number Generation and Monte Carlo Methods.
- Gentle, J.E. Elements of Computational Statistics.
- Lange, K. Numerical Analysis for Statisticians.
- Rizzo, M.L. Statistical Computing with R.