Lecturer	Prof. Felix Abramovich ( felix@post.tau.ac.il)
Teaching Assistant	Liad Shekel ( liad.shekel@gmail.com)
Lecture Hours	Thursday 16-18
Exercises

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Prerequisites:	Probability, Introduction to Statistics, Introduction to Computers
Course Requirements:	each student has to submit all projects required during the term.

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Topics:

1. 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
2. Bootstrap & jackknife
   • introduction to bootstrap
   • bootstrap variance and bias estimation
   • bootstrap confidence intervals
   • jackknife: introduction, variance and bias estimation
3. Computaions in multivariate linear regression
   • least squares estimators
   • QR decomposition
   • Gram-Schmidt orthogonalization
4. Numerical methods for optimization and estimation
   • maximum likelihood estimation
   • Newton-Raphson and Fisher scoring methods
   • logistic regression
   • nonlinear regression, Gauss-Newton method

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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.