Statistical Computing

(0365.2101)

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:

  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

Literature