Monte Carlo Methods in Statistics
Objectives and Content
Topics that are discussed are:
- Random number generation for various distributions.
- Monte Carlo estimation of higher dimensional integrals including variance reduction techniques such as importance sampling, antithetic sampling and Raolackwellization.
- Methods for finding maximum likelihood estimators such as Quasi-Newton methods, simulated annealing and the EM algorithm.
- Elements of Bayesian theory and Markov Chain theory on a general state space.
- The Metropolis-Hastings as well as the Gibbs sampling algorithm to calculate Bayesian estimators.
The material covered is mainly from the book Monte Carlo Statistical Methods by Christian P. Robert og George Casella. 2.ed. Springer-Verlag, 2004.
The objective of the course is to enable students to solve non-trivial problems in computational statistics.
Recommended Previous Knowledge
The course is rather advanced, and the prerequisites should be at least corresponding to Stat 110, Stat 111 and one of the statistics courses at the 200 level. Stat 220 would be an advantage. Less background will make the course very demanding.
Forms of Assessment
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.