+972-3-640-8826.

Fall Semester 2002/2003

Time: Mondays 16:00-19:00

Room: 114 Shenkar

The goals of this course are:

To provide graduate students in Statistics and related fields with an introduction to estimation under Incomplete Data, the EM algorithm, Hidden Markov models and Probabilistic Expert Systems.

- Likelihood, score function, Fisher information. Maximum Likelihood estimation (MLE) - its consistency and asymptotic normality. The exponential family.
- The incomplete data model. Complete and incomplete data. Examples: censoring and interval data, missing data, mixtures.
- Theoretical analysis of the incomplete data model. The EM algorithm. Dempster et al techniques.
- Alternatives to the EM algorithm and estimation of the asymptotic variance of the MLE under the EM algorithm.
- Applications of and to Reliability and censoring.
- Applications of and to mixture models.
- The Hidden Markov model (HMM). Baum et al techniques - the forward and backward construction.
- Implementation of the EM algorithm on HMM.
- Applications of EM and HMM to some Pattern Recognition problems.
- Applications of HMM to the detection of ``mental states'' from neuronal firing.
- Applications of HMM to financial problems and Insurance.
- An introduction to Probabilistic Expert Systems (or Influence Diagrams), as an extension of HMM to finite Markov fields. The ideas of Lauritzen, Spiegelhalter, Dawid and others. Analysis of the ASIA standard example.

- Baum, L. E., Petri, T., Soules, G. and Weiss, N (1970). A maximization technique occuring in the statistical analysis of probabilistic functions of Markov chains. Ann. Math. Statist., 41, 164-171.
- Dempster, A. P., Laird. N. M. and Rubin, D. B. (1977) Maximum Likelihood from Incomplete Data via the EM algorithm (with Discussion). JRSS(B), 39, 1-38.
- Lauritzen, S. L. and Spiegelhalter, D. J. (1988). Local computations with probabilities on graphical structures and their application to expert systems (with discussion). JRSS(B), 50, 157-224.
- Little, R. J. A. and Rubin, D. B. (1987). Statistical Analysis with Missing Data. New York: John Wiley.
- Meilijson, I. (1989). A Fast Improvement to the EM algorithm on its Own Terms. JRSS(B), 51, 127-138.