Incomplete Data methods in Statistics

Isaac Meilijson
Department of Statistics and Operations Research
Weekly office hour at 311 Scheiber: Sundays 16-17.
Phone: +972-3-640-8826.

Tel Aviv University course number: 0365-4400-01

Class Hours:

Fall Semester 2002/2003

Time: Mondays 16:00-19:00

Room: 114 Shenkar

Course Content:

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.

Course Pre-requisites: Theory of Statistics, Introduction to Stochastic Processes


  1. Likelihood, score function, Fisher information. Maximum Likelihood estimation (MLE) - its consistency and asymptotic normality. The exponential family.
  2. The incomplete data model. Complete and incomplete data. Examples: censoring and interval data, missing data, mixtures.
  3. Theoretical analysis of the incomplete data model. The EM algorithm. Dempster et al techniques.
  4. Alternatives to the EM algorithm and estimation of the asymptotic variance of the MLE under the EM algorithm.
  5. Applications of and to Reliability and censoring.
  6. Applications of and to mixture models.
  7. The Hidden Markov model (HMM). Baum et al techniques - the forward and backward construction.
  8. Implementation of the EM algorithm on HMM.
  9. Applications of EM and HMM to some Pattern Recognition problems.
  10. Applications of HMM to the detection of ``mental states'' from neuronal firing.
  11. Applications of HMM to financial problems and Insurance.
  12. 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.

Partial list of helpful references

Last update: October 16, 2002