Courses

STAT6841 - Statistical Inference (Winter)

Outline

Calendar Description: Bayesian and likelihood methods, large sample theory, nuisance parameters, profile, conditional and marginal likelihoods, EM algorithms and other optimization methods, estimating functions, MonteCarlo methods for exploring posterior distributions and likelihoods, data augmentation, importance samling and MCMC methods.

Intended Students: Statistics graduate students who have already taken STAT*4340 or a very similar course. **This course is not suitable for students who have not taken STAT*4340 or a very similar course.**

Objectives: The student will obtain a rigorous understanding of important concepts in classical frequentist, likelihood, and Bayesian inference. The depth of the coverage of the material will notably greater than that in STAT*4340.

Contents: This course represents a continuation of the material presented in STAT*4340. The topics covered will include the following.

1) Inferential paradigms and foundational concepts.

2) Decision theory

3) The Likelihood Principle, the MLE, asymptotic properties of the MLE.

4) Properties of the expected Fisher information.

5) Inference in the multiparameter case.

6) Higher-order theory.

7) Bayesian inference and computational methods.

8) The EM algorithm and the MM principle.

Representative Texts: 

1. 'In All Likelihood: Statistical Modelling and Inference Using Likelihood', Pawitan, Oxford Science.

2. 'Essentials of Statistical Inference', Young and Smith, Cambridge.

3. ‘Principles of Statistical Inference’, Cox, Cambridge

4. 'Theoretical Statistics', Cox and Hinkley, Chapman & Hall / CRC.

5. 'Statistical Inference', Garthwaite, Jollife and Jones, 2nd Edition, Oxford Science.

6. 'Comparative Statistical Inference', Barnett, 3rd Edition, John Wiley & Sons.

7. 'Statistical Inference', Casella and Berger, 2nd Edition, Nelson Canada.

8. 'The Bayesian Choice', Robert, 2nd Edition, Springer.

Evaluation: Assignments, midterms and a final exam.