STA422F-STA2162F - Theory of Statistical Inference


There will be a class held on November 11 12-1 in our usual room. This is to make up for the class we missed due to Thanksgiving.

Project is due Dec. 10.

Course website:

Course Schedule

M12, R12-2 in SS 2111 with office hours immediately after class in SS5027D.

Course Description

Statistical inference is concerned with using the evidence, available from observed data, to draw inferences about an unknown probability measure. A variety of theoretical approaches have been developed to address this problem and these can lead to quite different inferences. A natural question is then concerned with how one determines and validates appropriate statistical m ethodology in a given problem. The course considers this larger statistical question. This involves a discussion of topics such as model specification and checking, the likelihood function and likelihood inferences, repeated sampling criteria, loss (utility) functions and optimality, prior specification and checking, Bayesian inferences, principles and axioms, etc. The overall goal of the course is to leave students with an understanding of the different approaches to the theory of statistical inference while developing a critical point-of-view.


Necessary background: mathematics-based course on the theory of statistics (e.g., at the level of STA352Y).


There will be three assignments worth 60% and a project worth 40%.


I will use a number of references (papers and books) throughout the course and will cite these as relevent.

Some Possible Projects

Note that the project must be approved and it need not be taken from this list, as these are only suggestions. As I think of them, I will add more. You need to discuss with me exactly how these are to be used.

  1. Cox, R.T. (1961) Algebra of Probable Inference.
  2. Jaynes, E.T. (2003) Probability Theory, The Logic of Science. (selected chapters)
  3. Hacking, I. (2001) An Introduction to Probability and Inductive Logic.
  4. Lindley, D.V. (2006) Understanding Uncertainty.
  5. Walley, P. (1991) Statistical Reasoning with Imprecise Probabilities (selected chapters, e.g. upper and lower previsions and properties)
  6. Inference based on minimum description length as found, for example, in Wallace, C.S. (2005) Statistical and Inductive Inference by Minimum Message Length.
  7. Papers by D.A. Freedman on Dutch book, Bayes method for bookies, etc.
  8. Fisher's fiducial inference.
  9. Fraser's structural inference, e.g., Fraser (1979) Inference and Linear Models.
  10. Ramsey, F. (1926) Truth and Probability (see Studies in Subjective Probability, Kyburg and Smokler(1980)).
  11. Li, M., and Vitanyi, P. (1993) An Introduction to Kolmogorov Complexity (Chapters 1 and 2 with emphasis on the definition of a random sequence).
  12. Papers by P. Dawid on Prequential Inference (e.g., NIPS 2008 tutorial).
  13. Causal inference, e.g., Morgan and Winship (2007) Counterfactuals and Causal Inference.
  14. Fraser, D.A.S. (2004) Ancillaries and conditional inference. Statistical Science 19, 333-369.