# STA422F-STA2162F - Theory of Statistical Inference

### Announcements

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: http://www.utstat.utoronto.ca/mikevans/sta442-2162.html

### 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.
### Prerequisites

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

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

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.

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