STA422/2162 - Theory of Statistical Inference (2026)
Announcements
- Jan. 5 - Details on organizing a Recognized Study Group for the course can be found at:
https://sidneysmithcommons.artsci.utoronto.ca/recognized-study-groups/
Students may find this helpful in studying the course material.
Instructor
Professor Michael Evans
Office:Ontario Power Building, 700 University Avenue, 9th floor, Room 9110
email: mevansthree.evans@utoronto.ca
Time and Place
Three hours of lectures per week every Thursday.
First class is Thursday, January 8, 5-8pm in WB119.
Website
http://www.utstat.utoronto.ca/mikevans/sta422/sta4222026.html
Office Hours
The in-person office hours will be on Thursdays 2-4pm.
Course Description
Statistical inference is concerned with using the evidence, available from observed data,
to draw inferences about aspects of 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 methodology 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.
The following topics will be covered.
- the meaning of probability
- the evidential versus behavioristic approaches to statistical theory
- pure and frequentist likelihood theory
- decision theory - frequentist and Bayesian
- Birnbaum's theorem
- fiducial theory and close associates such as structural inference
- relative belief and the definition of statistical evidence
Textbook
There is no textbook but several references will be helpful at different points in the course.
Some material will also be drawn from particular papers whose references will be provided.
- Berger, J. (2006) Statistical Decision Theory and Bayesian Analysis. Springer.
- Casella, G. and Berger, R. (1990) Statistical Inference. Duxbury.
- Cox, D.R.(2006) Principles of Statistical Inference. Cambridge.
- Evans, M. (2015) Measuring Statistical Evidence Using Relative Belief. Chapman & Hall. Available online through the U. of Toronto Library.
- Evans, M. and Rosenthal, J. (2010) Probabilty and Statistics: The Science of Uncertainty. Available online at
book.
- Fraser, D.A.S. (1979) Inference and Linear Models. McGraw-Hill.
- Robert, C. (2001) The Bayesian Choice. Springer.
- Royall, R. (1997) Statistical Evidence: A likelihood paradigm. Chapman & Hall.
Evaluation
There will be 2 midterms held during class, each worth 25%, and a final project worth 50%.
If a midterm is missed, then there will be a make-up.
Class Notes
I will post my class notes here before each class. There will be some Exercises associated with the notes that
help to prepare for the midterms.
- Lecture I
- what are the problems that a theory of statistical reasoning is supposed to address?, evidential versus behavioristic inference, specifying the inference bases used by different approaches to the problems
- Lecture II(a)
- the meaning of probability as measuring belief, the meaning of randomness, methods of assigning probabilities, frequency assignments, de Finetti's betting interpretation of probability
- Lecture II(b)
- cautions with conditional probability
- Lecture III(a)
- the likelihood function and the likelihood ordering