STA4522 - The Measurement of Statistical Evidence (2020)
Instructor
Professor Michael Evans
Office: ?
email: mevans@utstat.utoronto.ca
Website
The course will be run from this webpage:
http://www.utstat.utoronto.ca/mikevans/sta4522/STA4522.html
Course Description
The concept of statistical evidence is central to the field of statistics. In spite of many references
to “the evidence” in statistical applications, it is fair to say that there is no definition of this that
achieves broad support in the sense of serving as the core of a theory of statistics. The course
will examine the various attempts made to measure evidence in the statistical literature and
why these are not entirely satisfactory. A proposal to base the theory of statistical inference on
a particular measure, the relative belief ratio, is discussed and how this fits into a general
theory of statistical reasoning.
Announcements
- I will list some possible projects here although you are also free to pick something else. Consult with me, however, before making a final selection.
The idea is to see how far you can get in implementing at least some aspects of the approach to statistical reasoning being presented in the course in such a context.
I will continue to add to this list as the course progresses.
- One of Cox's Challenge Problems as listed in Fraser, Reid and Lin (2018) When should modes of inference disagree? Some simple but challenging examples.
Ann. Applied Stat., 12, 2, 750-770. Cox created a list of 8 problems that pose challenges for various approaches to inference. The problems are listed and discussed
in this paper and you could pick one of these.
- Estimate the mean (or variance) when sampling from a suitably conditioned normal distrbution with unkown mean and variance when the measurements are always positive.
- Inferences for a proportion when the proportion is constrained to a subinterval of [0,1].
- Bias calculations, model checking and checking for prior-data conflict
for negative-binomial.
- BFF 6.5 -- Virtual Workshop on Bayesian, Fiducial, and Frequentist Statistical Inference, Friday Feb. 4
Lecture Schedule
The online (synchronous) lectures start Thursday, Jan. 14, 10am-1pm and are once a week for 6 weeks.
I will make my slides available here before class so you can follow along. Hopefully there will be lots of discussion
concerning the content. A Zoom link to the class will be posted on the course Quercus page
just before class each week.
- Lecture 1
Read Chapter 1 in the book.
- Lecture 2
Read 2.1, 2.2, 2.3.2, 2.3.3, 2.3.5, 2.3.6, 2.4 in the book.
- Lecture 3
Read Chapter 3. This material will be covered over the next 2 weeks.
- Lecture 4
Read Chapter 4. This material will be covered over the next 2 weeks.
- Lecture 5
- Lecture 6
Assignment
Office hours
Online immediately after class.
Text
Evans, M. (2015) Measuring Statistical Evidence Using Relative Belief.
Monographs on Statistics and Applied Probability 144, CRC Press, Taylor & Francis Group
The book is available electronically through the University of Toronto library.
Evaluation
Evaluation will be based on a single project to be handed in shortly after the course lectures are finished.
The project involves applying the evidential approach to a statistical problem of the student's choice
(in consultaion with the instructor). More details on these steps will be provided during the course but the
following provides a rough outline of what a completed project comprises.
- The choice of the model for the problem together with the specification of the quantity of interest.
- An elicitation procedure for the prior.
- Specification of data collection aspects for the measuremant and control of
bias due to the choices made for 1 and 2.
- Model checking procedure based on the observed data.
- Checking for prior-data conflict based on the observed data and how to choose a less informative prior when conflict observed.
- Inferences (estimation and hypothesis assessment) for quantities of interest based on a measure of evidence.