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

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.

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.

  1. The choice of the model for the problem together with the specification of the quantity of interest.
  2. An elicitation procedure for the prior.
  3. Specification of data collection aspects for the measuremant and control of bias due to the choices made for 1 and 2.
  4. Model checking procedure based on the observed data.
  5. Checking for prior-data conflict based on the observed data and how to choose a less informative prior when conflict observed.
  6. Inferences (estimation and hypothesis assessment) for quantities of interest based on a measure of evidence.