STAC58H - Statistical Inference
The course surveys the various approaches that have been considered for the development of a theory of statistical reasoning. These include likelihood methods, Bayesian methods and frequentism. These are compared with respect to their strengths and weaknesses. To use statistics successfully requires a clear understanding of the meaning of various concepts such as likelihood, confidence, p-value, belief, etc. This is the purpose of the course.
Timetable
MO 11:00-12:00 IC 220
WE 10:00-12:00 IC 220
Announcements
Office Hours During Exam Period
Wednesday April 17 and April 24 12-3pm. Some Previous Years Final Exams
The content of the course differs slightly from year to year.
Evaluation
A midterm worth 40% and a final worth 60%.
References
The following texts will be used in the course. - Probability and Statistics; The Science of Uncertainty by M. Evans and J. Rosenthal - this is the text used for STAB52F/B57S and we will be focusing on chapters 6, 7, 8 and 9 but only some this will be review. The book is available for download on my website.`
- Measuring Statistical Evidence Using Relative Belief by M. Evans - this book gives a general discussion of the different approaches to inference. The book is available electronically from the University of Toronto Library.
Website
The course website is http://www.utstat.utoronto.ca/mikevans/stac58/stac58.html Notes and Exercises
I will post my (rough) lecture notes here and will put up various exercises that a student is to work at with the solutions appearing the following week. The notes are not a complete rendering of what I will discuss in class and students are expected to attend the lectures.
- Basics - read Chapter 5 E&R
Exercises 1 (total on question 1 should have been 215 not 205 but conditionals stay the same ) (solutions) and E&R 5.1.10, 5.2.17, 5.3.15, 5.3.18 (solutions).
- Probability - pages 4-5 modified Jan. 16 to fix a problem. Exercise - for the Three Prisoner problem show that P(A|C) = p/(1+p) in the randomized case. (solution)
- Pure Likelihood Theory - read 6.1-6.3 in E&R.
Exercises 3 (solutions) and E&R 6.1.8, 6.1.19, 6.1.20, 6.2.20, 6.3.25, 6.3.26, 6.3.27 (solutions) - Sufficiency (Exercises and Solutions)
- Frequentist Theories
Read Sections 8.1, 8.2. Exercises 8.1.8, 8.1.12, 8.1.16, 8.1.22, 8.2.8, 8.2.13, 8.2.14, 8.2.16, 8.2.20, 8.2.21 (the solution to 8.2.21 uses the approximate distribution theory of Section 8.2.5 and the exact solution is also available in this case). (Solutions)
Minimaxity and Admissibility Read Section 8.4, Exercises 8.4.8,8.4.9, 8.4.10. (Solutions)
- Bayesian Theory Read Sections 7.1, 7.2, 7.3, 7.4 and 8.3, Exercises 7.1.17, 7.1.18, 7.2.17, 7.2.18, 7.2.21, 7..2.23, 7.2.28, 7.2.32, 7.2.34, 7.3.11, 7.3.15, 7.4.3, 7.4.16, 7.4.17 (Solutions)