COURSE TOPICS Mathematics-Statistics 452H is an introduction
to the theory of statistical inference. Topics of study will include a
review of the interpretation of probability as an objective measure or
as a subjective measure of degree of belief; the "classical;" approach
to statistical inference including point estimation, interval estimation,
hypothesis testing and likelihood methods; the Bayes approach including
prior and posterior probabilities; the decision-theoretic approach including
utility, loss and decision functions; and, as time permits, "objective
inverse probability" methods including the fiducial and structural methods
of inference and/or resampling methods.
TEXT There is no specific text. Most of the material in the course
will be presented in lectures. Additional material for the course may be
found in the following references in the Bata Library:
Barnett, V. Comparative Statistical Inference (2nd edition)
(QA 276 B2848 1982)
Box, G.E.P. and Tiao, G.C. Bayesian Inference in Statistical Analysis
(QA 276 B677)
Chernoff, H. and Moses, L.E. Elementary Decision Theory (QA
Edwards, A.W.F. Likelihood (Q 175 E34)
Fraser, D.A.S. Inference and Linear Models (QA 276 F6583 1979)
Fraser, D.A.S. Probability and StatisticsÐTheory and Applications
(QA 273 F82)
Fraser, D.A.S. The Structure of Inference (QA 276 F67)
Freund, J.E. and Walpole, R.E. Mathematical Statistics (QA 276
Hartigan, J.A. Bayes Theory (QA 276 H392 1983)
Hacking, I. Logic of Statistical Inference (QA 276 H24)
Hogg, R.V. and Craig, A.T. Introduction to Mathematical Statistics
(QA 276 H59)
Kendall, M. and Stuart, A. The Advanced Theory of Statistics Vol
II (QA 276 K424)
Kyberg, H. The Logical Foundations of Statistical Inference
(QA 273.4 K92)
Lee, P. Bayesian Statistics: an Introduction (QA 279.5 L44 1989)
Messick, D. M. Mathematical Thinking in the Behavioral Sciences
(QA 7 M39)
Press, J. S. Bayesian Statistics: Principles, Models and Applications
(QA 279.5 P75 1989)
Raiffa, H. and Schlaifer, R. Applied Statistical Decision Theory
(QA 276 R3)
Roussas, G.G. A First Course in Mathematical Statistics (QA
Winkler, R.L. Introduction to Bayesian Inference and Decision
(QA 279.5 W55)
STUDENT BACKGROUND Students are required to have a background
in probability and statistics. The prerequisites for the course are MAST
251a and MAST 252b or MATH 355 or equivalent or permission of the instructor.
COURSE STRUCTURE There will be two one-hour meetings per week.
These meetings will be used for presentation of course material and for
discussions related to the course assignments. There will also be
a back-up one-hour meeting time to be used, if necessary, to discuss assignments.
MARKING SCHEME There will be three problem sets through the course.
Each problem set will contribute 25% of the final mark. There will be a
final three-hour examination. The final examination will contribute 25%
of the final mark.
|Vary from week to week but
are posted each week on the instructor's office door.
Discussing problems and working out solutions with other
students is a natural part of the learning process; however, students
ultimately must be able to do problems themselves. Students are
expected to produce and to write up their own final solutions individually.
Copying from other students is plagiarism. Students should note the
following university statement on plagiarism.
Plagiarism is an extremely serious academic offence and
carries penalties varying from failure in an assignment to debarment from
the University. Definitions, procedures and penalties for dealing
with plagiarism are set out in Trent Universityís Policy on Plagiarism
which is available on request from every department or college office or
from the Registrarís office.