Courses and Textbooks
Sample textbooks are given for prerequisite courses for graduate study in statistics. In some cases, these books were used in the past, and may not be used at present.
Assessing course equivalency in statistics and probability is not an easy task. For instance, a course entitled "Probability" could be taught at many mathematical levels, perhaps requiring only high school algebra, or several calculus courses or non-measure-theoretic real analysis or measure theory. The following information will help you assess the courses you have taken, and thus help us advise you in course selection at UBC.
We expect that all entering graduate students have had the first three courses.
Probability
Textbook: R.L. Scheaffer. Introduction to Probability and Its Applications, 2nd edition.
This is UBC course MATH/STAT 302.
Three semesters of calculus (up to and including multiple integration) are definitely required, but real analysis skills, like intricate epsilon-delta proofs, aren't required. Topics: axioms, combinatorics probability, random variables, discrete and continuous distributions, expectations, variances, continuous distributions and bivariate distributions.
Regression
Textbook: S. Weisberg: Applied Linear Regression, Wiley, latest edition.
This is UBC course STAT 305.
Statistical inference
Textbook: J. Rice: Mathematical Statistics and Data Analysis, Wadsworth & Brooks/Cole, 1988.
This is UBC course STAT 305. Topics: calculating maximum likelihood estimates and their asymptotic distributions, deriving generalized likelihood ratio tests, calculating Bayes estimates; some exact normal theory inference, like the t distribution, the chi-squared distribution and how to count degrees of freedom.
Some students entering the MSc program will have had some of these courses given below. If you haven't had them before entering the program, you will be required to take them during the program. Students entering the PhD program should have had all or most of these courses. These courses are crucial to graduate study in statistics.
Design of experiments and analysis of variance
Textbook: D. Montgomery: Design and Analysis of Experiments, Wiley, latest edition.
This is UBC course STAT 404.
Mathematical statistics
Textbook: G. Casella and R. L. Berger. Statistical Inference, Wadsworth & Brooks/Cole, 2001.
Older text: P. J. Bickel and K. A. Doksum. Mathematical Statistics. Holden-Day, Inc, 1977.
This is a year long sequence of courses at UBC: STAT 460 (=STAT 560) and STAT 461 (=STAT 561). The topics covered are similar to those covered in the text by Rice (mentioned above), but the level is much higher.
Advanced probability and stochastic processes
Textbook: G.R. Grimmett and D.R. Stirzaker: Probability and Random Processes, Second Edition, Oxford, 1992.
This is a year long sequence of courses at UBC: MATH 418 and MATH 419.
