Syllabus: Topics in Probability

Description: A graduate level course in probability with an emphasis on how the theory is applied in statistics, for example to construct statistical models (the important roles of independence, multivariate random variables, and stochastic processes), and to invert them (illustrative analysis of statistical estimators; Monte Carlo applications). We will cover a range of topics mainly from a user's point of view, starting from language and foundation, and then focussing on statistics-relevant topics selected from: convergence theorems, characteristic functions, conditioning, Poisson processes, Markov chains.

Prerequisite: Co-requisite: STAT 460 / 560 or equivalent. Ideally, one upper division undergraduate course in probability, and one in analysis (if you are not sure, come talk to me after one or two lectures).

Textbook:

G.R. Grimmett and D.R. Stirzaker, Probability and Random Processes, 3rd edition, Oxford, (2001). There is a solutions manual to this text: G.R. Grimmett and D.R. Stirzaker, One Thousand Exercises in Probability, Oxford, (2001).

Complement: A. Gut, Probability: A graduate course, 2nd edition. Springer. Note: the pdf of this textbook is freely available via UBC Library.

Other references:

Evaluation: See slides from the first lecture.

Office hours, piazza, etc: See Contact.