Stat 547C : Topics in Probability

General

• Instructor: Alexandre Bouchard
• Time and place
• Don't hesistate to contact me if you have questions: bouchard AT stat.ubc.ca (all emails should have a subject starting with the exact string 'STAT547C ')

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 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.

Pre-requisites

Co-requisite: STAT 460 / 560 or equivalent. Ideally, one upper division undergraduate course in probability, and one in analysis. If you are unsure, contact me by email with your (unofficial) graduate and undergraduate transcripts attached.

Textbook

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

Other References

• [Du] R. Durrett, Probability: Theory and Examples, 4th edition, Cambridge U. Press (2010). (See below for lecture notes following this textbook)
• [Bi] P. Billingsley, Probability and Measure, 3rd edition, John Wiley and Sons, New York (1995).
• Jim Pitman's Graduate Probability Notes: [html]
• 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).