NEW: extra Office Hours (Partha Dey): Monday, Dec 15-th 2-4 pm and Wednesday Dec 17-th 11-12, room 307 Evans
NEW: sample final. Note this year's final is not in the same "write on exam" format -- bring your own paper.
Instructor: David Aldous
Class Time: MWF 1:00 - 2:00 in room 2 Evans.
Teaching Assistant: Partha Dey:
Discussion session Mondays, 3.00 - 4.00, room 340 Evans. Starting September 8.
This is a second course in Probability (prerequisite: an undergraduate course) aimed at graduate students in the Statistics, Biostatistics, Computer Science, Electrical Engineering, Business and Economics Departments who expect their thesis work to involve probability.
In contrast to STAT 205 (which emphasizes rigorous proof techniques) this course will emphasize describing what's known and how to do calculations in a broader range of probability models. Students are encouraged to learn by doing exercises.
The discussion section is optional and will be used (according to student demand) to expand upon lecture material and to work practice problems.
A longer book, covering most of the same topics in more depth, and covering more topics, is G. Grimmett and D. Stirzaker Probability and Random Processes
Partha Dey (partha@stat) Mondays 4.00 - 5.00; Wednesday 11.00 - 12.00; Wednesday 4.00 - 5.00 (all in 307 Evans).
If you email us please put "STAT 204" in subject.
W 9/3: Measure theory: convergence of RVs and expectations.
F 9/5: Probability distributions.
M 9/8: Coupling.
W 9/10: Stein-Chen Poisson approximation: coupling version.
F 9/12 : examples (independent; coupon collector; large spacings).
M 9/15 : neighborhood version: example.
W 9/17 : conditional expectation.
F 9/19 : martingales -- definition and examples.
M 9/22 : stopping times, optional stopping theorem, Wald's equation, play red.
W 9/24 : fair game principle, poker tournament, Wright-Fisher fixation, patterns in IID sequences.
F 9/26 : boundary crossing; Azuma-Hoeffding inequality.
M 9/29 : Method of bounded differences, empty boxes, chromatic number of random graph.
W 10/1 : submartingales, convergence theorems, maximal inequalities.
F 10/3 : Inequalities (Markov, Jensen, Cauchy-S); use of change of density in Normal tail bounds.
M 10/6 : Second moment inequality, conditional expectation inequality.
W 10/8 : Expectations of maxima.
F 10/10 : Inclusion-Exclusion.
M 10/13 : the MM algorithm.
W 10/15 : Markov chains, transition matrix, etc
F 10/17 : stationary distributions.
M 10/20 : examples of stationary distributions.
W 10/22 : classification of states; statements of limit theorems.
F 10/24 : Coupling proof of convergence theorem. MCMC.
M 10/27 : Poisson distribution; construction and definition of abstract Poisson process.
W 10/29 : 5 general properties of abstract Poisson processes.
F 10/31 : Examples (traffic, postcards). Campbell formula.
M 11/3 : 1-dimensional Poisson processes.
W 11/5 : Continuous-time Markov chains.
F 11/7 : Simple examples.
M 11/10 : Kendall birth-death-immigration process.
W 11/12 : Galton-Watson branching processes: moments and extinction probabilities.
F 11/14 : Just-supercritical and conditioned GWBP. Lange's HIV example.
M 11/17 : Multitype continuous-time BPs. *** no lab today ****
W 11/19 Lab session in class slot
F 11/21 **** no class today ****
M 11/24 : Brownian motion as limit of SRW; definition of 1-dim diffusion;
change of variables formula.
W 11/26 : 2 examples of diffusions as limits of discrete processes: Ehrehfest urn odel and Wright-Fisher diffusion.
M 12/1 : Formula for first exit place; d-dimensional Brownian Motion.
W 12/3 : Formulas for stationary density and mean exit time; examples.
F 12/5 : Martingales associated with BM; geometric BM; Kelly diffusion.
M 12/8 : Review: cat and mouse; cover N-cycle; nearest neighbors.
W 12/10 : Review; bus schedule, umbrella, Buffon needle.