Index of /~pollard/Courses/251.spring09/Handouts

	Name	Last modified	Size	Description
	Parent Directory		-
	oldREADME.html	2009-02-08 23:01	1.2K
	engel.pdf	2009-02-25 23:04	79K
	Steele2001p142.pdf	2009-04-08 12:04	392K
	MCsummary.pdf	2009-02-23 11:37	790K
	Hammersley-Clifford.pdf	2004-02-15 12:25	111K
	DoyleSnell.pdf	2009-02-26 11:05	748K
	Chang-notes.pdf	2008-12-28 15:44	2.3M

Stochastic Calculus

Riffle shuffles

Give a complete account of the analysis of the riffle shuffle. Do not use the language of convolutions for walks on finite groups; use the methods developed during the course.

• David Aldous and Persi Diaconis, Shuffling cards and stopping times, American Mathematical Monthly 93 (1986), 333-348.   [JSTOR]
• Brad Mann, How many times should you shuffle a deck of cards?, The UMAP Journal v. 15 (Winter 1994) p. 303-38.   [UMAP]

Simulated annealing

• S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, Optimization by Simulated Annealing, Science 220 (1983), 671-680.  [JSTOR]
• Stuart Geman and Donald Geman, Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images, IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume PAMI-6, Issue 6, Nov. 1984 Page(s):721 - 741, Digital Object Identifier 10.1109/TPAMI.1984.4767596 .  [IEEE]

Image analysis

Do something clever with Markov chains

The decoding example described by Diaconis, The Markov Chain Monte Carlo Revolution, Bulletin of the American Mathematical Society, 46 (2009), 179-205  & [AMS] looks promising.

Random walks and electrical networks

Write a complete probabilistic account of Rayleigh's Monotonicity Law (see section 1.4 of Doyle and Snell).

Optimal stopping

Explain the solution to the classical Secretary Problem. Then explain how the solution can be derived using the Snell envelope. Maybe apply the same method to derive pricing for an American option over a finite set of trading times.

• Notes on optimal stopping by Tom Ferguson
• Section 8 (Example 8.5 and pp111-116) of: P. Billingsley (1979), Probability and Measure (first edition). Wiley.

Algorithms for HMM and Graphical models

First read Chapter 3 of the Chang notes. Maybe move on to the Jordan article. Explain how the message-passing schemes work (on a tree, at least). Implement. Of course I expect you to go beyond what is in the Chang notes.

• Michael I. Jordan, Graphical Models, Statistical Science, Vol. 19, No. 1 (Feb., 2004), pp. 140-155.  [JSTOR]
• See also other papers and notes by Jordan and by Wainwright at the YPNG web site.

Engel algorithm?

Maybe too easy. Not quite enough for a whole project just to understand material in engel.pdf.