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

[ICO]NameLast modifiedSizeDescription

[PARENTDIR]Parent Directory   -  
[   ]Hammersley-Clifford.pdf2004-02-15 12:25 111K 
[   ]Chang-notes.pdf 2008-12-28 15:44 2.3M 
[TXT]oldREADME.html 2009-02-08 23:01 1.2K 
[   ]MCsummary.pdf 2009-02-23 11:37 790K 
[   ]engel.pdf 2009-02-25 23:04 79K 
[   ]DoyleSnell.pdf 2009-02-26 11:05 748K 
[   ]Steele2001p142.pdf 2009-04-08 12:04 392K 

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

Stochastic Calculus

The page Steele2001p142.pdf is taken from the very good book Stochastic Calculus and Financial Applications by J. Michael Steele. The book is written at a slightly higher level than Stat 251/551, but it contains much wisdom, wit, and insight. If you ever decide to get really serious about Stochastic Calculus, this book should be high on your list of essential references.


Students should discuss their planned projects with DP in the first week after the break.

Some possible topics

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.

Simulated annealing

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.

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.

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