Markovian modelling and Bayesian learning, fall 2012
Lecturer
Scope
5 cu.
Type
Advanced studies
Prerequisites
Basic calculus, linear algebra, introductory course on probability and statistical inference are absolutely necessary. First course level knowledge on algebra, probability and inference will be recommendable for many parts of the course.
Lectures
Weeks 4450, Tuesday 1214 and Thursday 1214 in room B120. NB! No lectures on Nov 1st, Nov 15th, Dec 4th. These lectures are replaced by ADDITIONAL lectures for which time & place is announced later on this webpage.
Exercises.
During weeks 4549 there will be a weekly exercise session in room B120 on Thursdays 1416, except on Dec 6th which is a public holiday. The exercise session for that week is held in room C124 on Friday 7th between 1214. The teacher responsible for the exercise sessions is Lu Cheng (first.last@helsinki.fi).
Exercises for week 45 are available here
Exercises for week 46 are available here
Exercises for week 47 are available here
Exercises for week 48 are available here
Exercises for week 49 are available here
Exams
To gain the credits from this course, it is necessary to do at least 50% of the exercises and a home exam. Additional solved exercises will yield bonus points for the grade. The home exam will consist of a number of larger assignments that must be returned by May 1st 2013 to the lecturer. Home exam assignments are available here.
Preliminary lecture diary
Week 44:
Tue
Teaser trailer, Eyeopener on conditional probabilities and Bayes' theorem, basic properties of Markov chains. This excerpt from the HMM book by T. Koski is mainly used during the lectures and also this short excerpt on periodicity from the book of Isaacson & Madsen, Markov chains. For further illustrations and mathematical details on Markov chains, see the link to Sirl and Norris in Bibliography.
Thu
Basic properties of Markov chains continued. To get going with the basics of simulating Markov chains, you might find these Matlab codes useful.
Week 45:
Tue
Properties of Markov chains continued. Basics of ML and Bayesian learning, see this excerpt from the HMM book by T. Koski.
Thu
Statistical learning for DTMC's, see this excerpt from the HMM book by T. Koski. Also, this appendix from the HMM book is useful for refreshing details on various distributions.
Week 46:
Tue
A primer on Occham's razor and Bayesian model comparison for Markov chains, Informationtheoretic book by D MacKay where Ch 28 contains a detailed explanation of the Occham's razor principle and Bayesian model comparison, Bayesian learning of the order of a DTMC, continuoustime Markov chains (see the ebook by Koski.).
Thu
Continuoustime Markov chains.
Week 47:
Continuoustime Markov chains, basic properties of hidden Markov models, see: Ch. 10,Ch. 12,Ch. 13,Ch. 14 from the HMM book. An example of using HMM in classification.
Weeks 4849:
Week 50: CTMS and HMMs continued, Variable Length Markov chains (see the article by Mächler & Buhlmann mentioned in the bibliography)
Bibliography
Various references will be used during the course. The lecture diary will also include links to some additional materials. Parts of the following books will be considered:
Baclawski, Kenneth. Introduction to probability with R. Chapman & Hall, 2008.
Timo Koski. Hidden Markov models for bioinformatics. Kluwer, 2001.
Timo Koski & John M. Noble. Bayesian networks: An introduction. Wiley, 2009.
Timo Koski. Lectures at RNI on Probabilistic Models and Inference for Phylogenetics. Free ebook available here.
In addition, we will consider a number of articles & tutorials (articles not directly linked here are generally available form JSTOR collection or are otherwise online):
Braun, J.V. & Muller, HG. Statistical methods for DNA sequence segmentation. Statistical Science, 13, 142162, 1998.
Sirl, D. Markov Chains: An Introduction/Review. pdf.
Norris, J. Markov chains. CUP, see online resource.
Gu, L. Notes on Dirichlet distribution with relatives. This document provides a concise recapitulation of some of the central formulas that are needed in the exercises and assignments when doing Bayesian learning. More comprehensive derivations can be found in several books on Bayesian modeling, e.g. in Koski & Noble (2009), which is listed above.
Mächler, M. & Buhlmann, P. Variable length Markov chains: Methodology, computing and software. Journal of Computational and Graphical Statistics 13, 435455, 2004. Preprint available here
Kass, R.E. & Raftery, A.E. Bayes factors. Journal of the American Statistical Association, 90, 773795, 1995.
Smith, A.F.M. & Gelfand, A.E. Bayesian statistics without tears: A samplingresampling perspective. The American Statistician, 46, 8488, 1992.
Jordan, M.I. Graphical models. Statistical Science, 19, 140155, 2004. Preprint available here
Registration
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Exercise groups
Group  Day  Time  Place  Instructor 

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