5 cu.
=20Advanced studies
=20Basic calculus, linear algebra, introductory course on probability and s= tatistical inference are absolutely necessary. First course level knowledge= on algebra, probability and inference will be recommendable for many parts= of the course.
=20Weeks 4450, Tuesday 1214 and Thursday 1214 in room B120. NB! No lectu= res during weeks 48 and 49. These lectures are replaced by the following AD= DITIONAL lectures in room B120 during weeks 47 and 50: Mon 21.11. 1416, We= d 23.11. 1214, Mon 12.12. 1416. Exercise sessions will be held normally d= uring weeks 48,49.
=20During weeks 4549 there will be a weekly exercise session in room C124 = on Fridays between 1214. The teacher responsible for the exercise sessions= is Ali Amiryousefi (amiryous@mappi.helsinki.f= i).
=20Exercises 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=20
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 b= onus points for the grade. The home exam will consist of a number of larger= assignments that must be returned by May 1st 2012 to the lecturer. Home ex= am assignments are available here.
=20Week 44:
Tue 1.11.
Teaser =
trailer, Eyeopener on conditi=
onal probabilities and Bayes' theorem, basic properties of Markov chains. <=
a class=3D"externallink" href=3D"http://www.helsinki.fi/bsg/filer/Koski2.p=
df" rel=3D"nofollow">This excerpt from the HMM book by T. Koski is main=
ly used during the lectures and also this sho=
rt excerpt on periodicity from the book of Isaacson & Madsen, Marko=
v chains. For further illustrations and mathematical details on Markov chai=
ns, see the link to Sirl and Norris in Bibliography.
Thu 3.11.
Basi=
c properties of Markov chains continued. To get going with the basics of si=
mulating Markov chains, you might find these Matlab codes usef=
ul.
Week 45:
Tue 8.11.
Properties of Markov chains continued. B=
asics of ML and Bayesian learning, see this excerpt from the HMM book by T. Koski.
Thu 10.11.
Statistical learning f=
or 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.
Wee=
k 46:
Tue 15.11.
Bayesian learning of the order of a DTMC, continuo=
ustime Markov chains (see the ebook by Koski.).
T=
hu 17.11.
Continuoustime Markov chains.
Week 47:
Continuousti=
me Markov chains, basic properties of hidden Markov models, see: Ch. 10,Ch. 12,Ch. 13,Ch. 14 from t=
he HMM book.
Weeks 4849: No lectures
Week 50: CTMS and HMMs contin=
ued, Variable Length Markov chains (see the article by M=C3=A4chler & B=
uhlmann mentioned in the bibliography)
Various references will be used during the course. The lecture diary wil= l also include links to some additional materials. Parts of the following b= ooks will be considered:
=20Baclawski, Kenneth. Introduction to probability with R. Chapman & Ha=
ll, 2008.
Timo Koski. Hidden Markov models for bioinformatics. Kluwer, =
2001.
Timo Koski & John M. Noble. Bayesian networks: An introductio=
n. 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 (arti= cles not directly linked here are generally available form JSTOR collection= or are otherwise online):
=20Braun, J.V. & Muller, HG. Statistical methods for DNA sequence segm=
entation. Statistical Science, 13, 142162, 1998.
Sirl, D. Markov Chain=
s: An Introduction/Review. pdf.
Norri=
s, J. Markov chains. CUP, see online resource. Gu, L. Notes on Dirichl=
et distribution with relatives. This document provides a concise recapi=
tulation of some of the central formulas that are needed in the exercises a=
nd assignments when doing Bayesian learning. More comprehensive derivations=
can be found in several books on Bayesian modeling, e.g. in Koski & No=
ble (2009), which is listed above.
M=C3=A4chler, M. & Buhlmann, P. =
Variable length Markov chains: Methodology, computing and software. Journal=
of Computational and Graphical Statistics 13, 435455, 2004. Preprint avai=
lable here
Kass, R.E. & Raftery, A.E. Ba=
yes factors. Journal of the American Statistical Association, 90, 773795, =
1995.
Smith, A.F.M. & Gelfand, A.E. Bayesian statistics without tea=
rs: A samplingresampling perspective. The American Statistician, 46, 8488=
, 1992.
Jordan, M.I. Graphical models. Statistical Science, 19, 140155=
, 2004. Preprint available here
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