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• Bayesian theory with applications, spring 2010
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# Bayesian theory with applications, lecture diary and course information

Jukka Corander

### Scope

5+3 cu. The additional 3 credits are gained by completing a project task.

### Type

Advanced studies. Bayesian theory is currently applied throughout the whole spectrum of scientific modeling and it is also a very important tool in a multitude of technological and engineering fields. The aims of the course are to decipher the Bayesian machinery, how and why it works, as well as to gain detailed understanding of an array of its applications.

### Prerequisites

Probability calculus, calculus, linear algebra are important pre-requisites. Stochastic processes and computational statistics are useful, but not obligatory.

see main page.

### Lecture diary (only tentative schedule).

Week 11: Recent article in NY Times about Bayesian statisticsCourse introduction, Introduction to subjective and epistemic perspective on probability, see Stanford Encyclopedia on probability, Bayes' theorem, dynamic revision of uncertainty using Bayes' theorem; see the example on perception and sensory integration which is demonstrated live in this BBC clip, Search & Rescue game sw, Search and Rescue demo case as a pdf, (note also that there is a real Bayesian search & rescue sw in use by coast guards, see here for a SAROPS demo), sequential Monte Carlo related computation. Revision of uncertainty and predictions for a 'cigar-box sampling problem', usefulness of systematic use of prior information in the context of infant mortality and SIDS (see this article by Gilbert et al. 2005). Use of Bayesian statistics to locate a missing plane, an example of Air France flight 447 and its relevance to MH370 search. This paper in Statistical Science discusses the AF447 case using SAROPS, and there are many other success stories listed here (a special Bayes issue of Statistical Science, the papers are also available on arxiv.org). Discussion of Bayesian inference and likelihood ratio calculations in forensics, for DNA evidence see these excellent slides (1) , (2)  , (3) and (4) from Richard Gill's homepage, for gunshot residue analysis, see this paper and these slides. This paper discusses more complicated evidence calculation in cases of mixture of DNA and this review by David Balding discusses several challenges in DNA based evidence.

Week 12: Exchangeability, de Finetti's representation theorem, subjective probability modeling, prior and posterior predictive distributions, illustrations with probabilistic classification of documents, SpamAssasin is the most widely used spam protection system with a Bayesian filter. Cormack and Lynam at U Waterloo present a nice study on the efficiency SpamAssasin and other filters, instead of modeling presence/absence of words, it is also possible to use data compression on text sequences for spam filtering.  In a more general setting, this recent paper discusses predictive classification and exchangeability, see also its sequel paper and these illustrative slides that summarize behavior of predictive inference under various classification circumstances. A February 2015 paper about predictive classifiers based on graphical models illustrates several improvements over the previous approaches. A useful approach to calculating integrals in Bayesian inference via 'visual pattern recognition' is explained in this document. A catalogue of conjugate prior distributions is here. Gu, L. has provided these useful Notes on Dirichlet distribution with relatives provides a concise recapitulation of some of the central formulas around the Dirichlet distribution.

Week 13: marginal and conditional independence, DAGs, graphs for representations of hierarchical models (see also this introductory article by M Jordan), choosing prior distributions. Vanilla introduction to hierarchical models as a case study on kidney cancers from the book by Gelman et al.

Week 14: kidney cancer story continued (with simulation in classroom), for a more realistic example of Bayesian smoothing of disease rates, see the excellent slides of Aki Vehtari, Bayesian inference procedures in practice, illustrating case-study with IQ estimation (with simulation in classroom), choosing priors continued, these slides and this article illustrate the impact of different prior/model choices for clustering data of genomic aberrations observed in cancers.

### Exams

See the course page for current year for the exam date. Participants are allowed to bring all the lecture and assignment materials with them to the exam.

A list of possible topics for a larger assignment task is available here, choose freely one project from the list. Reports on the larger assignment can be produced by working alone or in pairs. In case you decide to do the project jointly with another participant, return only a single report with names of both participants. The reports should be returned within three months from the written exam date. By completing both the written exam and a larger assignment participants will gain 8 credits for the course. In case you wish to suggest own topic for a larger assignment, contact the lecturer.

### Bibliography

Lecture slides are available here. In addition several classroom demonstrations and various case study materials are considered. Examples of useful books on Bayesian theory and modeling are Bernardo & Smith (1994), O'Hagan (1994), Schervish (1995), Gelman et al. (2004).

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