214: Statistics Probability and Statistical Models
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Course Information
- Prof: Scott Schmidler - Email: (put Sta 214 in subject line) [e-mail] - Oce: 223D Old Chem Building - Phone: [phone] - Oce hours: Mon 4-5pm or by appt. - Course homepage: http://www.stat.duke.edu/courses/Fall05/sta214/ - Course lectures: Mon/Wed 2:50-4:05pm, Old Chem Building 025
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Overview
This course covers theory, methodology, and computation for probabilistic modeling and inference from an applied perspective. Particular emphasis is given to the development and use of simulation methodology and applied probability models in statistical analysis. Applications are drawn from Bayesian statistical analysis, frequentist statistics, statistical mechanics, image processing, bioinformatics, articial intelligence, nance. The course emphasizes two major themes: - Modeling: Conditional independence and its role in specifying complex probabilistic models. Bayesian analysis of standard statistical models; Markov chains; missing data problems; mixture models; hidden Markov and state space models; Markov random elds; graphical models. - Computation: Inference in probabilistic models, with particular emphasis on Monte Carlo integration including Markov chain Monte Carlo. EM algorithm. Metropolis, Gibbs, and Langevin algorithms. Exact algorithms where feasible (HMMs, Kalman lters, Bayesian networks). Advanced topics in later lectures will be determined by time availability and student interests.
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Lecture Schedule
See the online lecture schedule on the course homepage for lecture and reading schedules.
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Readings
The text course is Monte Carlo Statistical Methods by Robert & Casella, SpringerVerlag (1999). We will follow this text loosely, covering signicant supplemental material. Other useful references include: - Taylor and Karlin, An Introduction to Stochastic Modeling, Academic Press (1994) - Ripley, Stochastic Simulation, Wiley (1987) - Gelman et al, Bayesian Data Analysis, Chapman & Hall (1995) - Gilks et al, Markov Chain Monte Carlo in Practice, Chapman & Hall (1996) - Lauritzen, Graphical Models, Oxford (1996) - Winkler, Image Analysis, Random Fields, and Dynamic Monte Carlo Methods, Springer-Verlag (1995)
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Homework and Grading
Homework (50%): 5-6 homework assignments will be handed out during the semester, approximately 1 every 2 weeks. Each assignment consists of both theoretical and computational problems, and will require computer programming. High-level languages (S-plus,Matlab) are preferred; C/C++/Java is ne; check with me for other languages. Project (50%): There will be a nal project in lieu of a nal exam. The project will ask you to identify a problem domain and/or data set, develop and implement one or more modeling techniques covered in the class, and write and present the resulting analysis. Theoretical projects will also be possible. More details will be handed out in later in the semester.
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Miscellaneous
- Oce hours will be determined during the rst week of class. You may also make an appointment or send me email. - Please check the course homepage regularly for updated information. - Please be sure you get added to the course mailing list.
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