Statistics 215: Statistical Models in Biology
Winter 2009 ● T Th 12:50-2:05 ● Room Hewlett 103
Nancy R. Zhang ● userid: nzhang domain name: stanford.edu ● Office Hours: Thurs 2:15-4:00 PM Sequoia Hall 141
Course content:
Markov chains in discrete and continuous time, branching processes, and Poisson processes. Applications to models of nucleotide evolution, the Wright-Fisher process, coalescence, epidemiology, and sequence analysis. Theoretical material approximately the same as in STATS 217, but emphasis is on examples drawn from applications in biology, especially genetics.
Announcements:
3/15: The final exam will be on Thursday Mar-19-2009, 7:00 PM-10:00 PM, in 260-008.
3/10: Practice final is here.
1/8: Luo will grade the odd numbered homeworks and Philip will grade the even numbered ones.
| TA: | Philip Labo OH Wed 2-4pm Sequoia Hall 204 |
(userid: plabo, domain name: stanford.edu) |
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| Luo Lu OH Mon 3-5pm Sequoia Hall 108 |
(userid: luolu, domain name: stanford.edu) |
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| Required Text: | Allen, L.J.S. (2003) Stochastic Processes with Applications to Biology. Prentice Hall. | |||
| (This is made into a course reader and available in the bookstore.) | ||||
| References: | Hoel, Port and Stone, (1972) Introduction to Stochastic Processes. Houghton Mifflin Company. | |||
| Taylor, H.M. and Karlin, S. (1998) An Introduction to Stochastic Modeling, Academic Press: San Diego. | ||||
| Pre-requisites: | ||||
| Basic probability at the level of 116. | ||||
| Tentative Plan: | ||||
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Week | Date |
Tentative topics (HMS = Hoel, Port and Stone) |
Problem sets |
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1 | Tues |
Course overview, Introductory examples (Allen 1.5-1.6, HMS 1.1) |
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Thurs |
Discrete Time Markov Chains: Allen 2.2-2.4, HMS 1: Basic definitions, examples, Chapman-Kolmogorov Equations. |
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2 | Tues |
Discrete Time Markov Chains: Allen 2.4-2.5, HMS 1.5-1.6: Recurrent and Transient States. |
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Thurs |
Discrete Time Markov Chains: HMS 1.7-1.8: Extinction in birth and death and branching chains. |
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3 | Tues |
Discrete Time Markov Chains: Allen 2.5-2.6, HMS 2: Stationary Distributions. |
ps2 sol |
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Thurs |
Discrete Time Markov Chains: Allen 2.5-2.6, HMS 2: Stationary Distributions. |
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4 | Tues |
Discrete time branching process: Allen 2.7, HPS 1.6.1: Computing first passage times. |
ps3 sol |
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Thurs |
Review: Allen 4.2-4.4. Probability of population extinction. |
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5 | Tues |
Midterm midterm practice, midterm solutions |
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Thurs |
Continuous Time Markov Chains: Allen 5.1-5.5, HMS 3. |
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6 | Tues |
Continuous Time Markov Chains: Allen 6v , HMS 3. |
ps4.pdf |
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Thurs |
Continuous Time Markov Chains: Allen 6, HMS 3. |
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7 | Tues |
Continuous Time Markov Chains: Allen 6, HMS 3. |
ps5.pdf |
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Thurs |
Diffusion Processes: Allen 8, HMS 4. |
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8 | Tues |
Diffusion Processes: Allen 8, HMS 5. |
ps6.pdf |
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Thurs |
Diffusion Processes: Allen 8, HMS 5. |
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9 | Tues |
Diffusion Processes: Allen 8, HMS 5. |
ps7.pdf due Thurs, 3/12 |
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Thurs |
Diffusion Processes: Allen 8, HMS 6. |
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10 | Tues |
Diffusion Processes: Allen 8, HMS 6. |
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| Grading Policy: | ||||
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Homeworks (weekly): 40% Problem sets are assigned every Thursday, due at the beginning of lecture the following Thursday (unless otherwise noted). Solutions are posted on Friday. You can be late by at most one day on at most 2 problem sets, with deduction of 10% on grade. |
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| Midterm (in class): 20% | ||||
| Final: 40% | Practice final | |||