Statistics
215: Statistical Models in Biology
Fall 2010
● T Th 11:00-12:15 ●
Sequoia Hall Room 200
Nancy R.
Zhang ● userid: nzhang domain name: stanford.edu ●
Office Hours: Tues 2:15-3:15 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:
Announcements will be
posted here.
Teaching Assistant:
We have no TA for this class.
Required Text:
Hoel, Port and Stone, (1972) Introduction to Stochastic
Processes. Houghton Mifflin Company.
References:
Taylor, H.M. and Karlin, S. (1998) An Introduction to Stochastic Modeling,
Academic Press: San Diego.
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Tentative Plan: |
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Week |
Tentative topics (HPS = Hoel, Port and Stone) |
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1 |
Tues |
Course overview,
Introductory examples (HPS 1.1) |
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Thurs |
Discrete Time Markov
Chains: HPS 1: Basic definitions,
Chapman-Kolmogorov Equations. |
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2 |
Tues |
Discrete Time Markov
Chains: HPS 1.5-1.6: Recurrent and
Transient States. |
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Thurs |
Discrete Time Markov
Chains: HPS 1.7-1.8: Extinction in birth and
death and branching chains. |
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3 |
Tues |
Discrete Time Markov
Chains: HPS 2: Stationary
Distributions. |
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Thurs |
Discrete Time Markov
Chains: HPS 2: Stationary
Distributions. |
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4 |
Tues |
Discrete time
branching process: HPS 1.6.1:
Computing first passage times. |
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Thurs |
Review, Example: Probability of
population extinction. |
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5 |
Tues |
Midterm
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Thurs |
Continuous Time
Markov Chains: HPS 3. |
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6 |
Tues |
Continuous Time Markov
Chains: HPS 3. |
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Thurs |
Continuous Time
Markov Chains: HPS 3. |
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7 |
Tues |
Continuous Time
Markov Chains: HPS 3. |
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Thurs |
Continuous Time
Markov Chains: HPS 3. |
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8 |
Tues |
Continuous Time
Markov Chains: HPS 3. |
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Thurs |
Continuous time
Wright Fisher process with mutation. |
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9 |
Tues |
Hidden Markov Models,
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Thurs |
Application of Hidden
Markov Models, |
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10 |
Tues |
Review |
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Grading
Policy:
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 1 problem set, with deduction of 10% on grade.
Midterm (in class): 20%
Final (in class): 40%
Problem Sets: (Passed out Thursday, due next Thursday,
unless otherwise noted.)