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The course will cover basic
techniques of
probabilistic modeling. Models drawn
from mathematical biology will be used as "case studies" to motivate
and illustrate the mathematical methods as well as to introduce
classical areas
of mathematical biology such as population genetics
and evolution. The class
will present an introduction to probability
theory and stochastic processes, with particular focus on Markov
models. Other
topics will include evolutionary game theory, neural networks and
maximum
likelihood estimation. The class will include a computer laboratory
that will
teach the basics of programming in the statistical software R and
provide
computational tools for simulating and fitting probabilistic models
including
simulating stochastic processes, maximum likelihood estimation and
Monte Carlo
simulation.
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Week 1
Mathematical
population genetics and evolution Week 2
Introduction
to probability: probability rules, conditional
probabilities, independence Week 3
Evolutionary
game theory and models for evolution Week 4
Introduction
to probability (cont.): random variables,
discrete probability distributions Week 5
Intro to
probability (cont.): probability distributions,
expected values Week 6
Intro to
probability (cont.): central limit theorem;
Definition of a stochastic process Week 7
Poisson
processes, application to the release of
neurotransmitter at synapse Week 8
Discrete time
Markov models; Week 9
Birth and
death process; Midterm
exam; Week 10
Continuous
time Markov models, diffusion Week 11
Evolutionary dynamics; Markov models for animal behavior and
gene expression Week 12
Estimation: maximum likelihood,
graphical methods Week 13
Monte Carlo simulations and other
computer methods Week 14
Ising models in biology: Hopfield
neural networks Week 15
Application
of Ising models
to the yeast cell cycle Week 16
Geometric probability with applications
to stereology
(three-dimensional measurement in microscopy) |