- 1. Introduction (2 weeks)
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Basic probability, Combinatorics,
independence, covariance,
Reliability.
Random variables. Chebyshev Inequality.
- 2. Discrtet Distributions (2 weeks)
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Bernoulli, Binomial, Geometric, Poisson, and Multinomial distributions.
- 3. Continuous random variables and distributions (3 weeks)
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Probability density function, accumulative distribution function,
change of variables;
Uniform, Normal, Exponential, and Gamma distributions.
Memoryless property.
Central limit theorem.
Midterm Exam: Tuesday March 19.
- 4. Computer Simulations and Markov Chain Monte Carlo Methods (2 weeks)
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Sampling of continuous distributions
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*Metropolis Algorithm, *Heatbath/Gibbs Algorithm
- 5. Stochastic Process and Markov process (1.5 weeks)
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Random walk on a graph.
Poisson Process.
*Gaussian Process.
- 6. Parameter Estimation and Fitting a distribution (1 week)
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Method of moments,
Maximum Likelihood estimation.
- 7. Hidden Markov Models (2 week)
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- 8. Bayesian Networks (2 week)
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Joint Distribution factorization
Directed Acyclic Graph
Influence Propagation
- 9. Markov Random Fields (2 weeks)
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Markov condition on a graph.
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Ising Model
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Using Ising model for protein function prediction
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Graphical models and Bayesian Networks