CS395T: Probability and Statistics for Computer Sciences

Instructor: Dr. Maggie Myers

Text: Bayesian Core: A Practical Approach to Computational Bayesian Statistics by Jean-Michel Marin, Christian P. Robert (Springer Texts in Statistics)

Grading: Homework, midterm, projects

Topics:

The Basics:

Probability and Bayes Rule

Random Variables and Vectors: Discrete and Continuous

Expectation, Variance, and the Central Limit Theorem

Bayesian Inference

Bayesian Networks

Bayesian Modeling, Conjugate Priors, Posterior Distributions

MLE/MAP/EM Parameter Estimation

Mixture models

Hypothesis Testing

Dynamic Models

Random Walks

Hidden Markov Models

Markov Chain Monte Carlo Methods

Randomized Sampling algorithms (Monte Carlo)

Metropolis Hastings Algorithms

Gibbs Sampling

Data Fitting

Linear/ Non-linear Modeling

Goodness-of-fit

These concepts will be illustrated using various examples drawn from machine learning, computational biology, and other interests of the students enrolled. Students will apply techniques to data sets using R and other appropriate packages.