ECS 256

Prereqs

A calculus-based probability course such as MAT 135, STA 131A or ECS 132; basic linear algebra; programming skills.

General Coverage

Probabilistc modeling for data science applications. Primary focus on Markov models.

Topics:

• Review of undergrad probability (densities, expected value, famous distribution families). Central Limit Theorem, multivariate normal (MVN).
• Statistical estimation: MLE and Method of Moments; regression function as conditional mean; frequentist vs. Bayesian philosophies.
• Prediction: Regression function as conditional mean; parametric and nonparametric ("machine learning") estimation; connection of MVN to classical assumptions in linear, logistic models.
• Markov chains, discrete and continuous-time; long-run distribution; state classification.
• Markov chain applications, including Hidden Markov models (e.g. for speech detection), Markov Chain Monte Carlo (e.g. Bayesian integrals); graph theory models (e.g. disease detection); relation to Recurrent Neural Networks.
• Statistical estimation of Markov models, including with covariates.
• Markov models for time series.
• Discrete event simulation (using R simmer package); example: managing a call center.
• Basic queuing models.
• Survival reliability analysis: Exponential/Poisson duality; hazard functions; Cox regression.

Workload

3 homework assignments (math + computation), done in groups of 2 to 4, interactive grading; 2 exams, open book.