Statistical Machine Learning
Introduction to statistical concepts, models, and algorithms of machine learning. Explores supervised learning for regression and classification, unsupervised learning for clustering and principal components analysis, and related topics such as discriminant analysis, splines, lasso and other shrinkage methods, bootstrap, regression, and classification trees, and support vector machines, along with their tuning, diagnostics, and performance evaluation.
Data Science
State of the art computational tools for data science. This course builds on the R/tidyverse programming skills for the collection, organization, analysis, interpretation, and presentation of data. Possible topics include version control, web scraping, text mining, web application development with R Shiny, big data manipulation, R’s statistical modeling functions, and dimensionality reduction and clustering for data exploration
Time Series
An introduction to the theory of time-dependent data. The analysis includes modeling, estimation, and testing of data in the time domain using autoregressive and moving average models.
Stochastic Processes
Introduction to random walks, Markov chains and processes, Poisson processes, recurrent events, birth and death processes, and related subjects.
Generalized Linear Models
Extension of regression methodology to more general settings where standard assumptions for ordinary least squares are violated. Generalized least squares, robust regression, bootstrap, regression in the presence of auto-correlated errors, generalized linear models, logistic and Poisson regression.
Mathematical Statistics
Probability, random variables, probability distributions and functions of random variables, generating functions, order statistics, the theory of point estimation, (maximum likelihood, minimum variance unbiased estimators, confidence intervals), and theory of hypothesis testing (Neyman-Pearson, likelihood ratio, etc.).
Regression
Simple and multiple regression, least squares, curve fitting, graphic techniques, and tests and confidence intervals for regression coefficients.