Stat 8001: Probability and Statistics Theory I. This is a tier-1 graduate course, intended to provide a solid foundation of the basic ideas and methods (such as Basic Probability, standard univariate distributions, parametric and Nonparametric density modeling, goodness-of-fit, conditional distributions, linear and nonlinear correlation, a few multivariate distributions) that underlie the mathematical theory of statistics.
Stat 8002: Probability and Statistics Theory II. This is a sequel of stat 8001 which mainly focuses on data reduction (sufficiency principle), estimation techniques (MOM, least squares, MLE, Bayes estimation), theory of estimation (MSE; best unbiased estimators; lower bounds on variance; consistency, large sample properties), hypothesis testing (LRT, Neyman-Pearson Theorem; score tests), interval estimation (pivotal quantities, inversion of tests; confidence intervals, Bayesian credible intervals and bootstrap resampling technique.
Stat 8115: Nonparametric Methods I. This is a tier-2 graduate course which I have entirely redesigned. In this course, students are exposed to modern nonparametric statistical modeling tools and concepts to tackle: goodness of fit, two-sample modeling, multiple testing, ANOVA, and regression smoothing.
Stat 9190: New topics in Statistics: Nonparametric Methods II. This course is the sequel of Stat 8115 (developed from scratch), mainly targeting advanced graduate students. It introduces copula density modeling, nonlinear correlation, correspondence analysis, conditional density estimation, analysis of contingency table, meta-analysis, and learning from uncertain data. It also gave students hands-on experience in the form of contemporary real-world data analysis projects. Stat 8115 and 9190, combined, provide a comprehensive introduction to the theory and algorithms of “Nonparametric Data Science.”
Stat 9183: Directed Study in Statistics. My Ph.D. students generally take this course to delve deep into the “Nonparametric Data Science.”
Stat 110: Statistical Methods in Engineering and the Physical Sciences. This course introduces fundamental statistical concepts and principles for engineers and physical scientists. An approximate list of course topics (subject to change; as time permits): Exploratory Data Analysis, Basic Probability Theory, Discrete and Continuous Random Variables, Joint Distribution and Covariance, Basic Statistical Inference, Statistical Model Building via Goodness-of-fit, Regression, Correlation, Two-sample problem, K-sample problem. For more details: https://unitedstatalgo.com/courses-stat110
Stat 2103: Statistical Business Analytics. This is an undergraduate course. Some of the learning objectives are: Interpreting quantitative information and drawing inferences from it; Solving business problems using statistical methods; Communicating quantitative information: verbally, numerically, algebraically, or graphically; Apply critical thinking to business problems.
Stat 2501: Quantitative Foundations for Data Science. This is an undergraduate course that introduces the subjects linear algebra, probability and statistics hand in hand. Some of the learning objectives are: Obtain an acceptable level of mastery of linear algebra and optimization; Apply statistical tools for data science applications.