Below is the list of courses that I have taught, accompanied by the brief description. The course pages can be accessed by enrolled students through Brightspace.
Math 547: Methods of Statistical Inference – Introduction to the mathematical foundations of Statistical Learning Theory.
This course provides an introduction to the mathematical foundations of Statistical Learning Theory. How is modern high-dimensional statistics and learning theory different from the classical statistical techniques? As Leo Breiman wrote in 2001, “There is an old saying “If all a man has is a hammer, then every problem looks like a nail.” The trouble for statisticians is that recently some of the problems have stopped looking like nails.”
Learning theory framework often does not assume that the data we observe strictly follows the underlying model (e.g., Gaussian distribution). Instead, (quoting L. Breiman), “The approach is that nature produces data in a black box whose insides are complex, mysterious, and, at least, partly unknowable. What is observed is a set of x’s that go in and a subsequent set of y’s that come out. The problem is to find an algorithm f(x) such that for future x in a test set, f(x) will be a good predictor of y.”
Math 545: Methods of Statistical Inference – Introduction to the mathematical foundations of Statistical Learning Theory.
This course is a graduate level introduction to the theory and methods of the analysis of time series data.
In addition to understanding the methodology and the mathematics behind it, the course allows students to get hands-on experience analyzing real data sets using Matlab and R.
Math 542L: Analysis of Variance and Regression.
This course is an introduction to two of the most widely-used statistical tools: regression and analysis of variance.
During the semester, lectures go though the theory and highlight applications to real data sets. Significant focus is on gaining experience in applying the methods to datasets through practical assignments and class projects.
Math 541b: Introduction to Mathematical Statistics.
This course is a second part of graduate-level introduction to the Mathematical Statistics (first part is Math 541a).
The list of topics covered in the course includes the theory of Hypotheses testing (Neyman-Pearson lemma, permutation tests, invariance principle, likelihood ratio tests, asymptotics of the power function and efficiency), interval estimation, Bootstrap, Expectation-Maximization algorithm.
Math 408: Mathematical Statistics.
This course is an introduction to the fundamental ideas and techniques of mathematical statistics.
One of the definitions of Statistics is “the science of basing inferences on observed data and the entire problem of making decisions in the face of uncertainty” (Freund and Walpole `87).
In simple terms, statistics is the art of making conjectures about challenging and puzzling questions based on available data (“what are the effects of a new medical treatment?”, “what is the average income in the US?”, etc.)
To answer these questions, we will use powerful – the methods of probability theory, “the language of uncertainty.”