Statistics

The course covers many of the following topics: Random events, sigma-algebras, monotone classes. Measurable spaces, random variables - measurable functions. Measures, probability measures, signed measures. Borel sets in R^d, Lebesgue measure. Caratheodory extension theorem. Sequences of events and random variables, Borel-Cantelli lemma. Distributions of random variables. Independence of random variables. Integral of measurable functions - mathematical expectation,.
Moments of random variables, L_p spaces. Convergence concepts of measurable functions. Limit theorems for integrals. Weak and strong laws of large numbers. Completeness of L_p spaces. Conditional expectation and conditional distribution of random variables. Fubini's theorem.

This course examines statistics for students who aspire to major in Statistics or Risk Management. It focuses on the roles of statistics as a scientific tool with applications to a wide spectrum of disciplines, and as a science of reasoning which has revolutionized modern intellectual endeavours. It lays a panoramic foundation for a formal study of statistics at the university level. 

This course provides an overview of the fundamentals in probability and statistics. It aims to provide a good understanding of the methods of probability and statistical analysis of data. Students will be able to use these statistical methods for their own studies and later in professional practice. 

This is an advanced-level Data Science course, focusing on deep learning, which has witnessed great success over the past decade. Two of the most successful fields of deep learning are image processing and natural language processing. 

Some of the most successful applications of deep learning in image processing include object detection, image segmentation, and image classification. In natural language processing, deep learning has been used to develop applications such as machine translation, text classification, automatic summarization and question answering.  

The course begins with an overview of deep learning, and a review class for Python and the PyTorch library respectively. Then, the course studies linear algebra and calculus from numerical perspectives. The course also reviews the basics of statistics and information theory for deep learning and the basics of machine learning, including topics like overfitting, supervised and unsupervised learning, and stochastic gradient descent.  

The course introduces neural network models using the familiar linear and softmax regression, as well as the concept of multilayer perceptrons and the essential technique of backward propagation.  The course also studies various ways to regularize deep neural networks, such as putting norm penalties or allowing dropout, and how to do optimization for training these regularized deep neural networks. The latter half of the course focuses on convolutional neural networks for image processing and recurrent and recursive neural networks for natural language processing. Last, the recent important topic of fine-tuning a pre-trained large language model will also be covered. 

This course offers a panoramic view of several tools available for predictive modeling. It explores the main concepts in linear models and their extensions. Topics include: simple linear regression; multiple linear regression; linear regression extensions; logistic regression.

This course examines numerical methods and statistics essential in a wide range of engineering disciplines. Numerical methods covers computing with real numbers, numerical differentiation, integration, interpolation and curve fitting (regression analysis), solution of linear and nonlinear algebraic equations, matrix operations and applications to solution of systems of linear equations, elimination and tri-diagonal matrix algorithms, and an introduction to numerical solution of ordinary and partial differential equations. Statistics covers exploratory data analysis, probability and distribution theory including the Binomial, Poisson and Normal distributions, large sample theory including the Central Limit Theorem, elements of statistical inference including estimation, confidence intervals and hypothesis testing, one sample and two-sample t-tests and F-tests, simple and multiple linear regression and analysis of variance and statistical quality control.

In this course, students learn to engage with information visually. They learn to recognize and critique oversimplifying, biased, or misleading forms of visual representation, and to create their own visualizations to explore and communicate data that matters to them. Using examples from a wide range of academic disciplines - from economics, to literature, meteorology, history, urban design, or computer science - students discover key principles of visual thinking and communication and learn how to create their own charts and maps. Historically, data visualization has often been used to discriminate, control, and police. In this course, students also explore interventions by critical data scientists, scholars, and activists who visualize data to expose injustice, challenge unfair classification systems, and speak truth to power. The course does not involve any coding and does not require previous technical knowledge.

This course is an introduction to research study design and the analysis of structured data. It covers blocking, randomization, and replication in designed experiments, as well as clusters, stratification, and weighting in samples.

This course examines basic concepts and methods for estimating various quantities of interest in the analysis of survival data. A distinct feature of the type of data that is covered in this course is that the main response of interest, survival time, is subject to censoring, which leads to an incomplete observation. Topics include survival models, censoring and truncation, functions characterizing survival times, nonparametric estimation of survival function and other functions, comparison of survival functions for different groups, parametric and semiparametric regression models, mathematical and graphical methods for assessing goodness of fit, analysis of multivariate failure time data, competing risks analysis, cohort-sampling designs, and other advanced topics.