A friendly introduction to statistical concepts and reasoning with emphasis on developing statistical intuition rather than on mathematical rigor. Topics include design of experiments, descriptive statistics, correlation and regression, probability, chance variability, sampling, chance models, and tests of significance.
This is only a request to create zero credit recitation for STAT1001UN Intro to Stat Reasoning starting in Fall 2026.
This course introduces core ideas in probability and statistics with a focus on building a foundation for data science. Topics include probability theory basics, common probability distributions, sampling and estimation, confidence intervals and hypothesis testing, and simple linear regression, resampling methods, smoothing techniques, and an introduction to the Bayesian inference. The course also offers a brief introduction to programming in R and Python.
Prerequisites: intermediate high school algebra. Designed for students in fields that emphasize quantitative methods. Graphical and numerical summaries, probability, theory of sampling distributions, linear regression, analysis of variance, confidence intervals and hypothesis testing. Quantitative reasoning and data analysis. Practical experience with statistical software. Illustrations are taken from a variety of fields. Data-collection/analysis project with emphasis on study designs is part of the coursework requirement.
RECITATION FOR STAT1101UN INTRODUCTION TO STATISTICS
Prerequisites: one semester of calculus. Designed for students who desire a strong grounding in statistical concepts with a greater degree of mathematical rigor than in STAT W1111. Random variables, probability distributions, pdf, cdf, mean, variance, correlation, conditional distribution, conditional mean and conditional variance, law of iterated expectations, normal, chi-square, F and t distributions, law of large numbers, central limit theorem, parameter estimation, unbiasedness, consistency, efficiency, hypothesis testing, p-value, confidence intervals, maximum likelihood estimation. Serves as the pre-requisite for ECON W3412.
RECITATION FOR STAT1201UN CALC-BASED INTRODUCTION TO STATISTICS
RECITATION FOR STAT2102UN APPLIED STATISTICAL COMPUTING
Corequisites: An introductory course in statistic (STAT UN1101 is recommended). This course is an introduction to R programming. After learning basic programming component, such as defining variables and vectors, and learning different data structures in R, students will, via project-based assignments, study more advanced topics, such as conditionals, modular programming, and data visualization. Students will also learn the fundamental concepts in computational complexity, and will practice writing reports based on their data analyses.
Prerequisites: An introductory course in statistics (STAT UN1101 is recommended). Students without programming experience in R might find STAT UN2102 very helpful. Develops critical thinking and data analysis skills for regression analysis in science and policy settings. Simple and multiple linear regression, non-linear and logistic models, random-effects models. Implementation in a statistical package. Emphasis on real-world examples and on planning, proposing, implementing, and reporting.
Introduction to exploratory data analysis (EDA) and the foundations of statistical learning. Statistical graphics, EDA workflow, elements of regression and classification problems. Linear and logistic regression, principal components analysis, elements of clustering.
This course aims to develop practical skills in statistical data analysis by providing opportunities for mentored intramural statistical consulting. The emphasis is on translating researchers’ subject-matter knowledge and research goals into statistical models and analytic goals, and applying appropriate statistical methods to researchers’ data. Under the supervision of the instructor, student-consultants will meet with clients, discuss cases in class, research appropriate methods as needed, and conduct analyses and write reports. Students will mostly work in small groups, and assignments will be made to reflect students’ previous coursework. This course should be of interest to students seeking mentored research experience.
This is a course in intermediate statistical inference techniques in the context of applied research
questions in data science. Assuming some prior exposure to probability and statistics, this course will
first introduce the student to the principles of Bayesian inference, then apply them in estimation and
prediction in the context of linear and generalized linear models, counting and classification, mixture and
multilevel models, including scientific computation (like MCMC methods). Students will also learn
about the main benefits of using Bayesian vs. frequentist methods, like naturally combining prior
information with the data; posterior probabilities as easier to interpret alternatives to p-values; parameter
estimation “pooling” in hierarchical model and so on.
Prerequisites: At least one, and preferably both, of STAT UN2103 and UN2104 are strongly recommended. Students without programming experience in R might find STAT UN2102 very helpful. This course is intended to give students practical experience with statistical methods beyond linear regression and categorical data analysis. The focus will be on understanding the uses and limitations of models, not the mathematical foundations for the methods. Topics that may be covered include random and mixed-effects models, classical non-parametric techniques, the statistical theory causality, sample survey design, multi-level models, generalized linear regression, generalized estimating equations and over-dispersion, survival analysis including the Kaplan-Meier estimator, log-rank statistics, and the Cox proportional hazards regression model. Power calculations and proposal and report writing will be discussed.
Prerequisites: STAT UN2103. Students without programming experience in R might find STAT UN2102 very helpful. This course is a machine learning class from an application perspective. We will cover topics including data-based prediction, classification, specific classification methods (such as logistic regression and random forests), and basics of neural networks. Programming in homeworks will require R.
Prerequisites: Calculus through multiple integration and infinite sums. A calculus-based tour of the fundamentals of probability theory and statistical inference. Probability models, random variables, useful distributions, conditioning, expectations, law of large numbers, central limit theorem, point and confidence interval estimation, hypothesis tests, linear regression. This course replaces SIEO 4150.
RECITATION FOR STAT4203GU PROBABILITY THEORY
RECITATION FOR STAT4204GU STATISTICAL INFERENCE
RECITATION FOR STAT4206GU PROGRAMMING FOR DATA SCIENCE
Prerequisites: At least one semester, and preferably two, of calculus. An introductory course (STAT UN1201, preferably) is strongly recommended. A calculus-based introduction to probability theory. A quick review of multivariate calculus is provided. Topics covered include random variables, conditional probability, expectation, independence, Bayes’ rule, important distributions, joint distributions, moment generating functions, central limit theorem, laws of large numbers and Markov’s inequality.
Prerequisites: STAT GU4203. At least one semester of calculus is required; two or three semesters are strongly recommended. Calculus-based introduction to the theory of statistics. Useful distributions, law of large numbers and central limit theorem, point estimation, hypothesis testing, confidence intervals maximum likelihood, likelihood ratio tests, nonparametric procedures, theory of least squares and analysis of variance.
Prerequisites: STAT GU4204 or the equivalent, and a course in linear algebra. Theory and practice of regression analysis. Simple and multiple regression, testing, estimation, prediction, and confidence procedures, modeling, regression diagnostics and plots, polynomial regression, colinearity and confounding, model selection, geometry of least squares. Extensive use of the computer to analyse data.
Prerequisites: STAT GU4204 and GU4205 or the equivalent. Introduction to programming in the R statistical package: functions, objects, data structures, flow control, input and output, debugging, logical design, and abstraction. Writing code for numerical and graphical statistical analyses. Writing maintainable code and testing, stochastic simulations, paralleizing data analyses, and working with large data sets. Examples from data science will be used for demonstration.
Prerequisites: STAT GU4203 and two, preferably three, semesters of calculus. Review of elements of probability theory. Poisson processes. Renewal theory. Walds equation. Introduction to discrete and continuous time Markov chains. Applications to queueing theory, inventory models, branching processes.
Modern statistics and machine learning rely heavily on optimization. Estimation, inference, and prediction often reduce to solving structured optimization problems such as least squares, maximum likelihood estimation, regularized regression, empirical risk minimization, and variational inference. This course introduces the optimization principles underlying modern statistical and machine learning methods. Students will study convex optimization, gradient-based algorithms, stochastic optimization, and large-scale learning problems, with applications to regression, classification, deep learning, and probabilistic modeling.
Prerequisites: STAT GU4205 or the equivalent. Least squares smoothing and prediction, linear systems, Fourier analysis, and spectral estimation. Impulse response and transfer function. Fourier series, the fast Fourier transform, autocorrelation function, and spectral density. Univariate Box-Jenkins modeling and forecasting. Emphasis on applications. Examples from the physical sciences, social sciences, and business. Computing is an integral part of the course.
Prerequisites: STAT GU4204 or the equivalent. Statistical inference without parametric model assumption. Hypothesis testing using ranks, permutations, and order statistics. Nonparametric analogs of analysis of variance. Non-parametric regression, smoothing and model selection.
This course introduces the Bayesian paradigm for statistical inference. Topics covered include prior and posterior distributions: conjugate priors, informative and non-informative priors; one- and two-sample problems; models for normal data, models for binary data, Bayesian linear models; Bayesian computation: MCMC algorithms, the Gibbs sampler; hierarchical models; hypothesis testing, Bayes factors, model selection; use of statistical software.
Prerequisites: A course in the theory of statistical inference, such as STAT GU4204 a course in statistical modeling and data analysis, such as STAT GU4205.
Prerequisites: STAT GU4205 or the equivalent. Survival distributions, types of censored data, estimation for various survival models, nonparametric estimation of survival distributions, the proportional hazard and accelerated lifetime models for regression analysis with failure-time data. Extensive use of the computer.
Prerequisites: STAT GU4204 or the equivalent. Introductory course on the design and analysis of sample surveys. How sample surveys are conducted, why the designs are used, how to analyze survey results, and how to derive from first principles the standard results and their generalizations. Examples from public health, social work, opinion polling, and other topics of interest.
This course is an introduction to Causal Inference at the masters and advanced undergraduate
level. Students will be introduced to a broad range of causal inference methods including randomized
experiments, observational studies, instrumental variables, di?erence-in-di?erences,
regression discontinuity design, and synthetic controls. In addition, the course will cover modern,
controversial debates regarding the foundations and limitations of causal inference.
The primary learning goal of this course will be to familiarize students with a variety of the
most popular causal inference methods: which causal e?ects they seek to estimate, basic assumptions
required for identi?cation and estimation, and their practical implementation. To
this end, the course will focus both on developing the pre-requisite statistical / methodological
theory and as well as gaining hands-on experience through implementation exercises with
real datasets. By the end of the course, students should have deep familiarity of various causal
inference methods and—more importantly—be able to determine which method is most appropriate
for a given applied problem and to judge whether the pre-requisite identifying conditions
are appropriate.
Prerequisites: STAT GU4206. The course will provide an introduction to Machine Learning and its core models and algorithms. The aim of the course is to provide students of statistics with detailed knowledge of how Machine Learning methods work and how statistical models can be brought to bear in computer systems - not only to analyze large data sets, but to let computers perform tasks that traditional methods of computer science are unable to address. Examples range from speech recognition and text analysis through bioinformatics and medical diagnosis. This course provides a first introduction to the statistical methods and mathematical concepts which make such technologies possible.
Project-based topics course in data science and artificial intelligence. Students build a portfolio by implementing and applying modern data science methods.
Prerequisites: STAT GU4205 or the equivalent. A fast-paced introduction to statistical methods used in quantitative finance. Financial applications and statistical methodologies are intertwined in all lectures. Topics include regression analysis and applications to the Capital Asset Pricing Model and multifactor pricing models, principal components and multivariate analysis, smoothing techniques and estimation of yield curves statistical methods for financial time series, value at risk, term structure models and fixed income research, and estimation and modeling of volatilities. Hands-on experience with financial data.
Prerequisites: STAT GU4204 or the equivalent. STAT GU4205 is recommended. Modeling and inference for random processes, from natural sciences to finance and economics. ARMA, ARCH, GARCH and nonlinear models, parameter estimation, prediction and filtering. This is a core course in the MS program in mathematical finance.
Prerequisites: STAT GU4203. STAT GU4207 is recommended. Basics of continuous-time stochastic processes. Wiener processes. Stochastic integrals. Ito's formula, stochastic calculus. Stochastic exponentials and Girsanov's theorem. Gaussian processes. Stochastic differential equations. Additional topics as time permits.
Prerequisites: STAT GU4264. Mathematical theory and probabilistic tools for modeling and analyzing security markets are developed. Pricing options in complete and incomplete markets, equivalent martingale measures, utility maximization, term structure of interest rates. This is a core course in the MS program in mathematical finance.
Prerequisites: STAT GU4205 and at least one statistics course numbered between GU4221 and GU4261. This is a course on getting the most out of data. The emphasis will be on hands-on experience, involving case studies with real data and using common statistical packages. The course covers, at a very high level, exploratory data analysis, model formulation, goodness of fit testing, and other standard and non-standard statistical procedures, including linear regression, analysis of variance, nonlinear regression, generalized linear models, survival analysis, time series analysis, and modern regression methods. Students will be expected to propose a data set of their choice for use as case study material.
Topics in Modern Statistics will provide MA Statistics students with an opportunity to study a specialized area of statistics in more depth and to meet the educational needs of a rapidly growing field.
Topics in Modern Statistics will provide MA Statistics students with an opportunity to study a specialized area of statistics in more depth and to meet the educational needs of a rapidly growing field.
Topics in Modern Statistics will provide MA Statistics students with an opportunity to study a specialized area of statistics in more depth and to meet the educational needs of a rapidly growing field.
This is a rigorous introduction to machine learning from a statistical perspective. While we will cover many of the same introductory elements of machine learning as courses in other departments, the statistical perspective emphasizes the distinction between spurious trends or patterns observed in data, and more stable patterns present in the actual population the data is drawn from. For instance, in prediction problems, while two variables might appear related in observed data, such relation might not be generalizable to the population. Such statistical perspective on ‘generalization’ from sample to population is fundamental to the design of prediction algorithms in modern machine learning, in addition to computational constraints. The course aims to explain how ‘generalization’ together with ‘computation’ drives every aspect of machine learning, from modeling assumptions, to common optimization procedures.
Major families of algorithms will be covered, from unsupervised procedures for clustering, to supervised procedures for classification and regression, along with an introduction to common optimization techniques. The course requires a good preparation in calculus up to multivariate calculus, and good understanding of linear algebra, and familiarity with basic probability and statistics. At the end of the course, students would be expected to have gained a sense of common approaches in ML, and importantly, the assumptions (on the data and the population) under which such approaches operate.
RECITATION FOR STAT5206 PROGRAMMING FOR DATA SCIENCE
Prerequisites: At least one semester of calculus. A calculus-based introduction to probability theory. Topics covered include random variables, conditional probability, expectation, independence, Bayes rule, important distributions, joint distributions, moment generating functions, central limit theorem, laws of large numbers and Markovs inequality.
Prerequisites: STAT GR5203 or the equivalent, and two semesters of calculus. Calculus-based introduction to the theory of statistics. Useful distributions, law of large numbers and central limit theorem, point estimation, hypothesis testing, confidence intervals, maximum likelihood, likelihood ratio tests, nonparametric procedures, theory of least squares and analysis of variance.
Prerequisites: STAT GR5203 and GR5204 or the equivalent. Theory and practice of regression analysis, Simple and multiple regression, including testing, estimation, and confidence procedures, modeling, regression diagnostics and plots, polynomial regression, colinearity and confounding, model selection, geometry of least squares. Extensive use of the computer to analyse data.
Course Overview:
This course introduces Python programming, covering data structures, control-flow, objects, and functions, along with libraries like re, requests, numpy, pandas, scikit-learn, scipy, and more. These skills are applied to real-world data science tasks, including AB testing, data manipulation, modeling, optimization, simulations, and data visualization.
Students will develop computational thinking abilities, including problem decomposition, pattern recognition, data representation, abstraction, and algorithm design, through practical exercises.
Corequisites: GR5203 or the equivalent. Review of elements of probability theory. Poisson processes. Renewal theory. Walds equation. Introduction to discrete and continuous time Markov chains. Applications to queueing theory, inventory models, branching processes.
Prerequisites: STAT GR5205 Least squares smoothing and prediction, linear systems, Fourier analysis, and spectral estimation. Impulse response and transfer function. Fourier series, the fast Fourier transform, autocorrelation function, and spectral density. Univariate Box-Jenkins modeling and forecasting. Emphasis on applications. Examples from the physical sciences, social sciences, and business. Computing is an integral part of the course.
Prerequisites: STAT GR5205 Statistical inference without parametric model assumption. Hypothesis testing using ranks, permutations, and order statistics. Nonparametric analogs of analysis of variance. Non-parametric regression, smoothing and model selection.
This course introduces the Bayesian paradigm for statistical inference. Topics covered include prior and posterior distributions: conjugate priors, informative and non-informative priors; one- and two-sample problems; models for normal data, models for binary data, Bayesian linear models, Bayesian computation: MCMC algorithms, the Gibbs sampler; hierarchical models; hypothesis testing, Bayes factors, model selection; use of statistical software.
Prerequisites: A course in the theory of statistical inference, such as STAT GU4204/GR5204 a course in statistical modeling and data analysis such as STAT GU4205/GR5205.
Prerequisites: STAT GR5205 Survival distributions, types of censored data, estimation for various survival models, nonparametric estimation of survival distributions, the proportional hazard and accelerated lifetime models for regression analysis with failure-time data. Extensive use of the computer.
Prerequisites: STAT GR5204 Introductory course on the design and analysis of sample surveys. How sample surveys are conducted, why the designs are used, how to analyze survey results, and how to derive from first principles the standard results and their generalizations. Examples from public health, social work, opinion polling, and other topics of interest.
This course is an introduction to Causal Inference at the masters level. Students will be introduced to a broad range of causal inference methods including randomized
experiments, observational studies, instrumental variables, di?erence-in-di?erences, regression discontinuity design, and synthetic controls. In addition, the course will cover modern, controversial debates regarding the foundations and limitations of causal inference.
The primary learning goal of this course will be to familiarize students with a variety of the most popular causal inference methods: which causal e?ects they seek to estimate, basic assumptions required for identi?cation and estimation, and their practical implementation. To this end, the course will focus both on developing the pre-requisite statistical / methodological theory and as well as gaining hands-on experience through implementation exercises with real datasets. By the end of the course, students should have deep familiarity of various causal inference methods and—more importantly—be able to determine which method is most appropriate
for a given applied problem and to judge whether the pre-requisite identifying conditions are appropriate.
Prerequisites: STAT GR5206 or the equivalent. The course will provide an introduction to Machine Learning and its core models and algorithms. The aim of the course is to provide students of statistics with detailed knowledge of how Machine Learning methods work and how statistical models can be brought to bear in computer systems - not only to analyze large data sets, but to let computers perform tasks that traditional methods of computer science are unable to address. Examples range from speech recognition and text analysis through bioinformatics and medical diagnosis. This course provides a first introduction to the statistical methods and mathematical concepts which make such technologies possible.
Project-based topics course in data science and artificial intelligence. Students build a portfolio by implementing and applying modern data science methods.
Prerequisites: STAT GR5204 or the equivalent. STAT GR5205 is recommended. A fast-paced introduction to statistical methods used in quantitative finance. Financial applications and statistical methodologies are intertwined in all lectures. Topics include regression analysis and applications to the Capital Asset Pricing Model and multifactor pricing models, principal components and multivariate analysis, smoothing techniques and estimation of yield curves statistical methods for financial time series, value at risk, term structure models and fixed income research, and estimation and modeling of volatilities. Hands-on experience with financial data.
Available to SSP, SMP Modeling and inference for random processes, from natural sciences to finance and economics. ARMA, ARCH, GARCH and nonlinear models, parameter estimation, prediction and filtering.
Prerequisites: STAT GR5203 or the equivalent. Basics of continuous-time stochastic processes. Wiener processes. Stochastic integrals. Ito's formula, stochastic calculus. Stochastic exponentials and Girsanov's theorem. Gaussian processes. Stochastic differential equations. Additional topics as time permits.
Prerequisites: STAT GR5264 Available to SSP, SMP. Mathematical theory and probabilistic tools for modeling and analyzing security markets are developed. Pricing options in complete and incomplete markets, equivalent martingale measures, utility maximization, term structure of interest rates.
Course Description
STAT GR5291 Advanced Data Analysis serves as one of the required capstone experiences for MA students in statistics. This course is project-based and covers advanced topics in traditional data analysis. Students are presented with a mix of theory and application in homework assignments. The final project is a major contribution to the final grade and is arguably considered the capstone project for the MA in Statistics Program.
Students will learn a myriad of topics related to data analysis and hypothesis testing, and are responsible for application through statistical packages or manual programming. Topics include, exploratory data analysis & descriptive statistics, review of sampling distribution, point estimation, review of hypothesis testing & confidence interval procedures, non-parametric tests, computational methods (Monte Carlo, bootstrap, permutation tests), categorical data analysis, linear regression, diagnostics & residual analysis, robust regression, model selection, non-linear regression & smoothers, aspects of experimental design (ANOVA, two-way ANOVA, blocking, multiple comparisons, ANCOVA, semi-parametric procedures, random effects models, mixed effects models, nested models, repeated measures), and general linear models (logistic regression, penalized logistic, multinomial regression, link functions).
Also, time permitting the class covers:
survival analysis (hazard function, survival curve), time series analysis (stationarity, ACF/PACF, MA, AR, ARMA, ARIMA, order selection, forecasting).
Topics in Modern Statistics will provide MA Statistics students with an opportunity to study a specialized area of statistics in more depth and to meet the educational needs of a rapidly growing field.
Topics in Modern Statistics will provide MA Statistics students with an opportunity to study a specialized area of statistics in more depth and to meet the educational needs of a rapidly growing field.
Topics in Modern Statistics will provide MA Statistics students with an opportunity to study a specialized area of statistics in more depth and to meet the educational needs of a rapidly growing field.
Topics in Modern Statistics will provide MA Statistics students with an opportunity to study a specialized area of statistics in more depth and to meet the educational needs of a rapidly growing field.
TOPICS IN MACHINE LEARNING AND AI will provide MA Statistics students with an opportunity to study specialized areas of statistics in more depth and to meet the educational needs of a rapidly growing field.