Statistics

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.

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 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.

RECITATION FOR STAT1101UN INTRODUCTION TO STATISTICS

RECITATION FOR STAT1101UN INTRODUCTION TO STATISTICS

RECITATION FOR STAT1101UN INTRODUCTION TO STATISTICS

RECITATION FOR STAT1101UN INTRODUCTION TO STATISTICS

RECITATION FOR STAT1101UN INTRODUCTION TO STATISTICS

RECITATION FOR STAT1101UN INTRODUCTION TO STATISTICS

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.

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 STAT1201UN CALC-BASED INTRODUCTION TO STATISTICS  

RECITATION FOR STAT1201UN CALC-BASED INTRODUCTION TO STATISTICS  

RECITATION FOR STAT1201UN CALC-BASED INTRODUCTION TO STATISTICS  

RECITATION FOR STAT1201UN CALC-BASED INTRODUCTION TO STATISTICS  

RECITATION FOR STAT2102UN APPLIED STATISTICAL COMPUTING

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 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: 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.

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 STAT4203GU PROBABILITY THEORY 

RECITATION FOR STAT4203GU PROBABILITY THEORY 

RECITATION FOR STAT4204GU STATISTICAL INFERENCE

RECITATION FOR STAT4204GU STATISTICAL INFERENCE

RECITATION FOR STAT4204GU STATISTICAL INFERENCE

RECITATION FOR STAT4206GU PROGRAMMING FOR DATA SCIENCE

RECITATION FOR STAT4206GU PROGRAMMING FOR DATA SCIENCE

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 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.

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.

Project-based topics course in data science and artificial intelligence. Students build a portfolio by implementing and applying modern data science methods.

Project-based topics course in data science and artificial intelligence. Students build a portfolio by implementing and applying modern data science methods.

Agentic AI promises to accelerate progress across multiple scientific fields. At the same time, large open data sets hold the promise of scientific discovery open to all. In the hands of experts, or in some verifiable domains, agentic tools can significantly accelerate scientific discovery. This leaves open an important question: can current agentic tools enable scientific discovery in non-verifiable domains, and without significant prior subject expertise? 

This class will explore these questions, focusing on an exciting recent large open dataset from the International Brain Laboratory: the Brainwide Map dataset, mapping neural activity in the context of a visual decision behavior across many thousands of neurons in the mouse brain. This is a well-curated, well-documented, large, and very rich dataset, equipped with existing agentic skill files: in short, a perfect testbed for big open agentic science. We will introduce the dataset, agentic toolset, and relevant scientific background, and pursue novel discoveries together, with an eye towards documenting our experience and improving the open-source tools as we go.

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

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.

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.

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.

Project-based topics course in data science and artificial intelligence. Students build a portfolio by implementing and applying modern data science methods.

Project-based topics course in data science and artificial intelligence. Students build a portfolio by implementing and applying modern data science methods.

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.

This course provides a rigorous statistical framework for measuring and managing financial risk. While the course follows the industry-standard workflow defined by the Financial Risk Manager (FRM) designation, it treats risk measurement as a statistical inference problem. Students will learn the standard industry metrics (Value-at-Risk, Expected Shortfall) and the mathematical theory required to implement them robustly. Key topics include Volatility Forecasting (GARCH), Extreme Value Theory (EVT) for heavy-tailed losses, Copulas for non-linear dependence, and Monte Carlo simulation methods.

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 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.

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.

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.

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.

This upcoming fall, we are going to kick off the “Practitioners Seminar” course, where successful practitioners from various industry fields (tech, finance, insurance, pharmaceutical, etc..) will have a chance to meet our students and present the projects they work on, technologies they utilize to achieve their goals, solutions they came up with etc. In addition, guest speakers will share their career development path (what kind of obstacles they faced, what pitfalls to avoid, and in general give advice on career development in their fields). We will finish up the meeting with a Q&A session with students.

This course is intended to provide a mechanism to MA students in Statistics who undertake on-campus project work or research. The course may be signed up with a faculty member from the Department of Statistics for academic credit. Students seeking to enroll in the course should identify an on-campus project and a congenial faculty member whose research is appealing to them, and who are able to serve as their mentor. Students should then submit an application to enroll in this course, which will be reviewed and approved by the Faculty Director of the MA in Statistics program.

Each year, approximately 10–15% of MA in Statistics students participate in on-campus academic research, contributing to advances in statistical methodology and applied areas. Some projects demonstrate exceptional promise and benefit from additional time and support for further development. The MA Research Specialization in Statistics allows qualified students to extend their MA program to a fourth semester to continue their research under the supervision of a faculty mentor. This competitive, merit-based program requires demonstrated research progress, a nomination from a faculty mentor, and an outstanding academic record. STAT GR5999 serves as the course through which students admitted to the MA Research Specialization fulfill their research requirements.

Prerequisites: STAT GR6101 Continuation of STAT GR6101.

Prerequisites: STAT GR6102 or instructor permission. The Deparatments doctoral student consulting practicum. Students undertake pro bono consulting activities for Columbia community researchers under the tutelage of a faculty mentor.

Prerequisites: STAT GR6201 Continuation of STAT G6201

Departmental colloquium in probability theory.

A colloquiim in applied probability and risk.

A colloquium on topics in mathematical finance