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 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.

This is only recitation for STAT UG1101. We are requesting 8 sections of recitation to align with the two sections of 1101 offered for Fall 2024. 

This is only recitation for STAT UG1101. We are requesting 8 sections of recitation to align with the two sections of 1101 offered for Fall 2024. 

This is only recitation for STAT UG1101. We are requesting 8 sections of recitation to align with the two sections of 1101 offered for Fall 2024. 

This is only recitation for STAT UG1101. We are requesting 8 sections of recitation to align with the two sections of 1101 offered for Fall 2024. 

This is only recitation for STAT UG1101. We are requesting 8 sections of recitation to align with the two sections of 1101 offered for Fall 2024. 

This is only recitation for STAT UG1101. We are requesting 8 sections of recitation to align with the two sections of 1101 offered for Fall 2024. 

This is only recitation for STAT UG1101. We are requesting 8 sections of recitation to align with the two sections of 1101 offered for Fall 2024. 

This is only recitation for STAT UG1101. We are requesting 8 sections of recitation to align with the two sections of 1101 offered for Fall 2024. 

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.

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.

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.

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.

This course provides a non-mathematical introduction to the principles and architectures of deep learning and generative AI models. Designed for undergraduates in the Applied Data Science minor, the curriculum covers the mathematical foundations of neural networks and their application to spatial, temporal, and multimodal data. Students will examine the mechanics of convolutional and recurrent architectures, the self-attention mechanism in Transformers, and the training objectives of Large Language Models (LLMs). The course also addresses optimization strategies, reinforcement learning for model alignment, and generative paradigms, including diffusion and autoregressive models. Emphasis is placed on understanding model internal representations, architectural tradeoffs, and the evaluation of complex AI systems.

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.

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.

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.

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.

This course covers various topics in advanced machine learning. Topics may include optimization algorithms, Python libraries for ML, principles for applied supervised and unsupervised learning, hyperparameter selection, computational trade-offs, modern neural network architectures such as ConvNets, LSTMs, and transformers for computer vision and natural language processing, and deep learning for LLMs.

This course covers various topics in advanced machine learning. Topics may include optimization algorithms, Python libraries for ML, principles for applied supervised and unsupervised learning, hyperparameter selection, computational trade-offs, modern neural network architectures such as ConvNets, LSTMs, and transformers for computer vision and natural language processing, and deep learning for LLMs.

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

Description. Unsupervised Learning is a masters level course on foundations, methods, practice, and applications in machine learning from data without associated labels or outcomes.  This course will focus on dimension reduction and clustering techniques while also covering graphical models, missing data imputation, anomaly detection, generative models, and others. The course will also emphasize conceptual understanding and practical applications of unsupervised learning in data visualization, exploratory data analysis, data pre-processing, and data-driven discovery.   

Topics in Modern Statistics provide students with an opportunity to study a specialized area of statistics in more depth to meet the educational needs of a rapidly changing field.

Topics in Modern Statistics provide students with an opportunity to study a specialized area of statistics in more depth to meet the educational needs of a rapidly changing field.

Topics in Modern Statistics provide students with an opportunity to study a specialized area of statistics in more depth to meet the educational needs of a rapidly changing field.

Topics in Modern Statistics provide students with an opportunity to study a specialized area of statistics in more depth to meet the educational needs of a rapidly changing field.

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: 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 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.

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.

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.

Description. Unsupervised Learning is a masters level course on foundations, methods, practice, and applications in machine learning from data without associated labels or outcomes.  This course will focus on dimension reduction and clustering techniques while also covering graphical models, missing data imputation, anomaly detection, generative models, and others. The course will also emphasize conceptual understanding and practical applications of unsupervised learning in data visualization, exploratory data analysis, data pre-processing, and data-driven discovery.   

Prerequisites.

STAT GR 5206 Statistical Computing and Intro to Data Science

STAT GR 5241 Statistical Machine Learning (strongly recommended)

STAT GR 5205 Linear Regression (recommended)

STAT GR 5203 Probability (recommended)

Students should also be familiar with linear algebra.

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.

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 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 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.

The course aims to teach MA in Statistics students how to manage their careers and develop professionally. Topics include resume and cover-letter writing, negotiation, mentoring, interviewing skills and communication across global teams. Top professionals from across the globe speak to students and help improve leadership skills. 

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.

This high-level course in linear regression delves deeply into the theoretical and geometric aspects of regression analysis, offering a comprehensive exploration of its foundational principles and advanced topics. Students will study regression within vector space contexts, emphasizing the role of inner products and orthogonal projections. The analysis of projection matrices will include their properties, such as idempotence and symmetry, and their implications for regression diagnostics and metrics. Students will explore why various test statistics follow t- and F-distributions, with careful attention to degrees of freedom and their derivations. As the course progresses, it will address the complexities of high dimensional regression scenarios.

This course is an introduction to probability and statistics for data science. Topics
include probability theory, probability distributions, simulations, parameters estima-
tion, hypothesis testing, simple regression. Python examples will be used throughout
the course for illustrations.

This course is an introduction to probability and statistics for data science. Topics
include probability theory, probability distributions, simulations, parameters estima-
tion, hypothesis testing, simple regression. Python examples will be used throughout
the course for illustrations.

This course is an introduction to probability and statistics for data science. Topics
include probability theory, probability distributions, simulations, parameters estima-
tion, hypothesis testing, simple regression. Python examples will be used throughout
the course for illustrations.

This course covers the following topics: Fundamentals of probability theory and statistical inference used in data science; Probabilistic models, random variables, useful distributions, expectations, law of large numbers, central limit theorem; Statistical inference; point and confidence interval estimation, hypothesis tests, linear regression.

This course covers the following topics: Fundamentals of probability theory and statistical inference used in data science; Probabilistic models, random variables, useful distributions, expectations, law of large numbers, central limit theorem; Statistical inference; point and confidence interval estimation, hypothesis tests, linear regression.

This course is covers the following topics: fundamentals of data visualization, layered grammer of graphics, perception of discrete and continuous variables, intreoduction to Mondran, mosaic pots, parallel coordinate plots, introduction to ggobi, linked pots, brushing, dynamic graphics, model visualization, clustering and classification.

This course is covers the following topics: fundamentals of data visualization, layered grammer of graphics, perception of discrete and continuous variables, intreoduction to Mondran, mosaic pots, parallel coordinate plots, introduction to ggobi, linked pots, brushing, dynamic graphics, model visualization, clustering and classification.

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 GR6102 Modern Bayesian methods offer an amazing toolbox for solving science and engineering problems. We will go through the book Bayesian Data Analysis and do applied statistical modeling using Stan, using R (or Python or Julia if you prefer) to preprocess the data and postprocess the analysis. We will also discuss the relevant theory and get to open questions in model building, computing, evaluation, and expansion. The course is intended for students who want to do applied statistics and also those who are interested in working on statistics research problems.

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 G6201 and STAT G6201 This course will mainly focus on nonparametric methods in statistics. A tentavie list of topics to be covered include nonparametric density and regression function estimation -- upper bounds on the risk of kernel estimators and matching lower bounds on the minimax risk, reproducing kernel Hilbert spaces, bootstrap and resampling methods, multiple hypothesis testing, and high dimensional stastistical analysis.

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

Independent Study with Faculty Advisor must be registered for every semester after first academic year

.

Departmental colloquium in probability theory.

A colloquiim in applied probability and risk.

A colloquium on topics in mathematical finance