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.

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 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.

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.

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.

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: the project mentors permission. This course provides a mechanism for students who undertake research with a faculty member from the Department of Statistics to receive academic credit. Students seeking research opportunities should be proactive and entrepreneurial: identify congenial faculty whose research is appealing, let them know of your interest and your background and skills.

Topics in Modern Statistics that provide undergraduate 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. Courses listed are reviewed and approved by the Undergraduate Advisory Committee of the Department of Statistics. A good working knowledge of basic statistical concepts (likelihood,
Bayes' rule, Poisson processes, Markov chains, Gaussian random vectors), including especially linear-algebraic concepts related to regression and principal components analysis, is necessary. No previous experience with neural data is required.

Course Description: This course focuses on discovering patterns, relationships, and insights in real-world data through exploratory techniques.

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.

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 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: Pre-requisite for this course includes working knowledge in Statistics and Probability, data mining, statistical modeling and machine learning. Prior programming experience in R or Python is required. This course will incorporate knowledge and skills covered in a statistical curriculum with topics and projects in data science. Programming will be covered using existing tools in R. Computing best practices will be taught using test-driven development, version control, and collaboration. Students finish the class with a portfolio of projects, and deeper understanding of several core statistical/machine-learning algorithms. Short project cycles throughout the semester provide students extensive hands-on experience with various data-driven applications.

Prerequisites: Pre-requisite for this course includes working knowledge in Statistics and Probability, data mining, statistical modeling and machine learning. Prior programming experience in R or Python is required. This course will incorporate knowledge and skills covered in a statistical curriculum with topics and projects in data science. Programming will be covered using existing tools in R. Computing best practices will be taught using test-driven development, version control, and collaboration. Students finish the class with a portfolio of projects, and deeper understanding of several core statistical/machine-learning algorithms. Short project cycles throughout the semester provide students extensive hands-on experience with various data-driven applications.

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.

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.

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.

Corequisites: STAT GR5204 and GR5205 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 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.

Prerequisites: Pre-requisite for this course includes working knowledge in Statistics and Probability, data mining, statistical modeling and machine learning. Prior programming experience in R or Python is required. This course will incorporate knowledge and skills covered in a statistical curriculum with topics and projects in data science. Programming will covered using existing tools in R. Computing best practices will be taught using test-driven development, version control, and collaboration. Students finish the class with a portfolio of projects, and deeper understanding of several core statistical/machine-learning algorithms. Short project cycles throughout the semester provide students extensive hands-on experience with various data-driven applications.

Prerequisites: Pre-requisite for this course includes working knowledge in Statistics and Probability, data mining, statistical modeling and machine learning. Prior programming experience in R or Python is required. This course will incorporate knowledge and skills covered in a statistical curriculum with topics and projects in data science. Programming will covered using existing tools in R. Computing best practices will be taught using test-driven development, version control, and collaboration. Students finish the class with a portfolio of projects, and deeper understanding of several core statistical/machine-learning algorithms. Short project cycles throughout the semester provide students extensive hands-on experience with various data-driven applications.

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).

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).

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).

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.

This course covers topics in statistical finance, with a focus on methodological and practical problems. Topics will include an overview of common financial data, regression and machine learning methods in prediction, models of volatility and covariance, and a survey of topics in risk management and portfolio construction.

This course covers topics in statistical finance, with a focus on methodological and practical problems. Topics will include an overview of common financial data, regression and machine learning methods in prediction, models of volatility and covariance, and a survey of topics in risk management and portfolio construction.

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 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 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 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.

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

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

.This seminar explores the principle of invariance and its role in causal reasoning. We will study algorithms that connect invariance to causality, how these ideas extend to representation learning, and examine applications across the sciences and social sciences. Some subjects will include invariant causal prediction, causal representation learning, robust learning from multiple environments, and empirical Bayes.

.

Departmental colloquium in probability theory.

A colloquiim in applied probability and risk.

A colloquium on topics in mathematical finance