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.

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 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: 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.

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.

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: 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.

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.

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: 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.

This course is an optional companion lab course for GR5242 Advanced Machine Learning.  The aim of this course is to help students acquire the basic computational skills in a python-based Deep Learning library (such as Troch, TensorFlow) to implement deep learning models.  lab class materials will be aligned closely with the topics covered in GR5242.  Google Colab will be used as the main tools for the hands-on lab exercises.

This course is an optional companion lab course for GR5242 Advanced Machine Learning.  The aim of this course is to help students acquire the basic computational skills in a python-based Deep Learning library (such as Troch, TensorFlow) to implement deep learning models.  lab class materials will be aligned closely with the topics covered in GR5242.  Google Colab will be used as the main tools for the hands-on lab exercises.

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.

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.

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.

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 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.

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.

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

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