# Statistics

**The Statistics Department Office:**

1005 School of Social Work (1255 Amsterdam Avenue); 212-851-2132

http://www.stat.columbia.edu

**Statistics Major and Concentration Advising:**

Ronald Neath, 612 Watson; 212-853-1398; rcn2112@columbia.edu

Gabriel Young, 610 Watson; 212-853-1395; gjy2107@columbia.edu

**Data Science Major Advising:**

*Computer Science: *Augustin Chaintreau, 610 CEPSR; 212-939-7082; augustin@cs.columbia.edu

*Statistics: *Ronald Neath, 612 Watson; 212-853-1398; rcn2112@columbia.edu

*Statistics: *Gabriel Young, 610 Watson; 212-853-1395; gjy2107@columbia.edu

**Economics - Statistics Major Advising:**

*Economics: *Susan Elmes, 1006 IAB; 212-854-9124; se5@columbia.edu

*Statistics: *Ronald Neath, 612 Watson; 212-853-1398; rcn2112@columbia.edu

*Statistics: *Gabriel Young, 610 Watson; 212-853-1395; gjy2107@columbia.edu

**Mathematics - Statistics Major Advising:**

*Mathematics: *Julien Dubedat, 601 Mathematics; 212-854-8806; jd2653@columbia.edu

*Statistics: *Ronald Neath, 612 Watson; 212-853-1398; rcn2112@columbia.edu

*Statistics: *Gabriel Young, 610 Watson; 212-853-1395; gjy2107@columbia.edu

**Political Science - Statistic Major Advising:**

*Political Science: *Alessandra Casella, 1030 IAB; 212-854-8059; acasella@columbia.edu

*Statistics: *Ronald Neath, 612 Watson; 212-853-1398; rcn2112@columbia.edu

*Statistics: *Gabriel Young, 610 Watson; 212-853-1395; gjy2107@columbia.edu

**Department Administrator:**

Dood Kalicharan, 1003 School of Social Work; 212-851-2130; dk@stat.columbia.edu

The Department offers several introductory courses. Students interested in statistical concepts, who plan on consuming, but not creating statistics, should take STAT UN1001 Introduction to Statistical Reasoning. The course is designed for students who have taken a pre-calculus course, and the focus is on general principles. It is suitable for students seeking to satisfy the Barnard quantitative reasoning requirements. Students seeking an introduction to applied statistics should take STAT UN1101 Introduction to Statistics. The course is designed for students who have some mathematical maturity, but who may not have taken a course in calculus, and the focus is on the elements of data analysis. It is recommended for pre-med students, and students contemplating the concentration in statistics. Students seeking a foundation for further study of probability theory and statistical theory and methods should take STAT UN1201 Calculus-Based Introduction to Statistics. The course is designed for students who have taken a semester of college calculus or the equivalent, and the focus is on preparation for a mathematical study of probability and statistics. It is recommended for students seeking to complete the prerequisite for econometrics, and for students contemplating the major in statistics. Students seeking a one-semester calculus-based survey of probability theory and statistical theory and methods should take STAT GU4001 Introduction to Probability and Statistics. This course is designed for students who have taken calculus, and is meant as a terminal course. It provides a somewhat abridged version of the more demanding sequence STAT GU4203 PROBABILITY THEORY and STAT GU4204 Statistical Inference. While some mathematically mature students take the more demanding sequence as an introduction to the field, it is generally recommended that students prepare for the sequence by taking STAT UN1201 Calculus-Based Introduction to Statistics.

The Department offers the Major in Statistics, the Concentration in Statistics, and interdisciplinary majors with Computer Science, Economics, Mathematics, and Political Science. The concentration is suitable for students preparing for work or study where substantial skills in data analysis are valued and may be taken without mathematical prerequisites. The concentration consists of a sequence of six courses in applied statistics, but students may substitute statistics electives numbered 4203 or above with permission of the concentration advisors. The major consists of mathematical and computational prerequisites, an introductory course, and five core courses in probability theory and theoretical and applied statistics together with three electives. The training in the undergraduate major is comparable to a masters degree in statistics.

Students may wish to consult the following guidelines when undertaking course planning. It is advisable to take STAT UN1101 Introduction to Statistics and STAT UN2102 Applied Statistical Computing before taking any of the more advanced concentration courses, STAT UN2103 Applied Linear Regression Analysis, STAT UN2104 Applied Categorical Data Analysis, STAT UN3105 Applied Statistical Methods, and STAT UN3106 Applied Data Mining. It is advisable to take STAT UN1201 Calculus-Based Introduction to Statistics, STAT GU4203 PROBABILITY THEORY, STAT GU4204 Statistical Inference, and STAT GU4205 Linear Regression Models in sequence. Courses in stochastic analysis should be preceded by STAT GU4203 PROBABILITY THEORY, and for many students, it is advisable to take STAT GU4207 Elementary Stochastic Processes before embarking on STAT GU4262 Stochastic Processes for Finance, STAT GU4264 STOCHASTC PROCSSES-APPLIC, or STAT GU4265 Stochastic Methods in Finance. Most of the statistics courses numbered from 4221 to 4234 are best preceded by STAT GU4205 Linear Regression Models. The data science courses STAT GU4206 Statistical Computing and Introduction to Data Science, STAT GU4241 Statistical Machine Learning, and STAT GU4242 Advanced Machine Learning should be taken in sequence.

## Advanced Placement

The Department offers three points of advanced credit for a score of 5 on the AP statistics exam. Students who are required to take an introductory statistics course for their major should check with their major advisor to determine whether this credit provides exemption from their requirement.

## Departmental Honors

Students are considered for department honors on the basis of GPA and the comprehensiveness and difficulty of their course work in the Department. The Department is generally permitted to nominate one tenth of graduating students for departmental honors.

## Undergraduate Research in Statistics and the Summer Internship

Matriculated students who will be undergraduates at Columbia College, Barnard College, the School of General Studies, or the School of Engineering and Applied Sciences may apply to the Department's summer internship program. The internship provides summer housing and a stipend. Students work with Statistics Department faculty mentors. Applicants should send a brief statement of interest and a copy of their transcript to Ms. Dood Kalicharan in the Statistics Department office by the end of March to be considered. If summer project descriptions are posted on the Department's website, please indicate in the statement of interest which project is of interest. Students seeking research opportunities with Statistics Department faculty during the academic year are advised to be entrepreneurial and proactive: identify congenial faculty whose research is appealing, request an opportunity to meet, and provide some indication of previous course work when asking for a project.

## Professors

- David Blei (with Computer Science)
- Mark Brown
- Richard R. Davis
- Victor H. de la Peña
- Andrew Gelman (with Political Science)
- Shaw-Hwa Lo
- David Madigan
- Liam Paninski
- Philip Protter
- Daniel Rabinowitz
- Michael Sobel
- Simon Tavaré
- Zhiliang Ying
- Ming Yuan
- Tian Zheng

## Associate Professors

- John Cunningham
- Yang Feng
- Jingchen Liu
- Marcel Nutz
- Peter Orbanz
- Bodhisattva Sen

## Assistant Professors

- Samory Kpotufe
- Arian Maleki
- Sumit Mukherjee
- Cynthia Rush

**Term Assistant Professors**

- Marco Avella
- Ruimeng Hu
- Linxi Liu
- Thibault Vatter

## Adjunct Professors

- Demissie Alemayehu
- Flavio Bartmann
- Guy Cohen
- Regina Dolgoarshinnykh
- Anthony Donoghue
- Vincent Dorie
- Hammou El Barmi
- Xiaofu He
- Irene Hueter
- Ying Liu
- Ha Nguyen
- Michael Shnaidman
- Larry Wright
- Rongning Wu

## Lecturers in Discipline

- Banu Baydil
- Wayne Lee
- Ronald Neath
- David Rios
- Joyce Robbins
- Gabriel Young

## Major in Statistics

*The requirements for this program were modified in March 2016. Students who declared this program before this date should contact the director of undergraduate studies for the department in order to confirm their options for major requirements.*

The major should be planned with the director of undergraduate studies. Courses taken for a grade of Pass/D/Fail, or in which the grade of D has been received, do not count toward the major. The requirements for the major are as follows:

Code | Title | Points |
---|---|---|

Mathematics and Computer Science Prerequisites | ||

MATH UN1101 | Calculus I | |

MATH UN1102 | Calculus II | |

MATH UN1201 | Calculus III | |

MATH UN2010 | Linear Algebra | |

One of the following five courses | ||

Honors Introduction to Computer Science | ||

Introduction to Computing for Engineers and Applied Scientists | ||

Introduction to Computer Science and Programming in MATLAB | ||

Applied Statistical Computing | ||

Introduction to Computer Science and Programming in Java | ||

Core courses in probability and statistics | ||

STAT UN1201 | Calculus-Based Introduction to Statistics | |

STAT GU4203 | PROBABILITY THEORY | |

STAT GU4204 | Statistical Inference | |

STAT GU4205 | Linear Regression Models | |

STAT GU4206 | Statistical Computing and Introduction to Data Science | |

STAT GU4207 | Elementary Stochastic Processes | |

Three approved electives in statistics or, with permission, a cognate field. |

- Students preparing for a career in actuarial science are encouraged to replace STAT GU4205 Linear Regression Models with STAT GU4282 Linear Regression and Time Series Methods, and should take as one of their electives STAT GU4281 Theory of Interest.
- Students preparing for graduate study in statistics are encouraged to replace two electives with MATH GU4061 INTRO MODERN ANALYSIS I and MATH GU4062 Introduction To Modern Analysis II .

## Concentration in Statistics

Courses taken for a grade of Pass/D/Fail, or in which the grade of D has been received, do not count towards the concentration. The requirements for the concentration are as follows.

Code | Title | Points |
---|---|---|

STAT UN1101 | Introduction to Statistics | |

STAT UN2102 | Applied Statistical Computing | |

STAT UN2103 | Applied Linear Regression Analysis | |

STAT UN2104 | Applied Categorical Data Analysis | |

STAT UN3105 | Applied Statistical Methods | |

STAT UN3106 | Applied Data Mining |

- Students may replace courses required for the concentration by approved Statistics Department courses.

## Minor in Statistics

Courses taken for a grade of Pass/D/Fail, or in which the grade of D, has been received do not count towards the minor. The requirements for the minor are as follows.

Code | Title | Points |
---|---|---|

STAT UN1101 | Introduction to Statistics | |

STAT UN2102 | Applied Statistical Computing | |

STAT UN2103 | Applied Linear Regression Analysis | |

STAT UN2104 | Applied Categorical Data Analysis | |

STAT UN3105 | Applied Statistical Methods | |

STAT UN3106 | Applied Data Mining |

- Students may replace courses required for the minor by approved Statistics Department courses.

## Major in Data Science

In response to the ever growing importance of "big data" in scientific and policy endeavors, the last few years have seen an explosive growth in theory, methods, and applications at the interface between computer science and statistics. The Statistics Department and the Department of Computer Science have responded with a joint-major that emphasizes the interface between the disciplines.

Courses taken for a grade of Pass/D/Fail, or in which the grade of D has been received, do not count toward the major. The requirements for the major are as follows:

Code | Title | Points |
---|---|---|

Mathematical Prerequisites | ||

Calculus I | ||

Calculus II | ||

Calculus III | ||

Linear Algebra | ||

Statistics Required Courses | ||

Calculus-Based Introduction to Statistics | ||

PROBABILITY THEORY | ||

Statistical Inference | ||

Linear Regression Models | ||

Statistical Machine Learning | ||

or COMS W4771 | Machine Learning | |

Statistics Electives | ||

Select two of the following courses: | ||

Applied Data Mining | ||

Statistical Computing and Introduction to Data Science | ||

Applied Data Science | ||

Bayesian Statistics | ||

Advanced Machine Learning | ||

Computer Science Introductory Courses | ||

Select one of the following courses: | ||

Introduction to Computer Science and Programming in Java | ||

Introduction to Computer Science and Programming in MATLAB | ||

Introduction to Computing for Engineers and Applied Scientists | ||

Honors Introduction to Computer Science | ||

And select one of the following courses: | ||

Data Structures in Java | ||

Data Structures with C/C++ | ||

Honors Data Structures and Algorithms | ||

Computer Science Required Courses | ||

Discrete Mathematics: Introduction to Combinatorics and Graph Theory | ||

Analysis of Algorithms I | ||

Computer Science Electives | ||

Select three of the following courses: | ||

Computer Science Theory | ||

Introduction to Computational Complexity | ||

Introduction to Computational Learning Theory | ||

Introduction to Databases | ||

Principles and Practice of Parallel Programming | ||

Any COMS W47xx course EXCEPT W4771 |

## Major in Economics-Statistics

Please read *Requirements for all Economics Majors, Concentrators, and Interdepartmental Majors* in the Economics section of this Bulletin.

Please read *Requirements for all Economics Majors, Concentrators, and Interdepartmental Majors* in the Economics section of this Bulletin.

The major in Economics-Statistics provides students with a grounding in economic theory comparable to that of the general economics major, but also exposes students to a more rigorous and extensive statistics training. This program is recommended for students with strong quantitative skills and for those contemplating graduate studies in economics.

Two advisers are assigned for the interdepartmental major, one in the Department of Economics and one in the Department of Statistics. The economics adviser can only advise on economics requirements and the statistics adviser can only advise on statistics requirements.

Students should be aware of the rules regarding the use of the Pass/D/Fail option. Courses in which a grade of D has been received do not count toward the major requirements.

The economics-statistics major requires a total of 59 points: 29 in economics, 15 points in statistics, 12 points in mathematics, and 3 points in computer science, as follows:

Code | Title | Points |
---|---|---|

Economics Core Courses | ||

Complete the Economics core courses. | ||

Economics Electives | ||

Select three electives at the 3000-level or above, of which no more than one may be a Barnard course. | ||

Mathematics | ||

Select one of the following sequences: | ||

MATH UN1101 - MATH UN1102 - MATH UN1201 - MATH UN2010 | Calculus I and Calculus II and Calculus III and Linear Algebra | |

MATH UN1101 - MATH UN1102 - MATH UN1205 - MATH UN2010 | Calculus I and Calculus II and Accelerated Multivariable Calculus and Linear Algebra | |

MATH UN1207 - MATH UN1208 | Honors Mathematics A and Honors Mathematics B | |

Statistics | ||

STAT UN1201 | Calculus-Based Introduction to Statistics | |

STAT GU4203 | PROBABILITY THEORY | |

STAT GU4204 | Statistical Inference | |

STAT GU4205 | Linear Regression Models | |

One elective from among courses numbered STAT GU4206 through GU4266. | ||

Computer Science | ||

Select one of the following courses: | ||

Introduction to Computer Science and Programming in Java | ||

Introduction to Computer Science and Programming in MATLAB | ||

Honors Introduction to Computer Science | ||

Introduction to Computing for Engineers and Applied Scientists | ||

Applied Statistical Computing | ||

Seminar | ||

ECON GU4918 | Seminar In Econometrics |

**Students who declared before Spring 2014:**

The requirements for this program were modified in 2014. Students who declared this program before Spring 2014 should contact the director of undergraduate studies for the department in order to confirm their options for major requirements.

## Major in Mathematics-Statistics

The program is designed to prepare the student for: (1) a career in industries such as finance and insurance that require a high level of mathematical sophistication and a substantial knowledge of probability and statistics; and (2) graduate study in quantitative disciplines. Students choose electives in finance, actuarial science, operations research, or other quantitative fields to complement requirements in mathematics, statistics, and computer science.

Courses taken for a grade of Pass/D/Fail, or in which the grade of D has been received, do not count toward the major. The requirements for the major are as follows:

Code | Title | Points |
---|---|---|

Mathematics | ||

Select one of the following sequences: | ||

MATH UN1101 | Calculus I | |

MATH UN1102 | Calculus II | |

MATH UN1201 | Calculus III | |

MATH UN2010 | Linear Algebra | |

MATH UN2500 | Analysis and Optimization | |

OR | ||

MATH UN1101 | Calculus I | |

MATH UN1102 | Calculus II | |

MATH UN1205 | Accelerated Multivariable Calculus | |

MATH UN2010 | Linear Algebra | |

MATH UN2500 | Analysis and Optimization | |

OR | ||

MATH UN1207 | Honors Mathematics A | |

MATH UN1208 | Honors Mathematics B | |

MATH UN2500 | Analysis and Optimization | |

Statistics required courses | ||

STAT UN1201 | Calculus-Based Introduction to Statistics | |

STAT GU4203 | PROBABILITY THEORY | |

STAT GU4204 | Statistical Inference | |

STAT GU4205 | Linear Regression Models | |

And select one of the following courses: | ||

STAT GU4207 | Elementary Stochastic Processes | |

STAT GU4262 | Stochastic Processes for Finance | |

STAT GU4264 | STOCHASTC PROCSSES-APPLIC | |

STAT GU4265 | Stochastic Methods in Finance | |

Computer Science | ||

Select one of the following courses: | ||

Introduction to Computer Science and Programming in Java | ||

Introduction to Computer Science and Programming in MATLAB | ||

Introduction to Computing for Engineers and Applied Scientists | ||

Honors Introduction to Computer Science | ||

or an advanced Computer Science offering in programming | ||

Electives | ||

An approved selection of three advanced courses in mathematics, statistics, applied mathematics, industrial engineering and operations research, computer science, or approved mathematical methods courses in a quantitative discipline. At least one elective must be a Mathematics Department course numbered 3000 or above. |

- Students interested in modeling applications are recommended to take MATH UN3027 Ordinary Differential Equations and MATH UN3028 Partial Differential Equations
- Students interested in finance are recommended to include among their electives,MATH GR5010 Introduction to the Mathematics of Finance, STAT GU4261 Statistical Methods in Finance, and STAT GU4221 Time Series Analysis.
- Students interested in graduate study in mathematics or in statistics are recommended to take MATH GU4061 INTRO MODERN ANALYSIS I and MATH GU4062 Introduction To Modern Analysis II.
- Students preparing for a career in actuarial science are encouraged to replace STAT GU4205 Linear Regression Models with STAT GU4282 Linear Regression and Time Series Methods, and to take among their electives STAT GU4281 Theory of Interest.

## Major in Political Science–Statistics

The interdepartmental major of political science–statistics is designed for students who desire an understanding of political science to pursue advanced study in this field and who also wish to have at their command a broad range of sophisticated statistical tools to analyze data related to social science and public policy research.

Students should be aware of the rules regarding the use of the Pass/D/Fail option. Courses in which a grade of D has been received do not count toward the major requirements.

Political science–statistics students are eligible for all prizes reserved for political science majors.

The political science-statistics major requires a minimum of 15 courses in political science, statistics, and mathematics, to be distributed as follows:

Code | Title | Points |
---|---|---|

Political Science | ||

Students must choose a primary subfield to study. Within the subfield, students must take a minimum of three courses, including the subfield's introductory course. The subfields and their corresponding introductory courses are as follows: | ||

American Politics: | ||

Introduction To American Government and Politics | ||

Comparative Politics: | ||

Introduction to Comparative Politics | ||

International Relations: | ||

INTERNATIONAL POLITICS | ||

Political Theory: | ||

Political Theory I | ||

Additionally, students must take a 4-point seminar in their primary subfield. | ||

Research Methods | ||

Students must take the following two research methods courses: | ||

POLS GU4710 | Principles of Quantitative Political Research | |

or POLS UN3704 | RESEARCH DESIGN: DATA ANALYSIS | |

POLS GU4712 | PRINC OF QUANT POL RESEARCH 2 | |

Statistics | ||

Select one of the following two sequences. | ||

Sequence recommended for students preparing for graduate study in statistics. | ||

Calculus I | ||

Calculus II | ||

Linear Algebra | ||

Calculus-Based Introduction to Statistics | ||

PROBABILITY THEORY | ||

Statistical Inference | ||

Linear Regression Models | ||

Statistical Computing and Introduction to Data Science | ||

Students taking the first track may replace the Mathematics prerequisites with both of MATH UN1207 and MATH UN1208 | ||

or | ||

Sequence recommend for students preparing to apply statistical methods in the social sciences. | ||

Introduction to Statistics | ||

Applied Statistical Computing | ||

Applied Linear Regression Analysis | ||

Applied Categorical Data Analysis | ||

Applied Statistical Methods | ||

Applied Data Mining | ||

Statistics elective: | ||

Students must take an approved elective in a statistics or a quantitatively oriented course in a social science. |

**Introductory Courses**

Students interested in statistical concepts, but who do not anticipate undertaking statistical analyses, should take STAT UN1001 Introduction to Statistical Reasoning. Students seeking an introduction to applied statistics or preparing for the concentration should take STAT UN1101 Introduction to Statistics (without calculus). Students seeking a foundation for further study of probability theory and statistical theory and methods should take STAT UN1201 Calculus-based Introduction to Statistics. Students seeking a one-semester calculus-based survey should take STAT GU4001 Introduction to Probability and Statistics. The undergraduate seminar STAT UN1202 features faculty lectures prepared with undergraduates in mind; students may attend without registering.

**STAT UN1001 Introduction to Statistical Reasoning.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement, BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

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.

Spring 2020: STAT UN1001 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 1001 | 001/46676 | M W 10:10am - 11:25am 428 Pupin Laboratories |
Guy Cohen | 3 | 101/86 |

STAT 1001 | 002/46677 | T Th 10:10am - 11:25am 717 Hamilton Hall |
Victor de la Pena | 3 | 44/86 |

STAT 1001 | 003/46678 | T 1:10pm - 2:25pm 233 Seeley W. Mudd Building |
Anthony Donoghue | 3 | 33/86 |

STAT 1001 | 003/46678 | T Th 6:10pm - 7:25pm 517 Hamilton Hall |
Anthony Donoghue | 3 | 33/86 |

Fall 2020: STAT UN1001 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

STAT 1001 | 001/12833 | T Th 10:10am - 11:25am Room TBA |
Guy Cohen | 3 | 110/110 |

STAT 1001 | 002/12834 | M W 6:10pm - 7:25pm Room TBA |
3 | 41/86 |

**STAT UN1101 Introduction to Statistics.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement, BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

Prerequisites: intermediate high school algebra.

Designed for students in fields that emphasize quantitative methods. Graphical and numerical summaries, probability, theory of sampling distributions, linear regression, analysis of variance, confidence intervals and hypothesis testing. Quantitative reasoning and data analysis. Practical experience with statistical software. Illustrations are taken from a variety of fields. Data-collection/analysis project with emphasis on study designs is part of the coursework requirement.

Spring 2020: STAT UN1101 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 1101 | 001/46713 | M W 8:40am - 9:55am 602 Hamilton Hall |
Banu Baydil | 3 | 72/86 |

STAT 1101 | 002/46714 | T Th 10:10am - 11:25am 702 Hamilton Hall |
David Rios | 3 | 60/86 |

STAT 1101 | 003/46715 | T Th 6:10pm - 7:25pm 602 Hamilton Hall |
Ha Nguyen | 3 | 58/86 |

Fall 2020: STAT UN1101 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

STAT 1101 | 001/12835 | M W 8:40am - 9:55am Room TBA |
Banu Baydil | 3 | 45/86 |

STAT 1101 | 002/12889 | T Th 6:10pm - 7:25pm Room TBA |
Ha Nguyen | 3 | 50/86 |

STAT 1101 | 003/12837 | M W 2:40pm - 3:55pm Room TBA |
Tian Zheng | 3 | 46/50 |

**STAT UN1201 Calculus-Based Introduction to Statistics.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement, BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

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*.

Spring 2020: STAT UN1201 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 1201 | 001/46671 | M W 10:10am - 11:25am 717 Hamilton Hall |
Hammou El Barmi | 3 | 62/86 |

STAT 1201 | 002/46672 | M W 8:40am - 9:55am 702 Hamilton Hall |
Joyce Robbins | 3 | 76/86 |

STAT 1201 | 003/46673 | T Th 8:40am - 9:55am 717 Hamilton Hall |
Joyce Robbins | 3 | 75/86 |

STAT 1201 | 004/46674 | M W 6:10pm - 7:25pm 517 Hamilton Hall |
David Rios | 3 | 57/86 |

Fall 2020: STAT UN1201 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

STAT 1201 | 001/12844 | M W 11:40am - 12:55pm Room TBA |
3 | 86/86 | |

STAT 1201 | 002/12845 | T Th 8:40am - 9:55am Room TBA |
3 | 34/86 | |

STAT 1201 | 003/12846 | M W 10:10am - 11:25am Room TBA |
Joyce Robbins | 3 | 86/86 |

STAT 1201 | 004/12847 | T Th 6:10pm - 7:25pm Room TBA |
Arian Maleki | 3 | 53/86 |

**STAT UN1202 Undergraduate Seminar.** *1 point*.

Prerequisites: Previous or concurrent enrollment in a course in statistics would make the talks more accessible.

Prepared with undergraduates majoring in quantitative disciplines in mind, the presentations in this colloquium focus on the interface between data analysis, computation, and theory in interdisciplinary research. Meetings are open to all undergraduates, whether registered or not. Presenters are drawn from the faculty of department in Arts and Sciences, Engineering, Public Health and Medicine.

Fall 2020: STAT UN1202 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 1202 | 001/12882 | F 10:10am - 12:00pm Room TBA |
Ronald Neath | 1 | 8/50 |

**STAT GU4001 Introduction to Probability and Statistics.** *3 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

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.

Spring 2020: STAT GU4001 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4001 | 001/13714 | T Th 1:10pm - 2:25pm 203 Mathematics Building |
Larry Wright | 3 | 54/125 |

STAT 4001 | 002/13715 | M W 6:10pm - 7:25pm 614 Schermerhorn Hall |
Daniel Rabinowitz | 3 | 88/120 |

Fall 2020: STAT GU4001 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

STAT 4001 | 001/12888 | T Th 2:40pm - 3:55pm Room TBA |
Larry Wright | 3 | 87/120 |

## Applied Statistics Concentration Courses

The applied statistics sequence, together with an introductory course, forms the concentration in applied statistics. STAT UN2102 Applied statistical computing may be used to satisfy the computing requirement for the major, and the other concentration courses may be used to satisfy the elective requirements for the major. (Students who sat STAT GU4205 Linear Regression for the major would find that they have covered essentially all of the material in STAT UN2103 Applied Linear Regression Analysis.

**STAT UN2102 Applied Statistical Computing.** *3 points*.

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 recursion, conditionals, modular programming, and data visualization. Students will also learn the fundamental concepts in computational complexity, and will practice writing reports based on their statistical analyses.

Spring 2020: STAT UN2102 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 2102 | 001/46679 | T Th 4:10pm - 5:25pm 402 Chandler |
Wayne Lee | 3 | 89/120 |

**STAT UN2103 Applied Linear Regression Analysis.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

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.

Spring 2020: STAT UN2103 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 2103 | 001/16758 | T Th 8:40am - 9:55am 627 Seeley W. Mudd Building |
Wayne Lee | 3 | 9/60 |

Fall 2020: STAT UN2103 |
|||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

STAT 2103 | 001/12883 | M W 6:10pm - 7:25pm Room TBA |
Daniel Rabinowitz | 3 | 40/60 |

**STAT UN2104 Applied Categorical Data Analysis.** *3 points*.

Prerequisites: STAT UN2103 is strongly recommended. Students without programming experience in R might find STAT UN2102 very helpful.

This course covers statistical models amd methods for analyzing and drawing inferences for problems involving categofical data. The goals are familiarity and understanding of a substantial and integrated body of statistical methods that are used for such problems, experience in anlyzing data using these methods, and profficiency in communicating the results of such methods, and the ability to critically evaluate the use of such methods. Topics include binomial proportions, two-way and three-way contingency tables, logistic regression, log-linear models for large multi-way contingency tables, graphical methods. The statistical package R will be used.

Spring 2020: STAT UN2104 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 2104 | 001/46719 | M W 11:40am - 12:55pm 603 Hamilton Hall |
Ronald Neath | 3 | 29/60 |

**STAT UN3105 Applied Statistical Methods.** *3 points*.

Prerequisites: At least one, and preferably both, of STAT UN2103 and UN2104 are strongly recommended. Students without programming experience in R might find STAT UN2102 very helpful.

This course is intended to give students practical experience with statistical methods beyond linear regression and categorical data analysis. The focus will be on understanding the uses and limitations of models, not the mathematical foundations for the methods. Topics that may be covered include random and mixed-effects models, classical non-parametric techniques, the statistical theory causality, sample survey design, multi-level models, generalized linear regression, generalized estimating equations and over-dispersion, survival analysis including the Kaplan-Meier estimator, log-rank statistics, and the Cox proportional hazards regression model. Power calculations and proposal and report writing will be discussed.

Fall 2020: STAT UN3105 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 3105 | 001/12884 | T Th 11:40am - 12:55pm Room TBA |
Wayne Lee | 3 | 24/60 |

**STAT UN3106 Applied Data Mining.** *3 points*.

Prerequisites: STAT UN2103. Students without programming experience in R might find STAT UN2102 very helpful.

This course will be taught as a machine learning class. 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; students without programming experience in R might find STAT UN2102 helpful.

Spring 2020: STAT UN3106 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 3106 | 001/16760 | T Th 2:40pm - 3:55pm 303 Hamilton Hall |
Vincent Dorie | 3 | 32/50 |

## Foundation Courses

The calculus-based foundation courses for the core of the statistics major. These courses are GU4203 Probability Theory, GU4204 Statistical Inference, GU4205 Linear Regression, GU4206 Statistical Computing and Introduction to Data Science, and GU4207 Elementary Stochastic processes. Ideally, students would take Probability theory or the equivalent before taking either Statistical Inference or Elementary Stochastic Processes, and would have taken Statistical Inference before, or at least concurrently with taking Linear Regression Analysis, and would have taken Linear Regression analysis before, or at least concurrently, with taking the computing and data science course. A semester of calculus should be taken before Probability, additional semesters of calculus are recommended before Statistical Inference, and a course in linear algebra before Linear Regression is strongly recommended. For the more advanced electives in stochastic processes, Probability Theory is an essential prerequisite, and many students would benefit from taking Elementary Stochastic Processes, too. Linear Regression and the computing and data science course should be taken before the advanced electives in machine learning and data science. Linear Regression is a strongly recommended prerequisite, or at least co-requisite, for the remaining advanced statistical electives.

Code | Title | Points |
---|---|---|

STAT GU4203 | PROBABILITY THEORY | |

STAT GU4204 | Statistical Inference | |

STAT GU4205 | Linear Regression Models | |

STAT GU4206 | Statistical Computing and Introduction to Data Science | |

STAT GU4207 | Elementary Stochastic Processes |

## Advanced Statistics Courses

Advanced statistics courses combine theory with methods and practical experience in data analysis. Undergraduates enrolling in advanced statistics courses would be well-advised to have completed STAT GU4203 (Probability Theory), GU4204 (Statistical Inference), and GU4205 (Linear Regression).

**STAT GU4221 Time Series Analysis.** *3 points*.

Prerequisites: STAT GU4205 or the equivalent.

Least squares smoothing and prediction, linear systems, Fourier analysis, and spectral estimation. Impulse response and transfer function. Fourier series, the fast Fourier transform, autocorrelation function, and spectral density. Univariate Box-Jenkins modeling and forecasting. Emphasis on applications. Examples from the physical sciences, social sciences, and business. Computing is an integral part of the course.

Spring 2020: STAT GU4221 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4221 | 001/46681 | M W 6:10pm - 7:25pm 501 Schermerhorn Hall |
Li Haoran | 3 | 10/25 |

STAT 4221 | 002/46682 | T Th 7:40pm - 8:55pm 428 Pupin Laboratories |
Rongning Wu | 3 | 11/25 |

Fall 2020: STAT GU4221 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

STAT 4221 | 001/12556 | T Th 1:10pm - 2:25pm Room TBA |
Flavio Bartmann | 3 | 6/50 |

**STAT GU4222 Nonparametric Statistics.** *3 points*.

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.

Spring 2020: STAT GU4222 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4222 | 001/16769 | M W 10:10am - 11:25am 309 Havemeyer Hall |
Marco Avella | 3 | 3/25 |

**STAT GU4223 Multivariate Statistical Inference.** *0 points*.

Prerequisites: STAT GU4205 or the equivalent.

Multivariate normal distribution, multivariate regression and classification; canonical correlation; graphical models and Bayesian networks; principal components and other models for factor analysis; SVD; discriminant analysis; cluster analysis.

Spring 2020: STAT GU4223 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4223 | 001/46683 | T Th 1:10pm - 2:25pm 501 Northwest Corner |
Banu Baydil | 0 | 7/25 |

**STAT GU4224 Bayesian Statistics.** *3 points*.

Prerequisites: STAT GU4204 or the equivalent.

Bayesian data analysis: building, fitting, evaluating and improving probability models. Prior information, hierachical models and combining information. Linear and nonlinear models. Simulation of fake data and evaluation of methods. Computing using R and Stan.

Spring 2020: STAT GU4224 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4224 | 001/16770 | T Th 6:10pm - 7:25pm 203 Mathematics Building |
Banu Baydil | 3 | 17/25 |

Fall 2020: STAT GU4224 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

STAT 4224 | 001/12490 | M W 1:10pm - 2:25pm Room TBA |
Ronald Neath | 3 | 24/35 |

**STAT GU4231 Survival Analysis.** *0 points*.

Prerequisites: STAT GU4205 or the equivalent.

Survival distributions, types of censored data, estimation for various survival models, nonparametric estimation of survival distributions, the proportional hazard and accelerated lifetime models for regression analysis with failure-time data. Extensive use of the computer.

**STAT GU4232 Generalized Linear Models.** *3 points*.

Prerequisites: STAT GU4205 or the equivalent.

Statistical methods for rates and proportions, ordered and nominal categorical responses, contingency tables, odds-ratios, exact inference, logistic regression, Poisson regression, generalized linear models.

Spring 2020: STAT GU4232 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4232 | 001/16771 | M W 7:40pm - 8:55pm 614 Schermerhorn Hall |
Michael Sobel | 3 | 1/35 |

**STAT GU4233 Multilevel Models.** *3 points*.

**Not offered during 2019-20 academic year.**

Prerequisites: STAT GU4205 or the equivalent.

Theory and practice, including model-checking, for random and mixed-effects models (also called hierarchical, multi-level models). Extensive use of the computer to analyse data.

**STAT GU4234 Sample Surveys.** *3 points*.

Prerequisites: STAT GU4204 or the equivalent.

Introductory course on the design and analysis of sample surveys. How sample surveys are conducted, why the designs are used, how to analyze survey results, and how to derive from first principles the standard results and their generalizations. Examples from public health, social work, opinion polling, and other topics of interest.

Fall 2020: STAT GU4234 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4234 | 001/12492 | M W 1:10pm - 2:25pm Room TBA |
Rongning Wu | 3 | 10/25 |

**STAT GU4241 Statistical Machine Learning.** *0 points*.

Prerequisites: STAT GU4206.

The course will provide an introduction to Machine Learning and its core models and algorithms. The aim of the course is to provide students of statistics with detailed knowledge of how Machine Learning methods work and how statistical models can be brought to bear in computer systems - not only to analyze large data sets, but to let computers perform tasks that traditional methods of computer science are unable to address. Examples range from speech recognition and text analysis through bioinformatics and medical diagnosis. This course provides a first introduction to the statistical methods and mathematical concepts which make such technologies possible.

Spring 2020: STAT GU4241 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4241 | 001/46685 | T Th 2:40pm - 3:55pm 327 Seeley W. Mudd Building |
Linxi Liu | 0 | 20/35 |

STAT 4241 | 001/46685 | M W 8:40am - 9:55am 401 Chandler |
Linxi Liu | 0 | 20/35 |

**STAT GU4261 Statistical Methods in Finance.** *3 points*.

Prerequisites: STAT GU4205 or the equivalent.

A fast-paced introduction to statistical methods used in quantitative finance. Financial applications and statistical methodologies are intertwined in all lectures. Topics include regression analysis and applications to the Capital Asset Pricing Model and multifactor pricing models, principal components and multivariate analysis, smoothing techniques and estimation of yield curves statistical methods for financial time series, value at risk, term structure models and fixed income research, and estimation and modeling of volatilities. Hands-on experience with financial data.

Spring 2020: STAT GU4261 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4261 | 001/16773 | Sa 9:10am - 11:40am 501 Schermerhorn Hall |
Zhiliang Ying | 3 | 10/15 |

Fall 2020: STAT GU4261 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

STAT 4261 | 001/12494 | F 10:10am - 12:55pm Room TBA |
Hammou El Barmi | 3 | 18/25 |

**STAT GU4263 Statistical Inference and Time Series Modelling.** *3 points*.

Prerequisites: STAT GU4204 or the equivalent. STAT GU4205 is recommended. Modeling and inference for random processes, from natural sciences to finance and economics. ARMA, ARCH, GARCH and nonlinear models, parameter estimation, prediction and filtering. This is a core course in the MS program in mathematical finance.

Fall 2020: STAT GU4263 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4263 | 001/12495 | T Th 6:10pm - 7:25pm Room TBA |
Li Haoran | 3 | 10/35 |

STAT 4263 | 002/12496 | Sa 10:10am - 12:40pm Room TBA |
Li Haoran | 3 | 5/35 |

**STAT GU4291 Advanced Data Analysis.** *3 points*.

Prerequisites: STAT GU4205 and at least one statistics course numbered between GU4221 and GU4261.

This is a course on getting the most out of data. The emphasis will be on hands-on experience, involving case studies with real data and using common statistical packages. The course covers, at a very high level, exploratory data analysis, model formulation, goodness of fit testing, and other standard and non-standard statistical procedures, including linear regression, analysis of variance, nonlinear regression, generalized linear models, survival analysis, time series analysis, and modern regression methods. Students will be expected to propose a data set of their choice for use as case study material.

Spring 2020: STAT GU4291 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4291 | 001/46720 | F 10:10am - 12:40pm 207 Mathematics Building |
Ronald Neath | 3 | 5/30 |

Fall 2020: STAT GU4291 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

STAT 4291 | 001/12515 | F 5:10pm - 7:40pm Room TBA |
Demissie Alemayehu | 3 | 25/25 |

## Actuarial Sciences Courses

Only students preparing for a career in actuarial sciences should consider the courses in this section. Such students may also be interested in courses offered through the School of Professional Studies M.S. Program in Actuarial Science, but must check with the academic advisors in their schools to know whether they are allowed to register for those courses. Students majoring in statistics and preparing for a career in actuarial science may take STAT GU4282 (Regression and Time Series Analysis) in place of the major requirement STAT GU4205 (Linear Regression Analysis).

Code | Title | Points |
---|---|---|

STAT GU4281 | Theory of Interest | |

STAT GU4282 | Linear Regression and Time Series Methods |

## Advanced Data Science Courses

In response to the ever growing importance of ``big data” in scientific and policy endeavors, the last few years have seen an explosive growth in theory, methods, and applications at the interface between computer science and statistics. The Department offers a sequence that begins with the core course STAT GU4206 (Statistical Computing and Introduction to Data Science) and continues with the advanced electives GU4241 (Statistical Machine Learning) and GU4242 (Advanced Machine Learning), and also the advanced elective STAT GU4243 (Applied Data Science). Undergraduate students without experience in programming would likely benefit from taking the statistical computing and data science course before attempting GU4241, GU4242, or GU4243.

Code | Title | Points |
---|---|---|

STAT GU4241 | Statistical Machine Learning | |

STAT GU4242 | Advanced Machine Learning | |

STAT GU4243 | Applied Data Science | |

STAT GU4702 | Exploratory Data Analysis and Visualization |

## Advanced Stochastic Processes Courses

The stochastic processes electives in this section have STAT GU4203 (Probability Theory) or the equivalent as prerequisites Most students would also benefit from taking STAT GU4207 (Elementary Stochastic Processes) before embarking on the more advanced stochastic processes electives.

Code | Title | Points |
---|---|---|

STAT GU4262 | Stochastic Processes for Finance | |

STAT GU4264 | STOCHASTC PROCSSES-APPLIC | |

STAT GU4265 | Stochastic Methods in Finance |