# 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:**

Banu Baydil, 611 Watson; 212-853-1397; bb2717@columbia.edu

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

**Data Science Major Advising:**

*Computer Science:* Adam Cannon, 459 CSB; 212-939-7016; cannon@cs.columbia.edu

*Statistics: *Banu Baydil, 611 Watson; 212-853-1397; bb2717@columbia.edu

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

**Economics - Statistics Major Advising:**

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

*Statistics: *Banu Baydil, 611 Watson; 212-853-1397; bb2717@columbia.edu

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

**Mathematics - Statistics Major Advising:**

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

*Statistics: *Banu Baydil, 611 Watson; 212-853-1397; bb2717@columbia.edu

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

**Political Science - Statistic Major Advising:**

*Political Science:* Robert Shapiro, 730 IAB; 212-854-3944; rys3@columbia.edu

*Statistics: *Banu Baydil, 611 Watson; 212-853-1397; bb2717@columbia.edu

*Statistics: *Ronald Neath, 612 Watson; 212-853-1398; rcn2112@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 Stochastic Processes and Applications, 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 Q4242 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
- Ioannis Karatzas (Mathematics)
- Liam Paninski
- Philip Protter
- Michael Sobel
- Daniel Rabinowitz
- Zhiliang Ying

## Associate Professors

- Jose Blanchet (with Industrial Engineering and Operations Research)
- Jingchen Liu
- Bodhisattva Sen
- Tian Zheng

## Assistant Professors

- John Cunningham
- Yang Feng
- Lauren Hannah
- Arian Maleki
- Sumit Mukherjee
- Marcel Nutz
- Peter Orbanz

**Term Assistant Professors**

- Yuchong Zhang
- Abolfazl Safikhani

## Adjunct Professors

- Demissie Alemayehu
- Flavio Bartmann
- Guy Cohen
- Regina Dolgoarshinnykh
- Anthony Donoghue
- Hammou Elbarmi
- Birol Emir
- Irene Hueter
- James Landwehr
- Ha Nguyen

## Lecturers in Discipline

- Banu Baydil
- Ronald Neath
- David Rios
- 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 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 Introduction To Modern Analysis I and MATH GU4062 Introduction To Modern Analysis II .

**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 2017: STAT UN1001 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 1001 | 001/76540 | T Th 6:10pm - 7:25pm 312 Mathematics Building |
Anthony Donoghue | 3 | 45/110 |

STAT 1001 | 002/73953 | T Th 2:40pm - 3:55pm 214 Pupin Laboratories |
Yayun Hsu | 3 | 17/50 |

STAT 1001 | 003/67625 | M W 10:10am - 11:25am 516 Hamilton Hall |
Louis Mittel | 3 | 46/50 |

Fall 2017: STAT UN1001 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

STAT 1001 | 001/25100 | M W 10:10am - 11:25am Room TBA |
Joyce Robbins | 3 | 65/86 |

STAT 1001 | 002/20569 | T Th 10:10am - 11:25am Room TBA |
Jonathan Auerbach | 3 | 50/50 |

STAT 1001 | 003/29529 | M W 6:10pm - 7:25pm Room TBA |
Anthony Donoghue | 3 | 31/86 |

**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 2017: STAT UN1101 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 1101 | 001/28974 | M W 11:40am - 12:55pm 203 Mathematics Building |
Banu Baydil | 3 | 63/86 |

STAT 1101 | 002/76665 | T Th 11:40am - 12:55pm 517 Hamilton Hall |
Banu Baydil | 3 | 69/86 |

STAT 1101 | 003/27319 | T Th 6:10pm - 7:25pm 717 Hamilton Hall |
Banu Baydil | 3 | 54/86 |

Fall 2017: STAT UN1101 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

STAT 1101 | 001/73141 | M W 11:40am - 12:55pm Room TBA |
David Rios | 3 | 39/86 |

STAT 1101 | 002/14935 | T Th 11:40am - 12:55pm Room TBA |
David Rios | 3 | 22/86 |

STAT 1101 | 003/15455 | T Th 6:10pm - 7:25pm Room TBA |
Ha Nguyen | 3 | 86/86 |

**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 2017: STAT UN1201 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 1201 | 001/19141 | T Th 10:10am - 11:25am C03 School Of Social Work |
David Rios | 3 | 46/86 |

STAT 1201 | 002/60742 | T Th 8:40am - 9:55am 207 Mathematics Building |
Joyce Robbins | 3 | 81/86 |

STAT 1201 | 003/67320 | M W 6:10pm - 7:25pm 602 Hamilton Hall |
Ha Nguyen | 3 | 78/86 |

STAT 1201 | 004/10614 | F 11:40am - 2:25pm 207 Mathematics Building |
Sheela Kolluri | 3 | 48/86 |

Fall 2017: STAT UN1201 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

STAT 1201 | 001/73218 | M W 8:40am - 9:55am Room TBA |
Joyce Robbins | 3 | 57/86 |

STAT 1201 | 002/76589 | T Th 8:40am - 9:55am Room TBA |
Joyce Robbins | 3 | 75/86 |

STAT 1201 | 003/68663 | M W 11:40am - 12:55pm Room TBA |
Arian Maleki | 3 | 86/86 |

STAT 1201 | 004/70129 | T Th 6:10pm - 7:25pm Room TBA |
Sheela Kolluri | 3 | 86/86 |

**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 2017: STAT UN1202 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 1202 | 001/60803 | F 10:10am - 12:00pm Room TBA |
Ronald Neath, Banu Baydil | 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 2017: STAT GU4001 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4001 | 001/21880 | T Th 1:10pm - 2:25pm 207 Mathematics Building |
David Rios | 3 | 86/110 |

STAT 4001 | 002/17296 | M W 2:40pm - 3:55pm 312 Mathematics Building |
Mark Brown | 3 | 91/110 |

Fall 2017: STAT GU4001 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

STAT 4001 | 001/65735 | Sa 10:10am - 12:55pm Room TBA |
Daniel Rabinowitz | 3 | 49/120 |

STAT 4001 | 002/62655 | M W 2:40pm - 3:55pm Room TBA |
Mark Brown | 3 | 103/120 |

## 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 stat STAT W4205 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.

**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.

Fall 2017: STAT UN2103 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 2103 | 001/12203 | M W 6:10pm - 7:25pm Room TBA |
Gabriel Young | 3 | 58/60 |

**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 2017: STAT UN2104 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 2104 | 001/82746 | M W 2:40pm - 3:55pm 313 Fayerweather |
James Landwehr | 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 2017: STAT UN3105 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 3105 | 001/67449 | T Th 1:10pm - 2:25pm Room TBA |
David Rios | 3 | 29/50 |

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

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

Data Mining is a dynamic and fast growing field at the interface of Statistics and Computer Science. The emergence of massive datasets containing millions or even billions of observations provides the primary impetus for the field. Such datasets arise, for instance, in large-scale retailing, telecommunications, astronomy, computational and statistical challenges. This course will provide an overview of current practice in data mining. Specific topics covered with include databases and data warehousing, exploratory data analysis and visualization, descriptive modeling, predictive modeling, pattern and rule discovery, text mining, Bayesian data mining, and causal inference. The use of statistical software will be emphasized.

Spring 2017: STAT UN3106 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 3106 | 001/81399 | T Th 2:40pm - 3:55pm 233 Seeley W. Mudd Building |
Gabriel Young | 3 | 47/50 |

## 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 2017: STAT GU4221 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4221 | 001/76456 | M W 7:40pm - 8:55pm 614 Schermerhorn Hall |
Abolfazal Safikhani | 3 | 30/40 |

STAT 4221 | 002/29812 | Sa 2:40pm - 5:25pm 312 Mathematics Building |
Rongning Wu | 3 | 12/40 |

Fall 2017: STAT GU4221 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

STAT 4221 | 001/11723 | M W 7:40pm - 8:55pm Room TBA |
Dan Wang | 3 | 20/30 |

**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 2017: STAT GU4222 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4222 | 001/73339 | M W 1:10pm - 2:25pm 209 Havemeyer Hall |
Pawel Polak | 3 | 8/35 |

**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 2017: STAT GU4223 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4223 | 001/73196 | T Th 1:10pm - 2:25pm 313 Fayerweather |
Pawel Polak | 0 | 5/35 |

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

Prerequisites: STAT GU4204 or the equivalent.

Bayesian vs frequentist, prior and posterior distributions, conjugate priors, informative and non-informative prior subjective and objective bayes, oneand two sample problems, models for normal data, models for binary data, multivariate normal shrinkage, bayesian linear models, bayesian computation (start early), MCMC algorithms, the Gibbs sampler, hierarchical models, empirical bayes, hypothesis testing, bayes factors, model selection, software: R and WinBUGS

Spring 2017: STAT GU4224 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4224 | 001/19142 | T Th 6:10pm - 7:25pm 833 Seeley W. Mudd Building |
Ronald Neath | 3 | 16/40 |

Fall 2017: STAT GU4224 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

STAT 4224 | 001/24790 | M W 2:40pm - 3:55pm Room TBA |
Ronald Neath | 3 | 20/20 |

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

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

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.

Spring 2017: STAT GU4231 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4231 | 001/12349 | M W 6:10pm - 7:25pm 903 School Of Social Work |
Michael Shnaidman | 0 | 2/25 |

**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 2017: STAT GU4232 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4232 | 001/93347 | T Th 4:10pm - 5:25pm 207 Mathematics Building |
Michael Sobel | 3 | 5/35 |

**STAT W4233 Multilevel Models.** *0 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).**Not offered during 2017-18 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 2017: STAT GU4234 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4234 | 001/61950 | T Th 6:10pm - 7:25pm Room TBA |
Ronald Neath | 3 | 7/15 |

**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 2017: STAT GU4241 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4241 | 001/29700 | T Th 6:10pm - 7:25pm 207 Mathematics Building |
Linxi Liu | 0 | 13/25 |

STAT 4241 | 002/11922 | T Th 7:40pm - 8:55pm 428 Pupin Laboratories |
Cynthia Rush | 0 | 13/25 |

**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 2017: STAT GU4261 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4261 | 001/73209 | Sa 9:10am - 11:40am 501 Schermerhorn Hall |
Zhiliang Ying | 3 | 22/25 |

Fall 2017: STAT GU4261 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

STAT 4261 | 001/13009 | F 10:10am - 12:55pm Room TBA |
Hammou ElBarmi | 3 | 20/20 |

**STAT W4263 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.

**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 2017: STAT GU4291 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

STAT 4291 | 001/14452 | F 10:10am - 12:40pm 312 Mathematics Building |
Hammou ElBarmi | 3 | 19/25 |

Fall 2017: STAT GU4291 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

STAT 4291 | 001/13628 | F 6:10pm - 8:55pm Room TBA |
Demissie Alemayehu | 3 | 15/25 |

## 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 Q4242 | Advanced Machine Learning | |

STAT GU4243 | Applied Data Science | |

STAT W4702 | 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 W3201 | Math Finance in Continuous Time | |

STAT GU4262 | Stochastic Processes for Finance | |

STAT GU4264 | Stochastic Processes and Applications | |

STAT W4265 | Stochastic Methods in Finance | |

STAT G4266 | Stochastic Control and Applications in Finance |