Statistics

Catalog Home › The College › Programs of Study › Statistics

This is an archived copy of the 2013-2014 catalog. To access the most recent version of the catalog, please visit http://catalog.uchicago.edu.

Contacts

Undergradute Primary Contact

Departmental Adviser for Majors and Honors
Mary Sara McPeek
E 129
773.702.7554 or 773.702.8333
Email

Departmental Adviser for Minors and Intro Courses
Linda Collins
E 107
773.834.7479 or 773.702.8333
Email

Administrative Contact

Student Affairs Specialist
Matt Johnston
E 108
773.702.0541
Email

Website

http://www.stat.uchicago.edu

Program of Study

The modern science of statistics involves the invention, study, and development of principles and methods for modeling uncertainty through mathematical probability; for designing experiments, surveys, and observational programs; and for analyzing and interpreting empirical data. Mathematics plays a major role in all statistical activity, whether of an abstract nature or dealing with specific techniques for analyzing data. Statistics is an excellent field for students with strong mathematical skills and an interest in applying these skills to problems in the natural and social sciences. A program leading to the bachelor's degree in Statistics offers coverage of the principles and methods of statistics in combination with a solid training in mathematics and some exposure to computing, which is essential to nearly all modern data analysis. In addition, there is considerable elective freedom enabling interested students to examine those areas of knowledge in the biological, physical, and social sciences that are often subjected to detailed statistical analysis. The major provides a base for graduate study in statistics or in other subjects with strong quantitative components. Students considering graduate study in statistics or related fields are encouraged to discuss their programs with the Departmental Adviser for Majors at an early stage, whether or not they plan to receive an undergraduate degree in Statistics.

Students who are majoring in other fields of study may also complete a minor in Statistics and are encouraged to discuss their course choices with the Departmental Adviser for Minors. Information on the minor follows the description of the major.

Statistics Courses for Students in Other Majors

Courses at the 20000 level are designed to provide instruction in statistics, probability, and statistical computation for students from all parts of the University. These courses differ in emphasis on theory or methods, on the mathematical level, and in the direction of applications. Most of the introductory courses make intensive use of computers to exemplify and explore statistical concepts and methods. The nature and extent of computer work varies according to the course and instructor. Statistics courses are not mathematics courses, but the mathematics prerequisites are a useful guide to the level of mathematical maturity assumed by a statistics course. Students with a background in calculus typically are advised to take STAT 22000 Statistical Methods and Applications or higher.

Explanations and comparisons of the various courses, both entry level and more advanced, are provided in the following sections. Students will also find the course descriptions to be helpful in choosing appropriate courses.

Introductory Courses and Sequences

To begin their studies in statistics, students can choose from several courses. These courses are outlined in this section and in the course descriptions. Students and College Advisers are encouraged to contact the Departmental Adviser for Introductory Courses for advice on choosing an appropriate first course.

For students who do not intend to continue to more advanced statistics courses, STAT 20000 Elementary Statistics is an alternative with no calculus prerequisite that places less emphasis on statistical techniques. STAT 20000 Elementary Statistics may not be taken either by students who have already taken STAT 22000 Statistical Methods and Applications or STAT 23400 Statistical Models and Methods or by students who have received AP credit for statistics.

For their introductory statistics course, students might choose either STAT 22000 Statistical Methods and Applications or STAT 23400 Statistical Models and Methods (not both). Students may count either STAT 22000 Statistical Methods and Applications or STAT 23400 Statistical Models and Methods, but not both, toward the 42 credits required for graduation.

STAT 22000 Statistical Methods and Applications, which typically is the statistics course taken first, is a general introduction to statistical concepts, techniques, and applications, to data analysis, and to problems in the design, analysis, and interpretation of experiments and observational programs. Computers are used throughout the course. A score of 4 or 5 on the AP Statistics test yields credit for STAT 22000 Statistical Methods and Applications, although this credit will not count toward the requirements for a major or minor in Statistics.

STAT 23400 Statistical Models and Methods covers much of the same material as STAT 22000 Statistical Methods and Applications, but at a somewhat higher mathematical level. STAT 23400 Statistical Models and Methods is a required course for students who are majoring in economics, but the class is a one-quarter introduction to statistics that is appropriate for any student with a good command of univariate calculus.

STAT 24400-24500 Statistical Theory and Methods I-II is recommended for students who wish to have a thorough introduction to statistical theory and methodology. STAT 24400-24500 Statistical Theory and Methods I-II is more mathematically demanding than either STAT 22000 Statistical Methods and Applications or STAT 23400 Statistical Models and Methods and assumes some familiarity with multivariate calculus and with linear algebra.

Students considering a major in Statistics are encouraged to take STAT 24400 Statistical Theory and Methods I rather than STAT 23400 Statistical Models and Methods. Although students with a strong mathematical background can and do take STAT 24400-24500 Statistical Theory and Methods I-II without prior course work in statistics or probability, some students find it helpful to take a more elementary course as preparation. Also, students who have already taken STAT 22000 Statistical Methods and Applications or STAT 23400 Statistical Models and Methods and wish to study statistics at a higher mathematical level are welcome to take STAT 24400-24500 Statistical Theory and Methods I-II.

STAT 24610 Pattern Recognition is a follow-up to STAT 24400-24500 Statistical Theory and Methods I-II that covers more advanced statistical methods. STAT 25100 Introduction to Mathematical Probability is an introductory course in probability. STAT 24400-24500 Statistical Theory and Methods I-II and STAT 25100 Introduction to Mathematical Probability form the core of the Statistics major. This is recommended as a cognate sequence to students in the quantitative sciences and Mathematics.

Additional Courses in Statistical Theory, Methods, and Applications

For students interested in exploring methods and their applications, STAT 22200 Linear Models and Experimental Design, STAT 22400 Applied Regression Analysis, STAT 22600 Analysis of Categorical Data, and STAT 22700 Biostatistical Methods are recommended. These courses each emphasize a class of methods for the analysis of data. Note that because there is some overlap between STAT 22600 Analysis of Categorical Data and STAT 22700 Biostatistical Methods, only one of these two courses, not both, may be counted toward a major or minor in Statistics. The courses STAT 22200 Linear Models and Experimental Design, STAT 22400 Applied Regression Analysis, and STAT 22600 Analysis of Categorical Data may be taken in any order. Each presumes a previous course in statistics (STAT 22000 Statistical Methods and Applications or equivalent) and experience using computers in data analysis (as in STAT 22000 Statistical Methods and Applications). STAT 22700 Biostatistical Methods has STAT 22400 Applied Regression Analysis as a prerequisite.

For students who have completed STAT 24400-24500 Statistical Theory and Methods I-II and are interested in more advanced statistical methodology courses, STAT 24610 Pattern Recognition, STAT 26100 Time Dependent Data, STAT 27400 Nonparametric Inference, and STAT 34300 Applied Linear Statistical Methods are recommended. In addition to STAT 34300 Applied Linear Statistical Methods, many other graduate courses in Statistics offer opportunities for further study of statistical theory, methods, and applications. For details, consult the instructor or the Departmental Adviser for Majors, or visit www.stat.uchicago.edu .

Courses in Probability

Students interested in probability can begin with STAT 25100 Introduction to Mathematical Probability, which can be taken separately from any statistics courses and can be supplemented with more advanced probability courses, such as STAT 25300 Introduction to Probability Models. Students with a strong mathematical background can take STAT 31200 Introduction to Stochastic Processes I, STAT 31300 Introduction to Stochastic Processes II, STAT 38100 Measure-Theoretic Probability I, and STAT 38300 Measure-Theoretic Probability III.

Program Requirements

Students majoring in Statistics should meet the general education requirements in the mathematical sciences with courses in calculus. The major program includes four additional prescribed mathematics courses and four prescribed statistics courses. Students should complete the four mathematics courses by the end of their third year. Additional requirements include three approved elective courses in Statistics, as well as one prescribed course in Computer Science for the BA or two prescribed courses in Computer Science for the BS. The BS also requires an approved two-quarter sequence at the 20000 level in a field to which statistics can be applied.

The four required Statistics courses are STAT 24400-24500 Statistical Theory and Methods I-II, STAT 25100 Introduction to Mathematical Probability, and either STAT 22400 Applied Regression Analysis or STAT 34300 Applied Linear Statistical Methods. STAT 24400 Statistical Theory and Methods I typically is suggested as a first course in Statistics or, if a more elementary introduction is desired, students can take STAT 22000 Statistical Methods and Applications or STAT 23400 Statistical Models and Methods as preparation for STAT 24400 Statistical Theory and Methods I. Candidates for the BA may count either STAT 22000 Statistical Methods and Applications or STAT 23400 Statistical Models and Methods, but not both, as one of the three approved electives, provided that they take the course before STAT 24400 Statistical Theory and Methods I. However, in that case, the other two electives must be approved courses in statistical methodology (e.g., not probability). Candidates for the BS may not count either STAT 22000 Statistical Methods and Applications or STAT 23400 Statistical Models and Methods toward the Statistics major.

Electives that can be counted toward the Statistics major include STAT 22200 Linear Models and Experimental Design, STAT 22600 Analysis of Categorical Data or STAT 22700 Biostatistical Methods (but not both), STAT 24610 Pattern Recognition, STAT 25300 Introduction to Probability Models or STAT 31200 Introduction to Stochastic Processes I (but not both), STAT 26100 Time Dependent Data, STAT 26700 History of Statistics, and STAT 27400 Nonparametric Inference.

All candidates must obtain approval of their course program from the Departmental Adviser for Majors. Not all combinations of Statistics electives are allowed. Specifically, at least two of the three electives must be courses in statistical methodology (e.g., not probability and not STAT 22000 Statistical Methods and Applications or STAT 23400 Statistical Models and Methods). NOTE: Students who are completing majors in both Statistics and Economics should follow the same mathematics requirements as Statistics majors. However, students who have already taken MATH 19520 Mathematical Methods for Social Sciences and MATH 19620 Linear Algebra should discuss with the Departmental Adviser for Majors how to best meet their mathematical requirements for the Statistics major. In particular, note that MATH 19620 Linear Algebra is not sufficient for the Statistics major and cannot be counted toward the major.

There are a number of differences between the BA and BS programs. In the BS program, there is some strengthening of requirements on the level of courses that must be taken to complete the program. For example, candidates for the BS who do not take STAT 34300 Applied Linear Statistical Methods must take at least one advanced course in statistical methodology, such as STAT 24610 Pattern Recognition, STAT 26100 Time Dependent Data, or STAT 27400 Nonparametric Inference. The BS also requires a second prescribed course in Computer Science and an approved, two-quarter sequence at the 20000 level in a field to which statistics can be applied. Generally this sequence should be in the natural or social sciences, but a sequence in another discipline may be acceptable. Courses in MATH or CMSC may not be used for this requirement. Sequences in which the first class is a prerequisite for the second are preferred. Example sequences include BIOS 20197 Evolution and Ecology-BIOS 20198 Biodiversity, CHEM 22000-22100 Organic Chemistry I-II, CHEM 26100-26200 Quantum Mechanics; Thermodynamics, ECON 20000-20100 The Elements of Economic Analysis I-II, GEOS 21000 Introduction to Mineralogy-GEOS 21100 Introduction to Petrology, PHYS 22500-22700 Intermediate Electricity and Magnetism I-II, and PHYS 23400-23500 Quantum Mechanics I-II. All sequences must be approved by the Departmental Adviser for Majors.

Students who are majoring in Statistics must receive a quality grade of at least C- in all of the courses required for their degree; a grade of P is not acceptable for any of these courses.

Summary of Requirements for the BA in Statistics

General Education
One of the following sequences: ^*		200
MATH 13100-13200	Elementary Functions and Calculus I-II
MATH 15100-15200	Calculus I-II
MATH 16100-16200	Honors Calculus I-II
Total Units		200

Major
One of the following: ^*		100
MATH 13300	Elementary Functions and Calculus III
MATH 15300	Calculus III
MATH 16300	Honors Calculus III
One of the following sequences:		200
MATH 20000-20100	Mathematical Methods for Physical Sciences I-II
MATH 20400-20500	Analysis in Rn II-III
MATH 20800-20900	Honors Analysis in Rn II-III
One of the following:		100
STAT 24300	Numerical Linear Algebra
MATH 25500	Basic Algebra II
MATH 25800	Honors Basic Algebra II
All of the following:		300
STAT 24400	Statistical Theory and Methods I
STAT 24500	Statistical Theory and Methods II
STAT 25100	Introduction to Mathematical Probability
One of the following:		100
STAT 22400	Applied Regression Analysis
STAT 34300	Applied Linear Statistical Methods
One of the following: ^**		100
CMSC 10500	Fundamentals of Computer Programming I
CMSC 10600	Fundamentals of Computer Programming II
CMSC 12100	Computer Science with Applications I
CMSC 15100	Introduction to Computer Science I
CMSC 16100	Honors Introduction to Computer Science I
Three approved elective courses in Statistics ^***		300
Total Units		1200

*	Credit may be granted by examination.
**	CMSC 10600 Fundamentals of Computer Programming II or higher preferred
***	Options include STAT 22200 Linear Models and Experimental Design, STAT 22600 Analysis of Categorical Data or STAT 22700 Biostatistical Methods (but not both), STAT 24610 Pattern Recognition, STAT 25300 Introduction to Probability Models or STAT 31200 Introduction to Stochastic Processes I (but not both), STAT 26100 Time Dependent Data, STAT 26700 History of Statistics, and STAT 27400 Nonparametric Inference. Candidates for the BA may count either STAT 22000 Statistical Methods and Applications or STAT 23400 Statistical Models and Methods, but not both, as one of the three approved electives, provided they take the course before STAT 24400 Statistical Theory and Methods I. However, in every case, at least two of the three electives must be courses in statistical methodology (e.g., not probability and not STAT 22000 Statistical Methods and Applications or STAT 23400 Statistical Models and Methods.

Summary of Requirements for the BS in Statistics

General Education
One of the following sequences: ^*		200
MATH 13100-13200	Elementary Functions and Calculus I-II
MATH 15100-15200	Calculus I-II
MATH 16100-16200	Honors Calculus I-II
Total Units		200

Major
One of the following: ^*		100
MATH 13300	Elementary Functions and Calculus III
MATH 15300	Calculus III
MATH 16300	Honors Calculus III
One of the following:		100
MATH 20000	Mathematical Methods for Physical Sciences I
MATH 20500	Analysis in Rn III
MATH 20900	Honors Analysis in Rn III
One of the following:		100
MATH 20100	Mathematical Methods for Physical Sciences II
MATH 27300	Basic Theory of Ordinary Differential Equations
One of the following:		100
STAT 24300	Numerical Linear Algebra
MATH 25500	Basic Algebra II
MATH 25800	Honors Basic Algebra II
All of the following:		300
STAT 24400	Statistical Theory and Methods I
STAT 24500	Statistical Theory and Methods II
STAT 25100	Introduction to Mathematical Probability
One of the following:		100
STAT 22400	Applied Regression Analysis
STAT 34300	Applied Linear Statistical Methods
One of the following sequences:		200
CMSC 12100-12200	Computer Science with Applications I-II
CMSC 15100-15200	Introduction to Computer Science I-II
CMSC 16100-16200	Honors Introduction to Computer Science I-II
Three approved elective courses in Statistics ^**		300
A coherent two-quarter sequence at the 20000 level in a field to which statistics can be applied ^***		200
Total Units		1500

*	Credit may be granted by examination.
**	Options include STAT 22200 Linear Models and Experimental Design, STAT 22600 Analysis of Categorical Data or STAT 22700 Biostatistical Methods (but not both), STAT 24610 Pattern Recognition, STAT 25300 Introduction to Probability Models or STAT 31200 Introduction to Stochastic Processes I (but not both), STAT 26100 Time Dependent Data, STAT 26700 History of Statistics, and STAT 27400 Nonparametric Inference. At least two of the three electives must be courses in statistical methodology (e.g., not probability). Candidates for the BS who do not take STAT 34300 Applied Linear Statistical Methods must take at least one advanced course in statistical methodology, such as STAT 24610 Pattern Recognition, STAT 26100 Time Dependent Data, STAT 27400 Nonparametric Inference, or an approved graduate course, to be counted as one of their three electives. Candidates for the BS may not count either STAT 22000 Statistical Methods and Applications or STAT 23400 Statistical Models and Methods toward the Statistics major.
***	Generally, this sequence should be in the natural or social sciences, but a sequence in another discipline might be acceptable. Courses in MATH or CMSC may not be used for this requirement. Sequences in which the first class is a prerequisite for the second are preferred. Example sequences include BIOS 20197 Evolution and Ecology-BIOS 20198 Biodiversity, CHEM 22000-22100 Organic Chemistry I-II, CHEM 26100-26200 Quantum Mechanics; Thermodynamics, ECON 20000-20100 The Elements of Economic Analysis I-II, GEOS 21000 Introduction to Mineralogy-GEOS 21100 Introduction to Petrology, PHYS 22500-22700 Intermediate Electricity and Magnetism I-II, and PHYS 23400-23500 Quantum Mechanics I-II. All sequences must be approved by the Departmental Adviser for Majors.

Grading

Students who are majoring in Statistics must receive a quality grade of at least C- in all of the courses required for their degree; a grade of P is not acceptable for any of these courses.

Subject to College and divisional regulations, and with the consent of the instructor, all students except majors in Statistics may register for quality grades or for P/F grading in any 20000-level Statistics course. A grade of P is given only for work of C- quality or higher.

The following policy applies to students who wish to receive a mark of I for a Statistics course. In addition to submitting the official Incomplete Form required by the College, students must have completed at least half of the total required course work with a grade of C- or better, and they must be unable to complete all of the course work by the end of the quarter due to an emergency.

Honors

The BA or BS with honors is awarded to students with Statistics as their primary major who have a GPA of 3.0 or higher overall and 3.25 or higher in the courses in the major and also complete an approved honors paper (STAT 29900 Bachelor's Paper). This paper typically is based upon a structured research program that students undertake with faculty supervision in the first quarter of their fourth year. Eligible students who wish to be considered for honors should consult the Departmental Adviser for Majors before the end of their third year. The research paper or project used to meet this requirement may not be used to meet the bachelor's paper or project requirement in another major or course. NOTE: Credit for STAT 29900 Bachelor's Paper will not count towards the courses required for a major in Statistics.

Joint BA/MS or BS/MS Program

This program enables unusually well-qualified undergraduate students to complete an MS in Statistics along with a BA or BS during their four years at the College. Although a student may receive a BA or BS in any field, a program of study other than Statistics is recommended.

Only a small number of students will be selected for the program through a competitive admissions process. Participants must apply to the MS program in Statistics by June 1 of their third year for admission to candidacy for an MS in Statistics during their fourth year. To be considered, students should have completed almost all of their undergraduate requirements, including all of their general education and language competence requirements, by the end of their third year. They should also have completed, at a minimum, STAT 24400-24500 Statistical Theory and Methods I-II with A or A- grades and all the mathematics requirements for the Statistics major with very high grades. While these are the minimum criteria, admission is competitive, and additional qualifications may be needed. Interested students are strongly encouraged to consult both the Departmental Adviser for Majors and the College Joint Degree Program Adviser early in their third year. (For an appointment with the College Joint Degree Program Adviser, call the College Advising Reception Desk at 773.702.8615.)

Participants in the joint BA/MS or BS/MS program must meet the same requirements as students in the MS program in Statistics. Of the nine courses that are required at the appropriate level, up to three may also meet the requirements of an undergraduate program. For example, STAT 24400-24500 Statistical Theory and Methods I-II and STAT 24610 Pattern Recognition, which are required for the MS in Statistics, could also be used to meet part of the requirements of a BA or BS program in Mathematics for courses outside of Mathematics.

Other requirements include a master's paper and participation in the Consulting Program of the Department of Statistics. For details, visit www.stat.uchicago.edu/admissions/ms-degree.shtml .

Minor Program in Statistics

The focus in the minor is on statistical methodology, whereas the Statistics major has a substantial theoretical component. Students can begin the Statistics minor with either STAT 22000 Statistical Methods and Applications or STAT 23400 Statistical Models and Methods as their introductory course, which require just two or three quarters of calculus as prerequisites. STAT 24500 Statistical Theory and Methods II (but not STAT 24400 Statistical Theory and Methods I) may also be used to satisfy the introductory statistics requirement.

The minor in Statistics requires an introductory course, one course in applied regression analysis, one course in statistical methods, and two approved electives on statistical topics chosen to complement a student's major or personal interest.

Summary of Requirements

Introductory Statistics
One of the following: *		100
STAT 22000	Statistical Methods and Applications
STAT 23400	Statistical Models and Methods
STAT 24500	Statistical Theory and Methods II ^**
One applied regression course:		100
STAT 22400	Applied Regression Analysis
Three of the following topics courses:		300
STAT 22200	Linear Models and Experimental Design ^***
STAT 22600	Analysis of Categorical Data ^***
STAT 22700	Biostatistical Methods ^***
STAT 24300	Numerical Linear Algebra ^**
STAT 24610	Pattern Recognition ^**
STAT 26100	Time Dependent Data
STAT 26700	History of Statistics
STAT 27400	Nonparametric Inference
STAT 31900	Causal Inference
STAT 35000	Principles of Epidemiology
STAT 35201	Introduction to Clinical Trials
STAT 35600	Applied Survival Analysis
STAT 35700	Epidemiologic Methods
STAT 35800	Statistical Applications
STAT 36900	Applied Longitudinal Data Analysis
SOCI 30112	Applications of Hierarchical Linear Models
HSTD 35100	Health Services Research Methods
Total Units		500

*	Only one introductory course may be included in the statistics minor. Further, if the introductory course is a required component of a student's major or if AP credit for STAT 22000 Statistical Methods and Applications is used to satisfy the introductory course requirement, then one additional statistical topics course must be chosen to complete the minimum five-course requirement for the minor in Statistics.
**	These courses have mathematical prerequisites at a level above that of MATH 13300 Elementary Functions and Calculus III, MATH 15300 Calculus III, or MATH 16300 Honors Calculus III.
***	At least one of the three topics courses must be STAT 22200 Linear Models and Experimental Design, STAT 22600 Analysis of Categorical Data, or STAT 22700 Biostatistical Methods. NOTE: Students may not include both STAT 22600 Analysis of Categorical Data and STAT 22700 Biostatistical Methods in the minor.

The topics courses on the list above are approved for the Statistics minor. Students may petition the Departmental Adviser for Minors for approval of another course. Such courses must have a minimum statistics prerequisite of STAT 22000 Statistical Methods and Applications or equivalent.

The following Statistics courses may not be included in a Statistics minor: STAT 20000 Elementary Statistics, STAT 24400 Statistical Theory and Methods I, STAT 25100 Introduction to Mathematical Probability, STAT 25300 Introduction to Probability Models, or any graduate courses in probability.

Any prerequisite mathematics courses needed are not a part of the Statistics minor and may be counted toward a major or toward general education requirements. If STAT 24500 Statistical Theory and Methods II is used as the introductory course in the Statistics minor, then the prerequisite STAT 24400 Statistical Theory and Methods I may not be counted toward the Statistics minor, but may be counted toward another major.

Students who elect the minor program in Statistics must meet with the Departmental Adviser for Minors before the end of Spring Quarter of their third year to declare their intention to complete the minor. Courses for the minor are chosen in consultation with the Departmental Adviser for Minors. The approval for the minor program signed by the Departmental Adviser for Minors should be submitted to a student's College Adviser by the deadline above on the Consent to Complete a Minor Program Form obtained from the College Advisers office or website.

Courses in the minor may not be double-counted toward the student's major(s), other minors, or general education requirements. Courses in the minor must be taken for quality grades and students must receive a grade of C- or higher in each course taken for the minor. More than half of the requirements for the minor must be met by registering for courses bearing University of Chicago course numbers.

College-level Statistics courses are shown below. Graduate-level courses can be found here.

Statistics Courses

STAT 20000. Elementary Statistics. 100 Units.

This course introduces statistical concepts and methods for the collection, presentation, analysis, and interpretation of data. Elements of sampling, simple techniques for analysis of means, proportions, and linear association are used to illustrate both effective and fallacious uses of statistics.

Terms Offered: Autumn, Winter, Spring
Note(s): This course is recommended for students who do not plan to take advanced statistics courses, and it may not be used in the statistics major. It is not open to students with credit for STAT 22000 or 23400 who matriculated in the College after August 2008. This course meets one of the general education requirements in the mathematical sciences.

STAT 22000. Statistical Methods and Applications. 100 Units.

This course introduces statistical techniques and methods of data analysis, including the use of computers. Examples are drawn from the biological, physical, and social sciences. Students are required to apply the techniques discussed to data drawn from actual research. Topics include data description, graphical techniques, exploratory data analyses, random variation and sampling, one- and two-sample problems, analysis of variance, linear regression, and analysis of discrete data.

Terms Offered: Autumn, Winter, Spring
Prerequisite(s): Two quarters of calculus
Note(s): Students who matriculate in the College after August 2008 may count either STAT 22000 or 23400, but not both, toward the forty-two credits required for graduation.
Equivalent Course(s): HDCP 22050

STAT 22200. Linear Models and Experimental Design. 100 Units.

This course covers principles and techniques for the analysis of experimental data and the planning of the statistical aspects of experiments. Topics include linear models; analysis of variance; randomization, blocking, and factorial designs; confounding; and incorporation of covariate information.

Terms Offered: Spring
Prerequisite(s): STAT 22000 or 23400 or 24500

STAT 22400. Applied Regression Analysis. 100 Units.

This course introduces the methods and applications of fitting and interpreting multiple regression models. The primary emphasis is on the method of least squares and its many varieties. Topics include the examination of residuals, the transformation of data, strategies and criteria for the selection of a regression equation, the use of dummy variables, tests of fit, nonlinear models, biases due to excluded variables and measurement error, and the use and interpretation of computer package regression programs. The techniques discussed are illustrated by many real examples involving data from both the natural and social sciences. Matrix notation is introduced as needed.

Terms Offered: Autumn
Prerequisite(s): STAT 22000 or 23400 or 24500 or HSTD 32100
Equivalent Course(s): HSTD 32400

STAT 22600. Analysis of Categorical Data. 100 Units.

This course covers statistical methods for the analysis of structured, counted data. Topics may include Poisson, multinomial, and product-multinomial sampling models; chi-square and likelihood ratio tests; log-linear models for cross-classified counted data, including models for data with ordinal categories and log-multiplicative models; logistic regression and logit linear models; and measures of association. Applications in the social and biological sciences are considered, and the interpretation of models and fits, rather than mathematical details of computational procedures, is emphasized.

Terms Offered: Winter
Prerequisite(s): STAT 22000 or 23400 or 24500
Equivalent Course(s): HSTD 32600

STAT 22700. Biostatistical Methods. 100 Units.

This course is designed to provide students with tools for analyzing categorical, count, and time-to-event data frequently encountered in medicine, public health, and related biological and social sciences. This course emphasizes application of the methodology rather than statistical theory (e.g., recognition of the appropriate methods; interpretation and presentation of results). Methods covered include contingency table analysis, Kaplan-Meier survival analysis, Cox proportional-hazards survival analysis, logistic regression, and Poisson regression.

Instructor(s): H. Cao Terms Offered: Winter
Prerequisite(s): HSTD 32400, STAT 22400 or STAT 24500 or equivalent or consent of instructor.
Equivalent Course(s): HSTD 32700

STAT 23400. Statistical Models and Methods. 100 Units.

This course is recommended for students throughout the natural and social sciences who want a broad background in statistical methodology and exposure to probability models and the statistical concepts underlying the methodology. Probability is developed for the purpose of modeling outcomes of random phenomena. Random variables and their expectations are studied; including means and variances of linear combinations and an introduction to conditional expectation. Binomial, Poisson, normal and other standard probability distributions are considered. Some probability models are studied mathematically, and others are studied via simulation on a computer. Sampling distributions and related statistical methods are explored mathematically, studied via simulation, and illustrated on data. Methods include, but are not limited to, inference for means and variances for one- and two-sample problems, correlation, and simple linear regression. Graphical description and numerical data description are used for exploration, communication of results, and comparing mathematical consequences of probability models and data. Mathematics employed is to the level of univariate calculus, but it is less demanding than that required by STAT 24400.

Terms Offered: Autumn, Winter, Spring
Prerequisite(s): MATH 13300, 15300, or 16300
Note(s): Students who matriculate in the College after August 2008 may count either STAT 22000 or 23400, but not both, toward the forty-two credits required for graduation.

STAT 24300. Numerical Linear Algebra. 100 Units.

This course is devoted to the basic theory of linear algebra and its significant applications in scientific computing. The main objective is to provide a working knowledge of linear algebra and matrix computation suitable for advanced studies in which numerical methods are in demand, such as in statistics, econometrics, and scientific data organization and computation. Topics covered will include: Gaussian elimination, LU decomposition, vector spaces, linear transformations and their matrix representations, orthogonality and projections, QR factorization, eigenvectors and eigenvalues, diagonalization of real symmetric and complex Hermitian matrices, the spectral theorem, Cholesky decomposition, and Singular Value Decomposition. In addition, students will program in MATLAB or R using basic algorithms for linear systems, eigenvalue problem, matrix factorization, and sensitivity analysis.

Terms Offered: Autumn
Prerequisite(s): Multivariate calculus (MATH 19520 or 20000, or equivalent)
Equivalent Course(s): STAT 30750

STAT 24400-24500. Statistical Theory and Methods I-II.

This course is a systematic introduction to the principles and techniques of statistics, as well as to practical considerations in the analysis of data, with emphasis on the analysis of experimental data. The first quarter covers tools from probability and the elements of statistical theory. Topics include the definitions of probability and random variables, binomial and other discrete probability distributions, normal and other continuous probability distributions, joint probability distributions and the transformation of random variables, principles of inference (including Bayesian inference), maximum likelihood estimation, hypothesis testing and confidence intervals, likelihood ratio tests, multinomial distributions, and chi-square tests. Examples are drawn from the social, physical, and biological sciences. The coverage of topics in probability is limited and brief, so students who have taken a course in probability find reinforcement rather than redundancy. The second quarter covers statistical methodology, including the analysis of variance, regression, correlation, and some multivariate analysis. Some principles of data analysis are introduced, and an attempt is made to present the analysis of variance and regression in a unified framework. Computers are used in the second quarter.

STAT 24400. Statistical Theory and Methods I. 100 Units.

Terms Offered: Autumn, Winter
Prerequisite(s): Multivariate calculus (MATH 19520 or 20000 or 20500, or equivalent)
Note(s): Some previous experience with statistics and/or probability and linear algebra helpful but not required.

STAT 24500. Statistical Theory and Methods II. 100 Units.

Terms Offered: Winter, Spring
Prerequisite(s): Multivariate calculus (MATH 19520 or 20000 or 20500, or equivalent) and linear algebra (MATH 19620 or 25500 or STAT 24300 or equivalent)
Note(s): Some previous experience with statistics and/or probability helpful but not required.

STAT 24610. Pattern Recognition. 100 Units.

This course treats statistical models and methods for pattern recognition and machine learning. Topics include a review of the multivariate normal distribution, graphical models, computational methods for inference in graphical models in particular the EM algorithm for mixture models and HMM’s, and the sum-product algorithm. Linear discriminative analysis and other discriminative methods, such as decision trees and SVM’s are covered as well.

Terms Offered: Spring
Prerequisite(s): Linear algebra at the level of STAT 24300. Knowledge of probability and statistical estimation techniques (e.g., maximum likelihood and linear regression) at the level of STAT 24400-24500
Equivalent Course(s): STAT 37500

STAT 25100. Introduction to Mathematical Probability. 100 Units.

This course covers fundamentals and axioms; combinatorial probability; conditional probability and independence; binomial, Poisson, and normal distributions; the law of large numbers and the central limit theorem; and random variables and generating functions.

Terms Offered: Spring
Prerequisite(s): MATH 20000 or 20500, or consent of instructor

STAT 25300. Introduction to Probability Models. 100 Units.

This course introduces stochastic processes as models for a variety of phenomena in the physical and biological sciences. Following a brief review of basic concepts in probability, we introduce stochastic processes that are popular in applications in sciences (e.g., discrete time Markov chain, the Poisson process, continuous time Markov process, renewal process and Brownian motion).

Terms Offered: Winter
Prerequisite(s): STAT 24400 or 25100
Equivalent Course(s): STAT 31700

STAT 26100. Time Dependent Data. 100 Units.

This course considers the modeling and analysis of data that are ordered in time. The main focus is on quantitative observations taken at evenly spaced intervals and includes both time-domain and spectral approaches.

Terms Offered: Winter or Spring
Prerequisite(s): MATH 15300 and STAT 24400, STAT 24500 or 22400, or consent of instructor
Note(s): Some previous exposure to Fourier series is helpful but not required.
Equivalent Course(s): STAT 33600

STAT 26700. History of Statistics. 100 Units.

This course covers topics in the history of statistics, from the eleventh century to the middle of the twentieth century. We focus on the period from 1650 to 1950, with an emphasis on the mathematical developments in the theory of probability and how they came to be used in the sciences. Our goals are both to quantify uncertainty in observational data and to develop a conceptual framework for scientific theories. This course includes broad views of the development of the subject and closer looks at specific people and investigations, including reanalyses of historical data.

Instructor(s): S. Stigler Terms Offered: Spring
Prerequisite(s): Prior statistics course
Equivalent Course(s): CHSS 32900,HIPS 25600,STAT 36700

STAT 27400. Nonparametric Inference. 100 Units.

Nonparametric inference is about developing statistical methods and models that make weak assumptions. A typical nonparametric approach estimates a nonlinear function from an infinite dimensional space rather than a linear model from a finite dimensional space. This course gives an introduction to nonparametric inference, with a focus on density estimation, regression, confidence sets, orthogonal functions, random processes, and kernels. The course treats nonparametric methodology and its use, together with theory that explains the statistical properties of the methods.

Terms Offered: Winter
Prerequisite(s): STAT 22400 or 24400
Equivalent Course(s): STAT 37400

STAT 27725. Machine Learning. 100 Units.

This course offers a practical, problem-centered introduction to machine learning. Topics covered include the Perceptron and other online algorithms; boosting; graphical models and message passing; dimensionality reduction and manifold learning; SVMs and other kernel methods; and a short introduction to statistical learning theory. Weekly programming assignments give students the opportunity to try out each learning algorithm on real world datasets.

Terms Offered: Winter
Prerequisite(s): CMSC 15300, CMSC 15400. STAT 22000 or STAT 23400 strongly recommended.
Equivalent Course(s): CMSC 25400

STAT 29700. Undergraduate Research. 100 Units.

This course consists of reading and research in an area of statistics or probability under the guidance of a faculty member. A written report must be submitted at the end of the quarter.

Terms Offered: Autumn, Winter, Spring
Prerequisite(s): Consent of faculty adviser and Departmental Adviser for Majors
Note(s): Students are required to submit the College Reading and Research Course Form. Open to all students, including nonmajors. May be taken either for quality grades or for P/F grading.

STAT 29900. Bachelor's Paper. 100 Units.

This course consists of reading and research in an area of statistics or probability under the guidance of a faculty member, leading to a bachelor's paper. The paper must be submitted at the end of the quarter.

Terms Offered: Autumn, Winter, Spring
Prerequisite(s): Consent of faculty adviser and Departmental Adviser for Majors
Note(s): Students are required to submit the College Reading and Research Course Form. Open only to students who are majoring in statistics. May be taken for P/F grading. Credit for STAT 29900 may not be counted toward the twelve courses required for a major in statistics.