Statistics

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Undergraduate Primary Contact

Professor Michael Stein
E 135
702.8326 or 702.8333
Email

Administrative Contact

Student Affairs Specialist Matt Johnston
E 108
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 BA 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 counselor 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. Information 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

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 test in statistics yields credit for STAT 22000 Statistical Methods and Applications, although this credit will not count toward the requirements for a major in statistics. covers much of the same material as 22000, 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. For their introductory statistics course, students should choose either STAT 22000 Statistical Methods and Applications or STAT 23400 Statistical Models and Methods (not both). For students who do not intend to continue to more advanced statistics courses, STAT 20000 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. STAT 25100 Introduction to Mathematical Probability is an introductory course in probability.

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 multiple integration 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, many students find it helpful to take a more elementary course as preparation. 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 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. Taking STAT 24400-24500 Statistical Theory and Methods I-II before STAT 25100 Introduction to Mathematical Probability is recommended but not required.

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 complementary second courses emphasize some class of methods for the analysis of data. They may be taken in any order, although there is some overlap between STAT 22600 Analysis of Categorical Data and STAT 22700 Biostatistical Methods. Also, STAT 22400 Applied Regression Analysis is a prerequisite for STAT 22700 Biostatistical Methods. 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). The emphasis is on linear models and experimental design in STAT 22200 Linear Models and Experimental Design, multiple regression and least squares in STAT 22400 Applied Regression Analysis, categorical data analysis in STAT 22600 Analysis of Categorical Data, and statistical methods for medical applications in STAT 22700 Biostatistical Methods. STAT 26100 Time Dependent Data, which covers time dependent data, is appropriate for students with some knowledge of linear models (STAT 22400 Applied Regression Analysis or STAT 24400-24500 Statistical Theory and Methods I-II) and a good familiarity with infinite series.

For students who have completed STAT 24500 Statistical Theory and Methods II, many graduate courses in statistics offer opportunities for further study of statistical theory, methods, and applications. The introductory probability course (STAT 25100 Introduction to Mathematical Probability) may be taken separately from any statistics courses and can be supplemented with more advanced probability courses, such as STAT 25300 Introduction to Probability Models (=STAT 31700 Introduction to Probability Models). Students with a strong mathematical background may 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. College students may register for a number of other 30000-level courses in statistics. For details, consult the instructor or the departmental counselor, or visit www.stat.uchicago.edu.

Program Requirements

Students pursuing the BA in statistics should meet the general education requirements in the mathematical sciences with courses in calculus. The 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 one course in computer science and three approved elective courses in statistics. The four required statistics courses are STAT 24400-24500 Statistical Theory and Methods I-II and 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 may take STAT 22000 Statistical Methods and Applications or STAT 23400 Statistical Models and Methods as preparation for STAT 24400 Statistical Theory and Methods I. If either STAT 22000 Statistical Methods and Applications or STAT 23400 Statistical Models and Methods is included in the program (students may not include both), it will be counted as one of three approved electives and must be taken before STAT 24400 Statistical Theory and Methods I. Candidates must obtain approval of their course program from the departmental counselor; not all combinations of statistics electives are allowed. Specifically, at least two of the three electives must be courses in statistical methodology beyond the introductory level. NOTE: Students who are completing majors in both statistics and economics and who already have taken MATH 19520-19620 should discuss with the departmental counselor how to best meet their mathematical requirements.

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
STAT 24400	Statistical Theory and Methods I	100
STAT 24500	Statistical Theory and Methods II	100
STAT 25100	Introduction to Mathematical Probability	100
STAT 22400	Applied Regression Analysis	100
or 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.
**	10600 or higher preferred
***	For example, 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, or STAT 26700 History of Statistics. Upon petition, one intermediate/advanced course in mathematics or computer science may be approved for this purpose by the statistics departmental counselor as relevant for a coherent degree program. The petition must include a documented strong case for the relevance.

Grading

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.

In addition to submitting the official Incomplete Form required by the College, the following policy applies to students who wish to receive a mark of I for a statistics course: 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.

Students who are majoring in statistics must receive a quality grade of at least C- in each of the twelve required courses in the major; a grade of P is not acceptable for any of these courses.

Honors

The BA 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 twelve required courses in the major, and who, in addition, 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 must consult the departmental counselor before the end of their third year. The research paper or project used to meet this requirement may not be used to meet the BA paper or project requirement in another major. NOTE: Credit for STAT 29900 Bachelor's Paper will not count towards the twelve courses required for a major in statistics.

Joint BA/MS Program

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

Participants must be admitted to the MS program in statistics. Students must submit applications by June 1 of their third year for admission to candidacy for an MS in statistics during their fourth year. Interested students are strongly encouraged to consult the departmental counselor and Ron Gorny, the BA/MS adviser, early in their third year. (For a appointment with Mr. Gorny, call the College Adviser's Reception Desk at 702-8615.)

Participants in the joint BA/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, two courses in statistical methods, and two approved electives on statistical topics chosen to complement a student's major or personal interest. 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, a third approved elective must be included to complete the statistics minor.

Summary of Requirements

Introductory Statistics
One of the following:		100
STAT 22000	Statistical Methods and Applications
STAT 23400	Statistical Models and Methods
Statistical Methods
STAT 22400	Applied Regression Analysis	100
One of the following:		100
STAT 22200	Linear Models and Experimental Design
STAT 22600	Analysis of Categorical Data
STAT 22700	Biostatistical Methods
Additional Topics in Statistics
Two of the following:		200
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 33200	Causal Inference
STAT 35000	Principles of Epidemiology
STAT 35600	Applied Survival Analysis
STAT 36900	Longitudinal Data Analysis
HSTD 32901	Introduction to Clinical Trials
Total Units		500

The topics courses on the list above are approved for the statistics minor. Students may petition the departmental counselor 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 25100 Introduction to Mathematical Probability, or STAT 25300 Introduction to Probability Models; or any graduate courses in probability. Students may not include both STAT 22600 Analysis of Categorical Data and STAT 22700 Biostatistical Methods in the minor. If either STAT 22000 Statistical Methods and Applications or STAT 23400 Statistical Models and Methods is required for another degree, then one additional statistical topics course must be chosen to complete the minimum five-course requirement for the minor in statistics. 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.

Students who elect the minor program in statistics must meet with the departmental counselor before the end of Spring Quarter of their third year to declare their intention to complete the minor. The approval of the departmental counselor for the minor program should be submitted to a student's College adviser by the deadline above on a form obtained from the College adviser. (The deadline for students graduating in June or August of 2010 is Friday of first week of Spring Quarter 2010.) Courses for the minor are chosen in consultation with the departmental counselor.

Courses in the minor (1) may not be double counted with the student's major(s) or with other minors and (2) may not be counted toward 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.

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.

Terms Offered: Winter
Prerequisite(s): HSTD 32400, STAT 22400 or STAT 24500
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 covers linear algebra, with special attention to topics useful in statistical applications. In addition to addressing theoretical and algorithmic aspects of solving systems of linear equations, topics may include least squares, orthogonal projections, positive-definite matrices, quadratic forms, matrix decompositions, and an introduction to vector spaces. Computers are used to study some computational issues and mathematical explorations.

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

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 equivalent) and linear algebra (MATH 19620, 25500 or STAT 24300 or equivalent)
Note(s): Some previous experience with statistics and/or probability 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 equivalent) and linear algebra (MATH 19620, 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 from pattern recognition and machine learning. Possible topics include linear discriminant analysis, logistic regression, mixture models, factor analysis, hidden Markov models, graphical models, the Expectation-Maximization [EM] algorithm as well as different sampling techniques including Markov chain Monte Carlo [MCMC]. The exact course content may vary from year to year.

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

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: 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 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 counselor
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; however, students who wish to count this course toward the requirements for a major in statistics must receive prior approval of the departmental counselor and must receive a quality grade.

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 counselor
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.

STAT 30100. Mathematical Statistics I. 100 Units.

Terms Offered: Winter
Prerequisite(s): STAT 30400 or consent of instructor

STAT 30200. Mathematical Statistics II. 100 Units.

Terms Offered: Spring
Prerequisite(s): STAT 30400 or consent of instructor

STAT 30400. Distribution Theory. 100 Units.

This course is a systematic introduction to random variables and probability distributions. Topics include standard distributions (i.e., uniform, normal, beta, gamma, F, t, Cauchy, Poisson, binomial, and hypergeometric); moments and cumulants; characteristic functions; exponential families; modes of convergence; central limit theorem; and Laplace's method.

Terms Offered: Autumn
Prerequisite(s): STAT 24500 and MATH 20500, or consent of instructor

STAT 30900. Mathematical Computation I: Matrix Computation Course. 100 Units.

This course covers the theory and practice of matrix computation, starting with the LU and Cholesky decompositions, the QR decompositions with applications to least squares, iterative methods for solving eigenvalue problems, iterative methods for solving large systems of equations, and (time permitting) the basics of the fast Fourier and fast wavelet transforms. The mathematical theory underlying the algorithms is emphasized, as well as their implementation in code.

Terms Offered: Autumn
Prerequisite(s): Linear algebra (STAT 24300 or equivalent) and some previous experience with statistics
Equivalent Course(s): CMSC 37810

STAT 31000. Mathematical Computation II: Optimization and Simulation. 100 Units.

This course covers the fundamentals of continuous optimization, including constrained optimization, and introduces the use of Monte Carlo methods in computer simulation and combinatorial optimization problems. Several substantial programming projects (using MATLAB) are completed during the course.

Terms Offered: Winter
Prerequisite(s): Solid grounding in multivariate calculus, linear algebra, and probability theory
Equivalent Course(s): CMSC 37811

STAT 31100. Mathematical Computation III: Numerical Methods for PDE's. 100 Units.

The first part of this course introduces basic properties of PDE's; finite difference discretizations; and stability, consistency, convergence, and Lax's equivalence theorem. We also cover examples of finite difference schemes; simple stability analysis; convergence analysis and order of accuracy; consistency analysis and errors (i.e., dissipative and dispersive errors); and unconditional stability and implicit schemes. The second part of this course includes solution of stiff systems in 1, 2, and 3D; direct vs. iterative methods (i.e., banded and sparse LU factorizations); and Jacobi, Gauss-Seidel, multigrid, conjugate gradient, and GMRES iterations.

Terms Offered: Spring
Prerequisite(s): Some prior exposure to differential equations and linear algebra
Equivalent Course(s): CMSC 37812

STAT 31200. Introduction to Stochastic Processes I. 100 Units.

This course introduces stochastic processes not requiring measure theory. Topics include branching processes, recurrent events, renewal theory, random walks, Markov chains, Poisson, and birth-and-death processes.

Terms Offered: Winter
Prerequisite(s): STAT 25100 and MATH 20500; STAT 30400 or consent of instructor

STAT 31300. Introduction to Stochastic Processes II. 100 Units.

Topics include continuous-time Markov chains, Markov chain Monte Carlo, discrete-time martingales, and Brownian motion and diffusions. Our emphasis is on defining the processes and calculating or approximating various related probabilities. The measure theoretic aspects of these processes are not covered rigorously.

Terms Offered: Spring
Prerequisite(s): STAT 31200 or consent of instructor

STAT 31700. Introduction to Probability Models. 100 Units.

Terms Offered: Winter
Prerequisite(s): STAT 24400 or 25100
Equivalent Course(s): STAT 25300

STAT 33100. Sample Surveys. 100 Units.

This course covers random sampling methods; stratification, cluster sampling, and ratio estimation; and methods for dealing with nonresponse and partial response.

Terms Offered: Autumn
Prerequisite(s): Consent of instructor

STAT 33200. Causal Inference. 100 Units.

Equivalent Course(s): HSTD 43200

STAT 33600. Time Dependent Data. 100 Units.

STAT 34300. Applied Linear Statistical Methods. 100 Units.

This course introduces the theory, methods, and applications of fitting and interpreting multiple regression models. Topics include the examination of residuals, the transformation of data, strategies and criteria for the selection of a regression equation, nonlinear models, biases due to excluded variables and measurement error, and the use and interpretation of computer package regression programs. The theoretical basis of the methods, the relation to linear algebra, and the effects of violations of assumptions are studied. Techniques discussed are illustrated by examples involving both physical and social sciences data.

Terms Offered: Autumn
Prerequisite(s): STAT 24500 or equivalent, and linear algebra (STAT 24300 or equivalent)

STAT 34500. Design and Analysis of Experiments. 100 Units.

This course introduces the methodology and application of linear models in experimental design. We emphasize the basic principles of experimental design (e.g., blocking, randomization, incomplete layouts). Many of the standard designs (e.g., fractional factorial, incomplete block, split unit designs) are studied within this context. The analysis of these experiments is developed as well, with particular emphasis on the role of fixed and random effects. Additional topics may include response surface analysis, the use of covariates in the analysis of designed experiments, and spatial analysis of field trials.

Terms Offered: Winter
Prerequisite(s): STAT 34300

STAT 34700. Generalized Linear Models. 100 Units.

This applied course covers factors, variates, contrasts, and interactions; exponential-family models (i.e., variance function); definition of a generalized linear model (i.e., link functions); specific examples of GLMs; logistic and probit regression; cumulative logistic models; log-linear models and contingency tables; inverse linear models; Quasi-likelihood and least squares; estimating functions; and partially linear models.

Terms Offered: Spring
Prerequisite(s): STAT 34300 or consent of instructor

STAT 35000. Principles of Epidemiology. 100 Units.

This course does not meet requirements for the biological sciences major. Epidemiology is the study of the distribution and determinants of health and disease in human populations. This course introduces the basic principles of epidemiologic study design, analysis, and interpretation through lectures, assignments, and critical appraisal of both classic and contemporary research articles.

Instructor(s): B. Lahey Terms Offered: Autumn
Prerequisite(s): Consent of Instructor
Equivalent Course(s): HSTD 30900,BIOS 29318,ENST 27400,PPHA 36400

STAT 35201. Introduction to Clinical Trials. 100 Units.

This course will review major components of clinical trial conduct, including the formulation of clinical hypotheses and study endpoints, trial design, development of the research protocol, trial progress monitoring, analysis, and the summary and reporting of results. Other aspects of clinical trials to be discussed include ethical and regulatory issues in human subjects research, data quality control, meta-analytic overviews and consensus in treatment strategy resulting from clinical trials, and the broader impact of clinical trials on public health.
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Instructor(s): J. Dignam Terms Offered: Spring
Prerequisite(s): HSTD 32100; STAT 22000; Introductory Statistics or Consent of Instructor
Equivalent Course(s): HSTD 32901

STAT 35400. Gene Regulation. 100 Units.

This course covers the fundamental theory of gene expression in prokaryotes and eukaryotes through lectures and readings in the primary literature. Natural and synthetic genetic systems arising in the context of E. coli physiology and Drosophila development will be used to illustrate fundamental biological problems together with the computational and theoretical tools required for their solution. These tools include large scale optimization, image processing, ordinary and partial differential equations, the chemical Langevin and Fokker-Planck equations, and the chemical master equation. A central theme of the class is the art of identifying biological problems which require theoretical analysis and choosing the correct mathematical framework with which to solve the problem.

Terms Offered: Winter
Prerequisite(s): Consent of instructor
Equivalent Course(s): ECEV 35400,MGCB 35401

STAT 35600. Applied Survival Analysis. 100 Units.

This course introduces principles and methods for the analysis of time-to-event data. This type of data occurs extensively in both observational and experimental biomedical and public health studies, as well as in industrial applications. While some theoretical statistical detail is given (at the level appropriate for a master's student in statistics), we primarily focus on data analysis. Problems are motivated from an epidemiologic and clinical perspective, concentrating on the analysis of cohort data and time-to-event data from controlled clinical trials.

Terms Offered: Autumn
Prerequisite(s): HSTD 32100, STAT 22000, introductory statistics, or consent of instructor
Equivalent Course(s): HSTD 33100

STAT 36700. History of Statistics. 100 Units.

Instructor(s): S. Stigler Terms Offered: Spring
Prerequisite(s): Prior statistics course
Equivalent Course(s): STAT 26700,CHSS 32900,HIPS 25600

STAT 36900. Longitudinal Data Analysis. 100 Units.

Longitudinal data consist of multiple measures over time on a sample of individuals. This type of data occurs extensively in both observational and experimental biomedical and public health studies, as well as in studies in sociology and applied economics. This course introduces principles and methods for the analysis of longitudinal data. Although some supporting statistical theory is given, we emphasize data analysis and interpretation of models for longitudinal data. Problems are motivated by applications in epidemiology, clinical medicine, health services research, and disease natural history studies.

Terms Offered: Autumn
Prerequisite(s): HSTD 32400, STAT 22400 or equivalent, and HSTD 32600, STAT 22600 or HSTD 32700, STAT 22700 or equivalent; or consent of instructor.
Equivalent Course(s): HSTD 33300

STAT 37710. Machine Learning. 100 Units.

This course introduces the theory and practice of machine learning, emphasizing statistical approaches to the problem. Topics include pattern recognition, empirical risk minimization and the Vapnik Chervonenkis theory, neural networks, decision trees, genetic algorithms, unsupervised learning, and multiple classifiers.

Instructor(s): J. Lafferty Terms Offered: Winter
Prerequisite(s): Consent of department counselor. CMSC 25010 or consent of instructor.
Equivalent Course(s): CMSC 35400

STAT 37900. Computer Vision. 100 Units.

This course covers deformable models for detecting objects in images. Topics include one-dimensional models to identify object contours and boundaries; two-dimensional models for image matching; and sparse models for efficient detection of objects in complex scenes. Mathematical tools needed to define the models and associated algorithms are developed. Applications include detecting contours in medical images, matching brains, and detecting faces in images. Neural network implementations of some of the algorithms are presented, and connections to the functions of the biological visual system are discussed.

Instructor(s): Y. Amit Terms Offered: Winter. Not offered 2012–13.
Prerequisite(s): Consent of department counselor and instructor
Equivalent Course(s): CMSC 35500,CMSC 25050

STAT 38100. Measure-Theoretic Probability I. 100 Units.

This course provides a detailed, rigorous treatment of probability from the point of view of measure theory, as well as existence theorems, integration and expected values, characteristic functions, moment problems, limit laws, Radon-Nikodym derivatives, and conditional probabilities.

Terms Offered: Autumn
Prerequisite(s): STAT 31300 or consent of instructor

STAT 38300. Measure-Theoretic Probability III. 100 Units.

This course continues material covered in STAT 38100, with topics that include Lp spaces, Radon-Nikodym theorem, conditional expectation, and martingale theory.

Terms Offered: Winter
Prerequisite(s): STAT 38100