DEPARTMENT OF STATISTICS
2019 Donald Bren
Hall; (949) 824-5392: Fax: (949) 824-9863
David van Dyk, Department Chair
Faculty / Undergraduate Program / Graduate Program / Courses
Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting, and presenting empirical data. Statistical principles and methods are important for addressing questions in public policy, medicine, industry, and virtually every branch of science. Interest in statistical methods has increased dramatically with the abundance of large databases in fields like computer science (Internet and Web traffic), business and marketing (transaction records), and biology (the human genome and related data). It is the substantive questions in such areas of application that drive the development of new statistical methods and motivate the mathematical study of the properties of these methods.
Undergraduate Program in Statistics
The Department of Statistics offers lower-division undergraduate courses designed to introduce students to the field of statistics (Statistics 7, 8, 67) and upper-division undergraduate courses on the theoretical foundations of probability and statistics (Statistics 120A-B-C, 121) and statistical methodology (Statistics 110-111-112). The Department is in the process of planning an undergraduate degree program in Statistics. In the interim, students interested in focusing on statistics are encouraged to consider a minor in Statistics along with a major in a field of interest.
MINOR IN STATISTICS
The minor in Statistics is designed to provide students with exposure to both statistical theory and practice. The minor requires a total of seven courses. These include a mathematics course, five core statistics courses, and an elective that may be taken from among several departments. Some of the courses used to complete the minor may include prerequisites that may or may not be part of a student's course requirements for their major. Because of this, the minor is somewhat intensive, but it is a useful complement to a variety of undergraduate fields for mathematically inclined students. The minor, supplemented with a few additional courses (mathematics and computing), would provide sufficient background for graduate study in statistics. Students considering a minor in Statistics should meet with the Director of Undergraduate Studies in Statistics as early as possible to plan their course work.
NOTE: Students may not receive both a minor in Statistics and a specialization in Statistics within the Mathematics major.
Requirements for the Minor
Six required courses: Mathematics 3A, Statistics 120A-B-C, Statistics 110-111.
One elective course: Students select one course from the following list, or can substitute another with approval of the Director of Undergraduate Studies: Statistics 7 or equivalent course (but only if taken prior to Statistics 110); Statistics 112; Statistics 121; Mathematics 105A or 105B; Mathematics 130B or 130C; Mathematics 132B or 132C; ICS 21.
Graduate Program in Statistics
Research in statistics can range from mathematical studies of the theoretical underpinnings of a statistical model or method to the development of novel statistical models and methods and a thorough study of their properties. Frequently, statistics research is motivated and informed by collaborations with experts in a particular substantive field. Their scientific studies and data collection efforts may yield complex data that cannot be adequately handled using standard statistical methodology. Statisticians aim to develop methods that address the scientific or policy questions of the researcher. In doing so, statisticians must consider how efficiently and effectively the proposed methodology can be implemented and what guarantees can be provided as to the performance of the proposed methods. Such questions can often be answered using a combination of mathematical, analytical, and computational techniques.
Background: Individuals from a variety of backgrounds can make significant contributions to the field of statistics as long as they have sufficient background in statistics, mathematics, and computing. Undergraduate preparation in statistics, mathematics, and computing should include multivariate calculus (the equivalent of UCI courses Mathematics 2A-B, 2D-E), linear algebra (121A), elementary analysis (140A-B), introductory probability and statistics (Statistics 120A-B-C), and basic computing (ICS 21). For students with undergraduate majors outside of mathematics and statistics, it is possible to make up one or two missing courses during the first year in the program.
Students may be admitted to either the master's program or the doctoral program. See page 347 for additional information about the Bren School of ICS's graduate programs and general information about admissions.
MASTER OF SCIENCE IN STATISTICS
Statistics Course Requirements: Intermediate Probability and Statistics (Statistics 200A-B-C); Statistical Methodology (Statistics 210, 211, 212); three quarters of Seminar in Statistics (Statistics 280); six other graduate courses in or related to statistics, at least three of which are offered by the Department of Statistics.
At most one of the six elective courses may be an Individual Study (Statistics 299), and only with prior approval of the Department Graduate Committee.
The entire program of courses must be approved by the Statistics Department Graduate Committee. Students with previous graduate training in statistics may petition the Committee to substitute other courses for a subset of the required courses. Students are required to pass a written comprehensive examination ordinarily at the end of the first year, covering the material from Statistics 200A-B-C, 210, 211, and 212.
DOCTOR OF PHILOSOPHY IN STATISTICS
Statistics Course Requirements: Intermediate Probability and Statistics (Statistics 200A-B-C); Statistical Methodology (Statistics 210, 211, 212); Advanced Probability and Statistics Topics (Statistics 220A-B); Bayesian Statistical Analysis (Statistics 225); Statistical Computing Methods (Statistics 230); five other graduate courses in or related to statistics, at least two of which are offered by the Department of Statistics. These courses must be completed prior to candidacy.
In addition, continual enrollment in Seminar in Statistics (Statistics 280) is required in all quarters.
Additional Ph.D. requirements:
Each Ph.D. student is required to take a written comprehensive examination, ordinarily at the end of the first year, covering the material from Statistics 200A-B-C, 210, 211, and 212. In addition, each student is required to take a written comprehensive examination after completion of the second year course work, covering material from Statistics 220A-B, 225, and 230.
Ph.D. students who have passed the written comprehensive examinations are required to give a post-comprehensive research presentation each year.
Ph.D. students are required to serve as teaching assistants for at least two quarters.
Ph.D. students are required to demonstrate substantive knowledge of an application area outside of statistics (e.g., computer science, economics, cognitive sciences, biology, or medicine). Such knowledge can be demonstrated by course work in the application area (three quarter courses), co-authorship of publishable research in the application area, or other evidence of supervised collaborative work that is substantiated by an expert in the field. In the case of a theoretically oriented student, the outside application area may be mathematics.
The normative time for advancement to candidacy is three years. The normative time for completion of the Ph.D. is five years, and the maximum time permitted is seven years.
MASTER OF SCIENCE IN STATISTICS FOR STUDENTS ENROLLED IN A DOCTORAL PROGRAM AT UCI
Students who are currently enrolled in a doctoral program at UCI and wish to pursue a Master of Science degree in Statistics at the same time should consult with the Director of Graduate Studies in Statistics to register their interest with the Department, to develop a program of study, and to establish a relationship with a faculty advisor in Statistics. The degree requirements including the comprehensive examination are the same as those listed under the Master of Science in Statistics. The Statistics Department Graduate Committee must be petitioned for permission to sit for the comprehensive examination. The petition should include the proposed plan of study and a current official UCI transcript. A petition for the degree must be filed with the Statistics Department Graduate Committee for approval two quarters before the degree is awarded.
Courses in Statistics
(Schedule of Classes designation: Stats)
7 Basic Statistics (4). Lecture, three hours; discussion, one to two hours. Introduces basic inferential statistics including confidence intervals and hypothesis testing on means and proportions, t-distribution, Chi Square, regression and correlation. F-distribution and nonparametric statistics included if time permits. Only one course from Statistics 7, Statistics 8, Management 7, or Biological Sciences 7 may be taken for credit. No credit for Statistics 7 if taken after Statistics 67. (V)
8 Introduction to Biological Statistics (4). Lecture, three hours; discussion, one hour. Teaches introductory statistical techniques used to collect and analyze experimental and observational data from health sciences and molecular, cellular, environmental, and evolutionary biology. Specific topics include exploration of data, probability and sampling distributions, basic statistical inference for means, proportions, linear regression, and analysis of variance. Only one course from Statistics 8, Statistics 7, Management 7, Biological Sciences 7, or Social Ecology 13 may be taken for credit. (V)
67 Introduction to Probability and Statistics for Computer Science (4). Lecture, three hours; discussion, two hours. Introduction to the basic concepts of probability and statistics with discussion of applications to computer science. Prerequisites: Mathematics 2B and ICS 6D. No credit for Statistics 7 or Management 7 if taken after Statistics 67. (V)
110 Statistical Methods for Data Analysis I (4). Lecture, three hours; laboratory, one hour. Introduction to statistical methods for analyzing data from experiments and surveys. Methods covered include two-sample procedures, analysis of variance, simple and multiple linear regression. Prerequisite: Statistics 7, or 120A-B-C, or knowledge of basic statistics. Concurrent with Statistics 201.
111 Statistical Methods for Data Analysis II (4). Lecture, three hours; laboratory, one hour. Introduction to statistical methods for analyzing data from surveys or experiments. Emphasizes application and understanding of methods for categorical data including contingency tables, logistic and Poisson regression, loglinear models. Prerequisite: Statistics 110 or equivalent. Concurrent with Statistics 202.
112 Statistical Methods for Data Analysis III (4). Lecture, three hours; laboratory, one hour. Introduction to statistical methods for analyzing longitudinal data from experiments and cohort studies. Topics covered include survival methods for censored time-to-event data, linear mixed models, non-linear mixed effects models, and generalized estimating equations. Prerequisite: Statistics 111 or equivalent. Concurrent with Statistics 203.
120A-B-C Introduction to Probability and Statistics (4-4-4). Lecture, three hours; discussion, one to two hours. Introductory course covering basic principles of probability and statistical inference. 120A: Axiomatic definition of probability, random variables, probability distributions, expectation. 120B: Point estimation, interval estimating, and testing hypotheses, Bayesian approaches to inference. 120C: Linear regression, analysis of variance, model checking. Prerequisites: for 120A-B: Mathematics 2A-B; 2D and 2J or 4; for 120C: Statistics 120A-B; Mathematics 3A or 6G. Same as Mathematics 131A-B-C. Only one course from Statistics 120A, Mathematics 130A, and Mathematics 132A may be taken for credit.
121 Probability Models (4). Advanced probability, discrete time Markov chains, Poisson processes, continuous time Markov chains. Queuing or simulation as time permits. Prerequisite: Statistics 120A. Concurrent with Computer Science 278.
199 Individual Study (2 to 5). Individual research or investigations under the direction of an individual faculty member. Prerequisite: consent of instructor.
200A-B-C Intermediate Probability and Statistical Theory (4-4-4). 200A: Basics of probability theory, random variables and basic transformations, univariate distributionsdiscrete and continuous, multivariate distributions. 200B: Random samples, transformations, limit laws, normal distribution theory, introduction to stochastic processes, data reduction, point estimation (maximum likelihood). 200C: Interval estimation, hypothesis testing, decision theory and Bayesian inference, basic linear model theory. Prerequisites: Statistics 120A-B-C or equivalent or consent of instructor.
201 Statistical Methods for Data Analysis I (4). Introduction to statistical methods for analyzing data from experiments and surveys. Methods covered include two-sample procedures, analysis of variance, simple and multiple linear regression. May not be taken for graduate credit by Statistics graduate students. Prerequisite: knowledge of basic statistics (at level of Statistics 7). Concurrent with Statistics 110.
202 Statistical Methods for Data Analysis II (4). Introduction to statistical methods for analyzing data from surveys or experiments. Emphasizes application and understanding of methods for categorical data including contingency tables, logistic and Poisson regression, loglinear models. May not be taken for graduate credit by Statistics graduate students. Prerequisite: Statistics 201 or equivalent. Concurrent with Statistics 111.
203 Statistical Methods for Data Analysis III (4). Introduction to statistical methods for analyzing longitudinal data from experiments and cohort studies. Topics covered include survival methods for censored time-to-event data, linear mixed models, non-linear mixed effects models, and generalized estimating equations. May not be taken for graduate credit by Statistics graduate students. Prerequisite: Statistics 202 or equivalent. Concurrent with Statistics 112.
210 Statistical Methods I: Linear Models (4). Statistical methods for analyzing data from surveys and experiments. Topics include randomization and model-based inference, two-sample methods, analysis of variance, linear regression and model diagnostics. Prerequisite: knowledge of basic statistics (at the level of Statistics 7), calculus, linear algebra.
211 Statistical Methods II: Regression Modeling Strategies (4). Introduction to non-linear regression methods for addressing scientific questions. Emphasizes strategies for appropriately selecting and implementing regression models for addressing questions that arise in multiple scientific areas including economics, public health, sociology, and biology. Prerequisite: Statistics 210 or equivalent.
212 Statistical Methods III: Generalized Linear Models (4). Development of the theory and application of generalized linear models. Topics covered include likelihood estimation and asymptotic distributional theory for exponential families and quasi-likelihood. Focuses on theoretical development and application of methodology for analyzing non-normal outcomes. Prerequisite: Statistics 211 or equivalent.
220A-B Advanced Probability and Statistics Topics (4-4). Advanced topics in probability and statistical inference including measure theoretic probability, large sample theory, decision theory, resampling and Monte Carlo methods, nonparametric methods. Prerequisites: Statistics 200A-B-C.
225 Bayesian Statistical Analysis (4). Introduction to the Bayesian approach to statistical inference. Topics include univariate and multivariate models, choice of prior distributions, hierarchical models, computation including Markov chain Monte Carlo, model checking, and model selection. Prerequisites: two quarters of upper-division or graduate training in probability and statistics, or consent of instructor.
226 Advanced Topics in Modern Bayesian Statistical Inference (4). Fundamental topics in modern Bayesian Statistics including theory of Markov chains, application of this theory to modern methods of Markov chain Monte Carlo sampling; mathematical background for Bayesian non-parametric and semiparametric modeling, including Dirichlet Process Mixtures and Mixtures of Polya Trees prior. Prerequisites: Statistics 200A-B-C.
230 Statistical Computing Methods (4). Numerical computations and algorithms with applications in statistics. Topics include optimization methods including the EM algorithm, random number generation and simulation, Markov chain simulation tools, and numerical integration. Prerequisites: two quarters of upper-division or graduate training in probability and statistics. Statistics 230 and CS 206 may not both be taken for credit.
235 Modern Data Analysis Methods (4). Introduces a variety of modern tools for data analysis. Emphasizes use of computational and resampling techniques for data analyses wherein the data do not conform to standard toolbox of regression models and/or complexity of modeling problem threatens validity of standard methods. Prerequisite: graduate standing in Statistics or Statistics 120C, or equivalent.
240 Multivariate Statistical Methods (4). Theory and application of multivariate statistical methods. Topics include: likelihood and Bayesian inference for the multivariate normal model, visualization of multivariate data, data reduction techniques, cluster analysis, and multivariate statistical models. Prerequisites: Statistics 200A-B-C and Mathematics 121A.
245 Time Series Analysis (4). Statistical models for analysis of time series from time and frequency domain perspectives. Emphasizes theory and application of time series data analysis methods. Topics include ARMA/ARIMA models, model identification and estimation, linear operators, Fourier analysis, spectral estimation, state space models, Kalman filter. Prerequisites: Statistics 200A-B-C.
250 Biostatistics (4). Statistical methods commonly used to analyze data arising from clinical studies. Topics include analysis of observational studies and randomized clinical trials, techniques in the analysis of survival and longitudinal data, approaches to handling missing data, meta-analysis, nonparametric methods. Prerequisite: Statistics 210.
254 Regression Methods for Correlated Data (4). Introduction to statistical methods for analyzing correlated data from experiments and cohort studies. Topics covered include repeated measures ANOVA, linear and non-linear mixed models, and generalized estimating equations. Emphasizes both theoretical development and application of methods. Prerequisite: Statistics 212 or equivalent.
255 Statistical Methods for Survival Data (4). Statistical methods for analyzing survival data from cohort studies. Topics include parametric and nonparametric methods, the Kaplan-Meier estimator, log-rank tests, regression models, the Cox proportional hazards model and accelerated failure time models, efficient sampling designs, discrete survival models. Prerequisite: Statistics 211.
257 Introduction to Statistical Genetics (4). Provides students with knowledge of the basic principles, concepts, and methods used in statistical genetic research. Topics include principles of population genetics, and statistical methods for family- and population-based studies. Prerequisites: two quarters of upper-division or graduate training in statistical methods. Same as Epidemiology 215.
260 Inference with Missing Data (4). Statistical methods and theory useful for analysis of multivariate data with partially observed variables. Bayesian and likelihood-based methods developed. Topics include EM-type algorithms, MCMC samplers, multiple imputation, and general location model. Applications from economics, education, and medicine are discussed. Prerequisites: Statistics 200A-B-C and 210.
262 Theory and Practice of Sample Surveys (4). Covers the basic techniques and statistical methods used in designing surveys and analyzing collected survey data. Topics to be covered include simple random sampling, ratio and regression estimates, stratified sampling, cluster sampling, sampling with unequal probabilities, multistage sampling, and methods to handle nonresponse. Prerequisites: Statistics 120A-B-C or equivalent.
265 Causal Inference (4). Various approaches to causal inference focusing on the Rubin causal model and propensity-score methods. Topics include randomized experiments, observational studies, non-compliance, ignorable and non-ignorable treatment assignment, instrumental variables, and sensitivity analysis. Applications from economics, politics, education, and medicine. Prerequisites: Statistics 200A-B-C and 210.
270 Stochastic Processes (4). Introduction to the theory and application of stochastic processes. Topics include Markov chains, continuous-time Markov processes, Poisson processes, and Brownian motion. Applications include Markov chain Monte Carlo methods and financial modeling (for example, option pricing). Prerequisites: Statistics 120A-B-C or consent of instructor. Statistics 270 and Mathematics 271A-B-C may not both be taken for credit.
280 Seminar in Statistics (.5) F, W, S. Periodic seminar series covering topics of current research in statistics and its application. Prerequisites: graduate standing and consent of instructor. Satisfactory/Unsatisfactory only. May be repeated for credit as topics vary.
281 Topics in Astrostatistics (1 to 4). Topics in statistical methods for astronomy, astrophysics, particle physics, and solar physics, typically including spectral analysis, image processing and analysis, time series, classification, clustering, massive data, etc. Emphasizes computationally intensive methods, Bayesian and frequentist methods, machine learning, and signal processing. Prerequisite: graduate standing or consent of instructor. May be repeated for credit as topics vary.
295 Special Topics in Statistics (4). May be repeated for credit as topics vary.
298 Thesis Supervision (2 to 12). Individual research or investigation conducted in preparation for the M.S. thesis option or the dissertation requirements for the Ph.D. program.
299 Individual Study (2 to 12). Individual research or investigation under the direction of an individual faculty member.