DEPARTMENT OF STATISTICS
2109 Donald Bren
Hall; (949) 824-5392: Fax: (949) 824-9863
E-mail: stat@uci.edu; World Wide Web:
http:www.stat.uci.edu/
Hal S. Stern, Department Chair
Daniel L. Gillen: Biostatistics, survival analysis and longitudinal methods, group sequential methods, design and analysis of clinical trials, applications to biological and clinical studies
Wesley O. Johnson: Bayesian semi-parametric inference, survival analysis, prediction, specification of priors, applications in epidemiology, diagnostic testing, longitudinal and mixed modeling, asymptotics
Gang Liang: Statistical inference, graphical models, and machine learning
Hal S. Stern: Bayesian methodology, model diagnostics, applications to biological and social sciences, sports and statistics
David van Dyk: Statistical computation, Bayesian methodology, hierarchical modeling, causal inference, and application in astronomy and the physical and social sciences
Yaming Yu: Statistical computation, Bayesian methodology, and missing data problems
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 various 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, 67) and upper-division undergraduate courses on the theoretical foundations of probability and statistics (Statistics 120A-B-C). The Department is in the process of planning an undergraduate degree program in statistics. Students interested in focusing on statistics are encouraged to consider the specialization in statistics offered by the Department of Mathematics.
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 363 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); six other graduate courses in or related to statistics, at least three of which are offered by the Department of Statistics.
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 given by the Statistics faculty.
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); Statistical Computing Methods (Statistics 230); six other graduate courses in or related to statistics, at least three of which are offered by the Department of Statistics.
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.
Ph.D. students who have passed the written comprehensive examination 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.
LOWER-DIVISION
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. Same as Mathematics 7. Only one course from Statistics 7/Mathematics 7, Biological Sciences 7, or Management 7 may be taken for credit. No credit for Statistics 7/Mathematics 7 if taken after Mathematics 67. (V) F, W offered for seniors only.
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 Mathematics 6D/ICS 6D. No credit for Statistics 7/Mathematics 7, Biological Sciences 7, or Management 7 if taken after Statistics 67/Mathematics 67. Same as Mathematics 67.
UPPER-DIVISION
100A-B-C Foundations of Applied Statistics I, II, III (4-4-4). Lecture, four hours; laboratory, three hours. 100A-B: Descriptive statistical concepts and techniques most widely used in social science research. Weekly laboratories employ computer graphics to investigate concepts. 100A: Pass/Not Pass only. 100C: Classical statistical inference, limited to simple random sampling or simple randomization designs. Characteristics of sampling distributions; bias, standard error, mathematical models, estimation, hypothesis testing. Same as Social Sciences 100A-B-C and Social Ecology 166A-B-C. (V)
101 Introduction to Statistical Computing with SAS (4). Lecture, two hours; laboratory, two hours. Data definition, data acquisition, and data management using SAS procedures and commands. Statistical procedures available from the SAS Statistical Software Package. SAS/GRAPH procedures for producing statistical graphics. Prerequisites: completion of one year of statistics, or concurrent enrollment in Statistics 100C, or consent of instructor. Pass/Not Pass only. Same as Social Ecology 166E and Social Science 101E.
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-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.
199 Individual Study (2 to 5). Individual research or investigations under the direction of an individual faculty member. Prerequisite: consent of instructor.
GRADUATE
200A-B-C Intermediate Probability and Statistical Theory (4-4-4). 200A: Basics of probability theory, random variables and basic transformations, univariate distributions—discrete 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).
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. Prerequisite: Statistics 201 or equivalent.
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: Advanced Statistical Modeling (4). Analysis of data using extensions of the traditional linear model. Topics include generalized linear models (logistic and poisson regression), linear mixed models. Different approaches to inference are considered including likelihood-based methods and estimating equations. Prerequisite: Statistics 210 or equivalent.
212 Statistical Methods III: Longitudinal Data Analysis (4). 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 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: either Economics 220A-B, Mathematics 201A-B, Mathematics 131A-B-C/Statistics 120A-B-C, Psychology 203A-B, 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; possible courses include Economics 220A-B, Mathematics 131A-B-C/Statistics 120A-B-C, Mathematics 201A-B, Psychology 203A-B, and Statistics 225. 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.
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.
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.
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.
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.