General Information | The Program | Requirements | Courses | PDF File ## Lower Division Courses## 10. Statistical Thinking (4)Lecture—3 hours; discussion/laboratory—1 hour. Prerequisite: two years of high school algebra. Statistics and probability in daily life. Examines principles of collecting, presenting and interpreting data in order to critically assess results reported in the media; emphasis is on understanding polls, unemployment rates, health studies; understanding probability, risk and odds. GE credit: SciEng or SocSci, Wrt | QL, SE.—III. (III.) ## 12. Introduction to Discrete Probability (4)Lecture—3 hours; laboratory—1 hour. Prerequisite: two years of high school algebra. Random experiments; countable sample spaces; elementary probability axioms; counting formulas; conditional probability; independence; Bayes theorem; expectation; gambling problems; binomial, hypergeometric, Poisson, geometric, negative binomial and multinomial models; limiting distributions; Markov chains. Applications in the social, biological, and engineering sciences. Offered in alternate years. GE credit: SciEng | QL, SE. ## 13. Elementary Statistics (4)Lecture—3 hours; discussion—1 hour. Prerequisite: two years of high school algebra or the equivalent in college. Descriptive statistics; basic probability concepts; binomial, normal, Student’s t, and chi-square distributions. Hypothesis testing and confidence intervals for one and two means and proportions. Regression. Not open for credit to students who have completed course 13V or higher. GE credit: SciEng | QL, SE.—I, II, III. (I, II, III.) ## 13V. Elementary Statistics (4)Lecture—1.5 hours; web virtual lecture—5 hours. Prerequisite: two years of high school algebra or the equivalent in college. Descriptive statistics; basic probability concepts; binomial, normal, Student’s t, and chi-square distributions. Hypothesis testing and confidence intervals for one and two means and proportions. Regression. Not open for credit to students who have completed course 13 or higher. GE credit: SciEng | QL, SE.—I. (I.) ## 32. Basic Statistical Analysis Through Computers (3)Lecture—3 hours. Prerequisite: Mathematics 16B or 17B or 21B; ability to program in a high-level computer language such as Pascal. Overview of probability modeling and statistical inference. Problem solution through mathematical analysis and computer simulation. Recommended as alternative to course 13 for students with some knowledge of calculus and computer programming. Only two units of credit allowed to students who have taken course 13, or 102; not open for credit to students who have taken course 100. GE credit: SciEng | SE, QL.—II, III. (II, III.) ## 90X. Seminar (1-2)Seminar—1-2 hours. Prerequisite: high school algebra and consent of instructor. Examination of a special topic in a small group setting. ## 98. Directed Group Study (1-5)Prerequisite: consent of instructor. (P/NP grading only.) ## 99. Special Study for Undergraduates (1-5)Prerequisite: consent of instructor. (P/NP grading only.) ## Upper Division Courses## 100. Applied Statistics for Biological Sciences (4)Lecture—3 hours; laboratory—1 hour. Prerequisite: Mathematics 16B or the equivalent. Descriptive statistics, probability, sampling distributions, estimation, hypothesis testing, contingency tables, ANOVA, regression; implementation of statistical methods using computer package. Only two units credit allowed to students who have taken course 13, 32 or 103. Not open for credit to students who have taken course 102. GE credit: SciEng | QL, SE.—I, II, III. (I, II, III.) ## 102. Introduction to Probability Modeling and Statistical Inference (4)Lecture—3 hours; discussion—1 hour. Prerequisite: two years of high school algebra; upper division standing. Introductory probability and statistics at a rigorous yet precalculus level. Rigorous precalculus introduction to probability and parametric/nonparametric statistical inference with computing; binomial, Poisson, geometric, normal, and sampling distributions; exploratory data analysis; regression analysis; ANOVA. Not open for credit to students who have taken course 100. GE credit: SciEng | QL, SE, SL.—I, III. (I, III.) ## 103. Applied Statistics for Business and Economics (4)Lecture—3 hours; discussion—1 hour. Prerequisite: course 13, 32, or 102; and Mathematics 16A, 16B; course 100 may replace courses 13, 32, or 102. Descriptive statistics; probability; random variables; expectation; binomial, normal, Poisson, other univariate distributions; joint distributions; sampling distributions, central limit theorem; properties of estimators; linear combinations of random variables; testing and estimation; Minitab computing package. Two units credit given to students who have completed course 100. GE credit: SciEng | QL, SE.—I, II, III. (I, II, III.) ## 104. Applied Statistical Methods: Nonparametric Statistics (4)Lecture—3 hours; laboratory—1 hour. Prerequisite: course 13, 32, or 102; course 100 may replace courses 13, 32, or 102. Sign and Wilcoxon tests, Walsh averages. Two-sample procedures. Inferences concerning scale. Kruskal-Wallis test. Measures of association. Chi square and Kolmogorov-Smirnov tests. Offered in alternate years. GE credit: SciEng | QL, SE.—(II.) ## 106. Applied Statistical Methods: Analysis of Variance (4)Lecture—4 hours. Prerequisite: course 13, 32, or 102; course 100 may replace courses 13, 32, or 102. One-way and two-way fixed effects analysis of variance models. Randomized complete and incomplete block design, Latin squares. Multiple comparisons procedures. One-way random effects model. GE credit: SciEng | QL, SE, SL.—I, II. (I, II.) ## 108. Applied Statistical Methods: Regression Analysis (4)Lecture—3 hours; discussion—1 hour. Prerequisite: course 13, 32, or 102; course 100 may replace courses 13, 32, or 102. Simple linear regression, variable selection techniques, stepwise regression, analysis of covariance, influence measures, computing packages. GE credit: SciEng | QL, SE, SL.—I, II, III. (I, II, III.) ## 120. Probability and Random Variables for Engineers (4)Lecture—3 hours; discussion—1 hour. Prerequisite: Mathematics 21A, B, C, and D. Basic concepts of probability theory with applications to electrical engineering, discrete and continuous random variables, conditional probability, combinatorics, bivariate distributions, transformation or random variables, law of large numbers, central limit theorem, and approximations. No credit for students who have completed course 131A or Civil and Environmental Engineering 114. GE credit: SciEng | QL, SE.—I, III. (I, III.) Mueller ## 130A. Mathematical Statistics: Brief Course (4)Lecture—3 hours; discussion—1 hour. Prerequisite: Mathematics16B. Basic probability, densities and distributions, mean, variance, covariance, Chebyshev’s inequality, some special distributions, sampling distributions, central limit theorem and law of large numbers, point estimation, some methods of estimation, interval estimation, confidence intervals for certain quantities, computing sample sizes. Only 2 units of credit allowed to students who have taken course 131A. GE credit: QL, SE.—I. (I.) ## 130B. Mathematical Statistics: Brief Course (4)Lecture—3 hours; discussion—1 hour. Prerequisite: course 130A. Transformed random variables, large sample properties of estimates. Basic ideas of hypotheses testing, likelihood ratio tests, goodness-of-fit tests. General linear model, least squares estimates, Gauss-Markov theorem. Analysis of variance, F-test. Regression and correlation, multiple regression. Selected topics. GE credit: QL, SE.—II. (II.) ## 131A. Introduction to Probability Theory (4)Lecture—3 hours; discussion—1 hour. Prerequisite: Mathematics 21A, 21B, 21C, and 22A. Fundamental concepts of probability theory, discrete and continuous random variables, standard distributions, moments and moment-generating functions, laws of large numbers and the central limit theorem. Not open for credit to students who have completed Mathematics 135A. GE credit: QL, SE.—I, II, III. (I, II, III.) ## 131B. Introduction to Mathematical Statistics (4)Lecture—3 hours; discussion—1 hour. Prerequisite: course 131A or consent of the instructor. Sampling, methods of estimation, sampling distributions, confidence intervals, testing hypotheses, linear regression, analysis of variance, elements of large sample theory and nonparametric inference. GE credit: QL, SE.—II, III. (II, III.) ## 131C. Introduction to Mathematical Statistics (4)Lecture—3 hours; discussion—1 hour. Prerequisite: course 131B, or consent of the instructor. Sampling, methods of estimation, sampling distributions, confidence intervals, testing hypotheses, linear regression, analysis of variance, elements of large sample theory and nonparametric inference. GE credit: SE, QL.—III. (III.) ## 133. Mathematical Statistics for Economists (4)Lecture—3 hours; discussion—1 hour. Prerequisite: course 103 and Mathematics 16B, or the equivalents; no credit will be given to students majoring in Statistics. Probability, basic properties; discrete and continuous random variables (binomial, normal, t, chi-square); expectation and variance of a random variable; bivariate random variables (bivariate normal); sampling distributions; central limit theorem; estimation, maximum likelihood principle; basics of hypotheses testing (one-sample). GE credit: QL, SE.—I. (I.) ## 135. Multivariate Data Analysis (4)Lecture—3 hours; discussion—1 hour. Prerequisite: course 130B, and preferably course 131B. Multivariate normal distribution; Mahalanobis distance; sampling distributions of the mean vector and covariance matrix; Hotelling’s T2; simultaneous inference; one-way MANOVA; discriminant analysis; principal components; canonical correlation; factor analysis. Intensive use of computer analyses and real data sets. GE credit: QL, SE.—III. (III.) ## 137. Applied Time Series Analysis (4)Lecture—3 hours; term paper. Prerequisite: course 108 or the equivalent. Time series relationships, cyclical behavior, periodicity, spectral analysis, coherence, filtering, regression, ARIMA and state-space models; Applications to data from economics, engineering, medicine environment using time series software. GE credit: QL, SE.—III. (III.) ## 138. Analysis of Categorical Data (4)Lecture—3 hours; discussion—1 hour. Prerequisite: course 130B or 131B, or courses 106 and 108. Varieties of categorical data, cross-classifications, contingency tables, tests for independence. Multidimensional tables and log-linear models, maximum likelihood estimation; tests of goodness-of-fit. Logit models, linear logistic models. Analysis of incomplete tables. Packaged computer programs, analysis of real data. GE credit: SciEng | QL, SE.—I. (I.) ## 141. Statistical Computing (4)Lecture—3 hours; laboratory—1 hour. Prerequisite: one introductory class in Statistics (such as 13, 32, 100, or 102), or the equivalent. Organization of computations to access, transform, explore, analyze data and produce results. Concepts and vocabulary of statistical/scientific computing. GE credit: QL, SE.—I. (I.) ## 142. Reliability (4)Lecture—3 hours; discussion/laboratory—1 hour. Prerequisite: course 130B or 131B or consent of instructor. Stochastic modeling and inference for reliability systems. Topics include coherent systems, statistical failure models, notions of aging, maintenance policies and their optimization. Offered in alternate years. GE credit: QL, SE. ## 144. Sampling Theory of Surveys (4)Lecture—3 hours; discussion/laboratory—1 hour. Prerequisite: course 130B or 131B. Simple random, stratified random, cluster, and systematic sampling plans; mean, proportion, total, ratio, and regression estimators for these plans; sample survey design, absolute and relative error, sample size selection, strata construction; sampling and nonsampling sources of error. Offered in alternate years. GE credit: SciEng | QL, SE.—(I.) ## 145. Bayesian Statistical Inference (4)Lecture—3 hours; laboratory—1 hour. Prerequisite: courses 130A and 130B, or 131A and 131B, or the equivalent. Subjective probability, Bayes Theorem, conjugate priors, non-informative priors, estimation, testing, prediction, empirical Bayes methods, properties of Bayesian procedures, comparisons with classical procedures, approximation techniques, Gibbs sampling, hierarchical Bayesian analysis, applications, computer implemented data analysis. Offered in alternate years. GE credit: QL, SE.—(II.) ## 190X. Seminar (1-2)Seminar—1-2 hours. Prerequisite: one of courses 13, 32, 100, 102, or 103. In-depth examination of a special topic in a small group setting. ## 192. Internship in Statistics (1-12)Internship—3-36 hours; term paper. Prerequisite: upper division standing and consent of instructor. Work experience in statistics. (P/NP grading only.) ## 194HA-194HB. Special Studies for Honors Students (4-4)Independent study—12 hours. Prerequisite: senior qualifying for honors. Directed reading, research and writing, culminating in the completion of a senior honors thesis or project under direction of a faculty adviser. (Deferred grading only, pending completion of sequence.) GE credit: SE. ## 198. Directed Group Study (1-5)Prerequisite: consent of instructor. (P/NP grading only.) ## 199. Special Study for Advanced Undergraduates (1-5)Prerequisite: consent of instructor. (P/NP grading only.) ## Graduate Courses## 205. Statistical Methods for Research with SAS (4)Lecture—3 hours; laboratory—1 hour. Prerequisite: An introductory upper division statistics course and some knowledge of vectors and matrices; suggested courses are 100, or 102, or 103, or the equivalent. Focus on linear statistical models widely used in scientific research. Emphasis on concepts, methods and data analysis using SAS. Topics include simple and multiple linear regression, polynomial regression, diagnostics, model selection, variable transformation, factorial designs and ANCOVA.—III. (III.) ## 222. Biostatistics: Survival Analysis (4)Lecture—3 hours; discussion/laboratory—1 hour. Prerequisite: course 131C. Incomplete data; life tables; nonparametric methods; parametric methods; accelerated failure time models; proportional hazards models; partial likelihood; advanced topics. (Same course as Biostatistics 222.)—I. (I.) ## 223. Biostatistics: Generalized Linear Models (4)Lecture—3 hours; discussion/laboratory—1 hour. Prerequisite: course 131C. Likelihood and linear regression; generalized linear model; Binomial regression; case-control studies; dose-response and bioassay; Poisson regression; Gamma regression; quasi-likelihood models; estimating equations; multivariate GLMs. (Same course as Biostatistics 223.)—II. (II.) ## 224. Analysis of Longitudinal Data (4)Lecture—3 hours; discussion/laboratory—1 hour. Prerequisite: course/Biostatistics 222, 223 and course 232B or consent of instructor. Standard and advanced methodology, theory, algorithms, and applications relevant for analysis of repeated measurements and longitudinal data in biostatistical and statistical settings. (Same course as Biostatistics 224.)—III. (III.) ## 225. Clinical Trials (4)Lecture—3 hours; discussion/laboratory—1 hour. Prerequisite: course/Biosatistics 223 or consent of instructor. Basic statistical principles of clinical designs, including bias, randomization, blocking, and masking. Practical applications of widely-used designs, including dose-finding, comparative and cluster randomization designs. Advanced statistical procedures for analysis of data collected in clinical trials. (Same course as Biostatistics 225.) Offered in alternate years.—III. ## 226. Statistical Methods for Bioinformatics (4)Lecture—3 hours; discussion/laboratory—1 hour. Prerequisite: course 131C or consent of instructor; data analysis experience recommended. Standard and advanced statistical methodology, theory, algorithms, and applications relevant to the analysis of -omics data. (Same course as Biostatistics 226.) Offered in alternate years.—(II.) ## 231A. Mathematical Statistics I (4)Lecture—3 hours; discussion—1 hour. Prerequisite: course 131A-C, Mathematics 25 and Mathematics 125 A or equivalent. First part of three-quarter sequence on mathematical statistics. Emphasizes foundations. Topics include basic concepts in asymptotic theory, decision theory, and an overview of methods of point estimation.—I. (I.) ## 231B. Mathematical Statistics II (4)Lecture—3 hours; discussion—1 hour. Prerequisite: course 231A. Second part of a three-quarter sequence on mathematical statistics. Emphasizes: hyposthesis testing (including multiple testing) as well as theory for linear models.—II. (II.) ## 231C. Mathematical Statistics III (4)Lecture—3 hours; discussion—1 hour. Prerequisite: course 231A, 231B. Third part of three-quarter sequence on mathematical statistics. Emphasizes large sample theory and their applications. Topics include statistical functionals, smoothing methods and optimization techniques relevant for statistics.—III. (III.) ## 232A. Applied Statistics I (4)Lecture—3 hours; laboratory—1 hour. Prerequisite: courses 106, 108, 131A, 131B, 131C, and Mathematics 167. Estimation and testing for the general linear model, regression, analysis of designed experiments, and missing data techniques.—I. (I.) ## 232B. Applied Statistics II (4)Lecture—3 hours; laboratory—1 hour. Prerequisite: courses 106, 108, 131A, 131B, 131C, 232A and Mathematics 167. Alternative approaches to regression, model selection, nonparametric methods amenable to linear model framework and their applicationss.—II. (II.) ## 232C. Applied Statistics III (4)Lecture—3 hours; laboratory—1 hour. Prerequisite: courses 106, 108, 131C, 232B and Mathematics 167. Multivariate analysis: multivariate distributions, multivariate linear models, data analytic methods including principal component, factor, discriminant, canonical correlation and cluster analysis.—II. (II.) ## 233. Design of Experiments (3)Lecture—3 hours. Prerequisite: course 131C. Topics from balanced and partially balanced incomplete block designs, fractional factorials, and response surfaces. Offered in alternate years.—(III.) ## 235A-235B-235C. Probability Theory (4-4-4)Lecture—3 hours; term paper or discussion—1 hour. Prerequisite: 235A—Mathematics 125B and 135A or course 131A or consent of instructor; 235B—Mathematics 235A/course 235A or consent of instructor; 235C—Mathematics 235B/course 235B or consent of instructor. Measure-theoretic foundations, abstract integration, independence, laws of large numbers, characteristic functions, central limit theorems. Weak convergence in metric spaces, Brownian motion, invariance principle. Conditional expectation. Topics selected from martingales, Markov chains, ergodic theory. (Same course as Mathematics 235A-235B-235C.)—I-II-III. (I-II-III.) ## 237A-237B. Time Series Analysis (4-4)Lecture—3 hours; term paper. Prerequisite: course 131B or the equivalent; course 237A is a prerequisite for course 237B. Advanced topics in time series analysis and applications. Models for experimental data, measures of dependence, large-sample theory, statistical estimation and inference. Univariate and multivariate spectral analysis, regression, ARIMA models, state-space models, Kalman filtering. Offered in alternate years.—(I-II.) ## 238. Theory of Multivariate Analysis (4)Lecture—3 hours; term paper. Prerequisite: courses 131B and 135. Multivariate normal and Wishart distributions, Hotelling’s T-Squared, simultaneous inference, likelihood ratio and union intersection tests, Bayesian methods, discriminant analysis, principal component and factor analysis, multivariate clustering, multivariate regression and analysis of variance, application to data. Offered in alternate years.—II. ## 240A-240B. Nonparametric Inference (4-4)
Lecture—3 hours; term paper. Prerequisite: course 231C; courses 235A-235B-235C recommended. Comprehensive treatment of nonparametric statistical inference, including the most basic materials from classical nonparametrics, robustness, nonparametric estimation of a distribution function from incomplete data, curve estimation, and theory of resampling methodology. Offered in alternate years. ## 241. Asymptotic Theory of Statistics (4)Lecture—3 hours; term paper. Prerequisite: course 231C; courses 235A-235B-235C desirable. Topics in asymptotic theory of statistics chosen from weak convergence, contiguity, empirical processes, Edgeworth expansion, and semiparametric inference. Offered in alternate years. (III.) ## 242. Introduction to Statistical Programming (4)Lecture—3 hours; laboratory—1 hour. Prerequisite: courses 130A and 130B or equivalent. Essentials of statistical computing using a general-purpose statistical language. Topics include algorithms; design; debugging and efficiency; object-oriented concepts; model specification and fitting; statistical visualization; data and text processing; databases; computer systems and platforms; comparison of scientific programming languages. Offered in alternate years.—II. ## 243. Computational Statistics (4)Lecture—3 hours; laboratory—1 hour. Prerequisite: courses 130A and 130B or equivalent, and Mathematics 167 or Mathematics 67 or equivalent. Numerical analysis; random number generation; computer experiments and resampling techniques (bootstrap, cross validation); numerical optimization; matrix decompositions and linear algebra computations; algorithms (markov chain monte carlo, expectation-maximization); algorithm design and efficiency; parallel and distributed computing. Offered in alternate years.—II. ## 250. Topics in Applied and Computational Statistics (4)Lecture—3 hours; lecture/discussion—1 hour. Prerequisite: course 131A; course 232A recommended, not required. Resampling, nonparametric and semiparametric methods, incomplete data analysis, diagnostics, multivariate and time series analysis, applied Bayesian methods, sequential analysis and quality control, categorical data analysis, spatial and image analysis, computational biology, functional data analysis, models for correlated data, learning theory. May be repeated for credit with consent of graduate advisor. Not offered every year.—I, II, III. ## 251. Topics in Statistical Methods and Models (4)Lecture—3 hours; discussion—1 hour. Prerequisite: course 231B or the equivalent. Topics may include Bayesian analysis, nonparametric and semiparametric regression, sequential analysis, bootstrap, statistical methods in high dimensions, reliability, spatial processes, inference for stochastic process, stochastic methods in finance, empirical processes, change-point problems, asymptotics for parametric, nonparametric and semiparametric models, nonlinear time series, robustness. May be repeated for credit with consent of instructor. Not offered every year.—II. (II.) ## 252. Advanced Topics in Biostatistics (4)Lecture—3 hours; discussion/laboratory—1 hour. Prerequisite: course 222, 223. Biostatistical methods and models selected from the following: genetics, bioinformatics and genomics; longitudinal or functional data; clinical trials and experimental design; analysis of environmental data; dose-response, nutrition and toxicology; survival analysis; observational studies and epidemiology; computer-intensive or Bayesian methods in biostatistics. May be repeated for credit with consent of adviser when topic differs. (Same course as Biostatistics 252.) Offered in alternate years.—III. ## 280. Orientation to Statistical Research (2)Seminar—2 hours. Prerequisite: consent of instructor. Guided orientation to original statistical research papers, and oral presentations in class of such papers by students under the supervision of a faculty member. May be repeated one time for credit. (S/U grading only.)—III. (III.) ## 290. Seminar in Statistics (1-6)Prerequisite: consent of instructor. Seminar on advanced topics in probability and statistics. (S/U grading only.)—I, II, III. (I, II, III.) ## 292. Graduate Group in Statistics Seminar (1-2)Seminar—1-2 hours. Prerequisite: graduate standing. Advanced study in various fields of statistics with emphasis in applied topics, presented by members of the Graduate Group in Statistics and other guest speakers. (S/U grading only.)—III. (III.) ## 298. Directed Group Study (1-5)Prerequisite: graduate standing, consent of instructor. ## 299. Individual Study (1-12)Prerequisite: consent of instructor. (S/U grading only.) ## 299D. Dissertation Research (1-12)Prerequisite: advancement to candidacy for Ph.D., consent of instructor. (S/U grading only.) ## Professional Courses## 390. Methods of Teaching Statistics (2)Lecture/discussion—1 hour; laboratory—1 hour. Prerequisite: graduate standing. Practical experience in methods/problems of teaching statistics at university undergraduate level. Lecturing techniques, analysis of tests and supporting material, preparation and grading of examinations, and use of statistical software. Emphasis on practical training. May be repeated for credit. (S/U grading only.)—I. (I.) ## 396. Teaching Assistant Training Practicum (1-4)Prerequisite: consent of instructor; graduate standing. (S/U grading only.)—I, II, III. (I, II, III.) ## Professional Course## 401. Methods in Statistical Consulting (3)Lecture—3 hours; discussion—1 hour. Introduction to consulting, in-class consulting as a group, statistical consulting with clients, and in-class discussion of consulting problems. Clients are drawn from a pool of University clients. Students must be enrolled in the graduate program in Statistics or Biostatistics. May be repeated for credit with consent of graduate adviser. Not offered every year. (S/U grading only.)—I, II, III. (I, II, III.) |

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