Statistics enables us to make inferences about entire populations, based on samples extracted from those populations. Statistical methods can be applied to problems from almost every discipline and they are vitally important to researchers in agricultural, social, engineering, and medical sciences.
The Program. Statistics majors may receive either a Bachelor of Arts or a Bachelor of Science degree. The A.B. degree is very flexible, facilitating a double major or extensive elective course work in a field in which statistics is applied. The B.S. degree program has two options: one emphasizes mathematics and is especially recommended as preparation for graduate study in statistics; the other emphasizes computer science. All three programs require theoretical and applied course work and underscore the strong interdependence of statistical theory and the applications of statistics.
Preparatory Requirements. Before applying for either the A.B. or B.S. major in Statistics, students must ordinarily complete the following courses with at least C grades:
Mathematics 21A, 21B, 21C
Mathematics 22A, 22B
Computer Science Engineering 30 or Engineering 5
Statistics 32
In addition, due to space limitation in the B.S. major, students admitted to this major will normally be chosen from those having at least a 3.0 grade point average in the above courses. For further information, please contact a Statistics adviser.
Career Alternatives. Probability models and statistical methods are used in a great many fields, including the biological and social sciences, business and engineering. The wide applicability of statistics has created in both the public and private sectors a strong demand for graduates with statistical training. Current employment opportunities include state and federal government positions with a statistician designation, industrial positions (e.g., in the actuarial series within an insurance company or in the data management unit in a health science facility), and teaching positions.
| UNITS | ||
|---|---|---|
| Preparatory Subject Matter | 24-25 | |
| Mathematics 21A, 21B, 21C | 12 | |
| Mathematics 22A, 22B | 6 | |
| Computer Science Engineering 30 or Engineering 5 (or the equivalent) | 3-4 | |
| Statistics 32 | 3 | |
| Depth Subject Matter | 38-39 | |
| Statistics 106, 108 or the equivalent | 8 | |
| Statistics 131A, 131B, 131C | 12 | |
| Three Statistics courses with Statistics 131B as a prerequisite | 9-10 | |
| Related elective courses | 9 | |
| Three upper division courses approved by major adviser. They may be in mathematics, computer science or in quantitative aspects of a substantive discipline. | ||
| Total Units for the Major | 62-64 | |
| UNITS | ||
|---|---|---|
| Preparatory Subject Matter | 24-31 | |
| Mathematics 21A, 21B, 21C | 12 | |
| Mathematics 22A, 22B | 6 | |
| Computer science: | ||
| General option: Computer Science Engineering 30 or Engineering 5 (or the equivalent) | 3-4 | |
| Computer Science option: Computer Science Engineering 30 and 40 and Electrical and Computer Science Engineering 70 | 10 | |
| Statistics 32 | 3 | |
| Depth Subject Matter | ||
| Complete one of the two options below. | ||
| Statistics--General option | 51-54 | |
| Statistics 106, 108 or the equivalent | 8 | |
| Statistics 131A, 131B, 131C or the equivalent | 12 | |
| Four Statistics courses having Statistics 131B as a prerequisite | 12-13 | |
| Mathematics 167 | 3 | |
| Three upper division Mathematics courses selected from 108, 127A-127B-127C, 128A-128B-128C, 168 (Mathematics 127 strongly recommended for students considering graduate work in Mathematics or Statistics.) | 10-12 | |
| Related elective courses | 6 | |
| Two upper division courses approved by major adviser. These may be in mathematics, computer science or in quantitative aspects of a substantive discipline. | ||
| Total Units for the Major (General option) | 75-85 | |
| Statistics--Computer Science option | 49-53 | |
| Statistics 106, 108 (or the equivalent) | 8 | |
| Statistics 131A, 131B, 131C | 12 | |
| Two courses having Statistics 131B as a prerequisite | 6-7 | |
| Statistics 141 | 3 | |
| Computer Science Engineering 110, 150 | 4 | |
| Computer Science Engineering 165 or Mathematics 160 | 3-4 | |
| Two courses from Mathematics 128A, 128B, 132A, 132B, 167, 168 | 6-8 | |
| Computer Science Engineering 122, or Computer Science Engineering 175 | 3 | |
| Total Units for the Major (Computer Science option) | 73-84 | |
Major Adviser. A.P. Fenech.
Students are encouraged to meet with an adviser to plan a program as early as possible. Sometime before or during the first quarter of the junior year students planning to major in Statistics should consult with a faculty adviser to plan the remainder of their undergraduate programs.
The Division offers a minor program in Statistics that consists of a survey at the upper division level of the fundamentals of mathematical statistics and of the most widely used applied statistical methods.
| UNITS | ||
|---|---|---|
| Statistics | 19-20 | |
| Statistics 106, 108, and 130A-130B or 131A-131B | 16 | |
| One course in Statistics having Statistics 130B or 131B as a prerequisite | 3-4 | |
| Preparation: Statistics 13 or 32. | ||
Graduate Study. The Graduate Group in Statistics offers study and research leading to the M.S. and Ph.D. degrees in Statistics. Detailed information concerning these degree programs, as well as information on admissions and on financial support, is available from the Division of Statistics.
Graduate Adviser. W.O. Johnson, fall; J.-L. Wang, winter and spring.
Statistical Consulting. The Division provides a consulting service for researchers on campus. For more information, call the Statistical Laboratory Office (530-752-6096).
| Upper Division Courses | Graduate Courses | Professional Courses |
*Course not offered this academic year.
General Education (GE) credit: ArtHum = Arts and Humanities; SciEng = Science and Engineering; SocSci = Social Sciences; Div = Social-Cultural Diversity; Wrt = Writing Experience. Select this link to information on the General Education requirement.
10. Statistical Thinking (4) III. Utts
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.
*12. Introduction to Discrete Probability (4) I. The Staff (Chairperson in charge)
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.
13. Elementary Statistics (4) I, II, III. The Staff
Lecture--3 hours; discussion--1 hour. Prerequisite: two years of high school algebra or the equivalent in college. Measures of central tendency and dispersion; binomial, normal, Student-t, and chi-square distributions; testing hypotheses; confidence intervals, regression and correlation analysis. Not open for credit to students who have completed any statistics course numbered higher than 13, except for course 102. GE credit: SciEng.
32. Basic Statistical Analysis Through Computers (3) II, III. The Staff
Lecture--3 hours. Prerequisite: Mathematics 16B 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. GE credit: SciEng.
90X. Seminar (1-2) I, II, III. The Staff (Chairperson in charge)
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) I, II, III. The Staff (Chairperson in charge)
Prerequisite: consent of instructor. (P/NP grading only.)
100. Applied Statistics for Biological Sciences (4) I, II, III. The Staff
Lecture--3 hours; laboratory--2 hours. Prerequisite: Mathematics 16B or the equivalent. Probability computation/modeling, 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 or 32. Not open for credit to students who have taken course 102. GE credit SciEng.
102. Introduction to Probability Modeling and Statistical Inference (4) I, III. The Staff
Lecture--3 hours; discussion--1 hour. Prerequisite: two years of high school algebra, and 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. Only two units of credit allowed to students who have taken course 32. Not open for credit to students who have taken course 100. GE credit: SciEng.
103. Applied Statistics for Business and Economics (4) I, II, III. The Staff
Lecture--3 hours; discussion--1 hour. Prerequisite: course 13, 32, or 102; and Mathematics 16A, 16B. 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. GE credit: SciEng.
104. Applied Statistical Methods: Nonparametric Statistics (4) II. The Staff (Chairperson in charge)
Lecture--3 hours; laboratory--1 hour. Prerequisite: course 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.
106. Applied Statistical Methods: Analysis of Variance (4) I, II. The Staff
Lecture--4 hours. Prerequisite: course 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.
108. Applied Statistical Methods: Regression Analysis (4) I, II, III. The Staff
Lecture--3 hours; discussion--1 hour. Prerequisite: course 13, 32 or 102. Simple linear regression, variable selection techniques, stepwise regression, analysis of covariance, influence measures, computing packages. GE credit: SciEng.
120. Probability and Random Variables for Engineers (4) I, III. The Staff
Lecture--3 hours; discussion--1 hour. Prerequisite: Mathematics 21A, 21B, 21C, and 22A. Basic concepts of probability theory with applications to electrical engineering, discrete and continuous random variables, conditional probability, combinatorics, bivariate distributions, transformation of random variables, law of large numbers, central limit theorem, and approximations. No credit for students who have taken course 131A or Civil and Environmental Engineering 114. GE credit: SciEng.
130A. Mathematical Statistics: Brief Course (4) I. The Staff
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.
130B. Mathematical Statistics: Brief Course (4) II. The Staff
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.
131A. Introduction to Probability Theory (4) I. The Staff
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 taken Mathematics 131.
131B-131C. Introduction to Mathematical Statistics (4-4) II-III. The Staff
Lecture--3 hours; discussion--1 hour. Prerequisite: course 131A, or Mathematics 22A and 131. Sampling, methods of estimation, sampling distributions, confidence intervals, testing hypotheses, linear regression, analysis of variance, elements of large sample theory, and nonparametric inference.
133. Mathematical Statistics for Economists (4) I. The Staff
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 priniciple; basics of hypotheses testing (one-sample).
135. Multivariate Data Analysis (4) III. The Staff
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.
137. Applied Time Series Analysis (4) III. Shumway, Mack, Azari
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.
138. Analysis of Categorical Data (4) I. The Staff
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.
141. Statistical Computing (4) II. Levine
Lecture--3 hours; laboratory--1 hour. Prerequisite: course 130A or 131A, and one of courses 13, 32, 100, 102, or the equivalent, and experience in computer programming; course 130B or 131B recommended. Use of computers in statistics. Numerical foundations of statistical procedures. Computation of probabilities and quantiles. Random numbers. Monte Carlo method and bootstrap. Methods for parametric statistical models. Graphical methods and exploratory data analysis.
142. Reliability (4) III. Samaniego
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.
144. Sampling Theory of Surveys (4) II. Fenech, Samaniego
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.
145. Bayesian Statistical Inference (4) II. Johnson
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.
190X. Seminar (1-2) III. The Staff (Chairperson in charge)
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) I, II, III. The Staff (Chairperson in charge)
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) I-II. The Staff (Chairperson in charge)
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.)
198. Directed Group Study (1-5) I, II, III. The Staff (Chairperson in charge)
Prerequisite: consent of instructor. (P/NP grading only.)
199. Special Study for Advanced Undergraduates (1-5) I, II, III. The Staff (Chairperson in charge)
Prerequisite: consent of instructor. (P/NP grading only.)
205. Statistical Methods for Research (4) III. Utts, Drake, Azari
Lecture--3 hours; laboratory--1 hour. Prerequisite: course 106 or the equivalent. Topics in design of experiments include factorial designs, balanced and unbalanced experiments, random and mixed effects models, response surface methodology, nested design, repeated measures, cross-over design, analysis of covariance. Applications in engineering, biological sciences, medicine and environmental research. Offered in alternate years.
222. Biostatistics: Survival Analysis (4) III. The Staff
Lecture--3 hours; discussion/laboratory--1 hour. Prerequisite: course 131C or consent of instructor. Incomplete data; life tables; nonparametric methods; parametric models; accelerated failure time models; proportional hazards models; partial likelihood; advanced topics. Offered in alternate years.
*223. Biostatistics: Generalized Linear Models (4) II. The Staff
Lecture--3 hours; discussion/laboratory--1 hour. Prerequisite: course 131C or consent of instructor. Likelihood and linear regression; generalized linear model; Binomial regression; case-control studies; dose-response relations; Poisson regression; Gamma regression; quasi-likelihood models; estimating equations; multivariate GLMs. Offered in alternate years.
*224. Biostatistics: Clinical Trials and Advanced Topics (4) III. The Staff
Lecture--3 hours; discussion/laboratory--1 hour. Prerequisite: course 223 or consent of instructor. Clinical trials; sequential design; covariate adjustment; meta-analysis; applications of generalized linear models; longitudinal studies; random effects models; advanced topics. Offered in alternate years.
231A-231B-231C. Mathematical Statistics
(4-4-4) I-II-III. The Staff
Lecture--3 hours; discussion--1 hour. Prerequisite: course 131C and Mathematics 127A-127B or the equivalent. Distribution theory, decision theoretic methods, estimation and hypotheses testing, multivariate techniques, large sample theory.
232A-232B. Linear Model Theory (4-4) I-II. The Staff
Lecture--3 hours; discussion--1 hour. Prerequisite: course 131C. Estimation and testing for the general linear hypothesis, components of variance, multiple comparisons.
*233. Design of Experiments (3) II. The Staff
Lecture--3 hours. Prerequisite: course 131C. Topics from balanced and partially balanced incomplete block designs, fractional factorials, and response surfaces. Offered in alternate years.
235A-235B-235C. Probability Theory (3-3-3) I, II, III. The Staff
Lecture--3 hours. Prerequisite: Mathematics 127C and courses 131A-131B or the equivalent. Measure theoretic foundations, abstract integration, modes of convergence, limit theorems, independence, laws of large numbers, characteristic functions, central limit theorem, conditional expectations; topics from discrete time, Markov and stationary processes, ergodic theory, Brownian motion, weak convergence, Wiener and Poisson processes. (Same course as Mathematics 235A-235B-235C.)
237A-237B. Time Series Analysis (4-4) I-II. Shumway, Mack
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.
*238. Theory of Multivariate Analysis (4) II. Shumway, Johnson, Fenech
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.
240A-240B. Nonparametric Inference (4-4) II- III. The Staff (Chairperson in charge)
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) III. The Staff (Chairperson in charge)
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.
*250. Advanced Data Analysis (4) I. The Staff
Lecture--3 hours; discussion--1 hour. Prerequisite: courses 141, 232A and either course 230 or 231A. Resampling methods and one to three additional topics selected from nonparametric and semi-parametric methods, incomplete data analysis, diagnostics, nonstandard multivariate and time series analysis, applied Bayesian methods, sequential analysis and quality control, categorical data analysis. Offered in alternate years.
251. Topics in Advanced Theory of Statistics (4) I. The Staff (Chairperson in charge)
Lecture--3 hours; term paper. Prerequisite: course 231C. Bayesian, regression, sequential and survival analysis; bootstrap and reliability theory; change-point problems; empirical and spatial processes; asymptotic inference under dependence; asymptotic theory in linear, parametric and semiparametric models. Offered in alternate years.
280. Orientation to Statistical Research (2) I. The Staff
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 once for credit. (S/U grading only.)
290. Seminar in Statistics (1-6) I, II, III. The Staff (Chairperson in charge)
Prerequisite: consent of instructor. Seminar on advanced topics in probability and statistics. (S/U grading only.)
292. Graduate Group in Statistics Seminar
(1-2) III. The Staff
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.)
298. Group Study (1-5) I, II, III. The Staff (Chairperson in charge)
299. Individual Study (1-12) I, II, III. The Staff (Chairperson in charge)
Prerequisite: consent of instructor. (S/U grading only.)
299D. Dissertation Research (1-12) I, II, III. The Staff
Prerequisite: candidate for Ph.D. degree. Research in statistics under the supervision of major professor. (S/U grading only.)
390. Methods of Teaching Statistics (2) I. The Staff (Chairperson in charge)
Lecture/discussion--2 hours; workshop--1 hour. Prerequisite: graduate standing. Training in teaching methodology at the undergraduate level. Emphasis is on practical training exercises which are used to evaluate skills and improve these skills. Lecture exercises will be videotaped and critiqued. (S/U grading only.)
401. Methods in Statistical Consulting (3) III. The Staff
Lecture/discussion--3 hours; laboratory--1 hour. Prerequisite: graduate standing in Statistics. Introduction to consulting; in-class consulting as a group; individual or team consulting under supervision. May be repeated for credit. (S/U grading only.)
UC Davis 1999-2000 Online General Catalog. Posted July 30, 1999.
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Molly Theodossy, Keitha Hunter and Barbara Anderson, Editors
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