518
Statistics
Statistics
(College of Letters and Science)
Hans-Georg Müller, Ph.D., Chairperson of the
Department
Department Office. 4118 Mathematical Sciences Building
530-752-2361; http://www.stat.ucdavis.edu
Faculty
Ethan Anderes, Ph.D., Associate Professor
Alexander Aue, Ph.D., Associate Professor
Paul Baines, Ph.D., Assistant Professor
Prabir Burman, Ph.D., Professor
Hao Chen, Ph. D, Assistant Professor
Christiana Drake, Ph.D., Professor
Peter Hall, Ph.D., Professor
Fushing Hsieh, Ph.D., Professor
Jiming Jiang, Ph.D., Professor
Thomas Lee, Ph.D., Professor
Hans-Georg Müller, M.D., Ph.D., Professor
Debashis Paul, Ph.D., Associate Professor
Jie Peng, Ph.D., Associate Professor
Wolfgang Polonik, Ph.D., Professor
Duncan Temple Lang, Ph.D., Professor
Jane-Ling Wang, Ph.D., Professor
Emeriti Faculty
Rudolph Beran, Ph.D., Professor Emeritus
P.K. Bhattacharya, Ph.D., Professor Emeritus
Alan P. Fenech, Ph.D., Professor Emeritus
Yue-Pok (Ed) Mack, Ph.D., Professor Emeritus
George G. Roussas, Ph.D., Professor Emeritus
Francisco J. Samaniego, Ph.D., Professor Emeritus
Robert H. Shumway, Ph.D., Professor Emeritus
Alvin D. Wiggins, Ph.D., Professor Emeritus
Affiliated Faculty
Rahman Azari, Ph.D., Lecturer
The Major Program
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, biological, environmental, social, engineering, and
medical sciences.
The Program. Statistics majors may receive either
a Bachelor of Arts or a Bachelor of Science degree.
The B.S. degree program has three options: General
Option, Applied Statistics Option, and Computational Statistics Option. Both the A.B. and the B.S.
programs require theoretical and applied course
work and underscore the strong interdependence of
statistical theory and the applications of statistics.
B.S. in Statistics-General Option emphasizes
statistical theory and is especially recommended as
preparation for graduate study in statistics.
B.S. in Statistics-Applied Statistics Option
emphasizes statistical applications. This major is recommended for students who do not plan to pursue
graduate studies in statistics and those who are interested in combining the statistics study with a second
major or minor program in the social and life sciences.
B.S. in Statistic-Computational Statistics
Option emphasizes computing. This major is recommended for students interested in the computational and data management aspects of statistical
analysis.
A.B. in Statistics-Applied Statistics Option
emphasizes statistical applications. This major is recommended for students who do not plan to pursue
graduate studies in statistics and those who are interested in combining the statistics study with a second
major or minor program in the social sciences or
who wish to pursue a Bachelor of Arts degree.
Career Alternatives. Probability models and statistical methods are used in a great many fields,
including the biological and social sciences, busi-
ness and engineering. The wide applicability of statistics has created in both the public and private
sectors a strong demand for graduates with statistical training. Employment opportunities include
careers in data and policy analysis in government,
financial management, quality control, insurance
and health care industry, actuarial work, engineering, public health, biological and pharmaceutical
research, law, and education. Some students have
entered advanced studies in statistics, economics,
psychology, medicine and other professional school
programs.
A.B. Major Requirements:
Statistics 130A, 130B ............................ 8
Three courses selected from Statistics 104,
135, 137, 142, 144, 145 ................... 12
Five upper division elective courses outside of
Statistics. ........................................15-20
Electives are chosen with and must be
approved by the major adviser. Electives
should follow a coherent sequence in one
single disciple where statistical methods
and models are applied: at least three of
them should cover the quantitative aspects
of the discipline.
Total Units for the Major .................. 77-87
UNITS
Preparatory Subject Matter ............. 19-23
Mathematics 16A, 16B, 16C; or 17A, 17B,
17C; or 21A, 21B, 21C .................... 9-12
Mathematics 22A................................... 3
Computer Science Engineering 30 or
Computer Science Engineering 40 (or the
equivalent) ............................................ 4
Statistics 32........................................ 3-4
Depth Subject Matter ....................... 45-48
Statistics 106, 108, 138 or the
equivalent ........................................... 12
Statistics 130A, 130B............................. 8
Statistics 137 or 141.............................. 4
Three courses from: Statistics 104, 135, 137,
141, 142, 144, 145............................ 12
Related elective courses ..................... 9-12
Three upper division courses approved by
major adviser; they should follow a
coherent sequence in a single discipline in
the social sciences where statistical methods
and models are applied and should cover
the quantitative aspects of the discipline.
Total Units for the Major .................. 64-71
Computational Statistics option
B.S. Major Requirements:
General Statistics option
Major Adviser. A. Aue
UNITS
Preparatory Subject Matter ............. 30-32
Mathematics 21A, 21B, 21C, 21D ........ 16
Mathematics 22A or 67....................... 3-4
Mathematics 25..................................... 4
Computer Science Engineering 30 or
Computer Science Engineering 40 (or the
equivalent) ............................................ 4
Any one introductory statistics course except
Statistics 10........................................ 3-4
Depth Subject Matter ....................... 51-52
Statistics 106, 108, 138....................... 12
Statistics 131A, 131B, 131C ................ 12
Three courses from: Statistics 104, 135, 137,
141, 142, 144, 145............................ 12
Mathematics 125A, 108 or 125B, and
167.................................................... 12
Related elective courses ....................... 3-4
One upper division course approved by
major adviser; it should be in mathematics,
computer science or in quantitative aspects
of a substantive discipline.
Total Units for the Major .................. 81-84
Applied Statistics option
Preparatory Subject Matter ............. 26-31
Mathematics 16A, 16B, 16C; or 17A, 17B,
17C; or 21A, 21B, 21C (21 series
recommended).................................. 9-12
Mathematics 22A................................... 3
Computer science Engineering 30 or
Computer Science Engineering 40 (or the
equivalent) ............................................ 4
Two introductory courses serving as the
prerequisites to upper division courses in a
chosen discipline to which statistics is
applied.............................................. 7-8
Any one introductory statistics course except
Statistics 10........................................ 3-4
Depth Subject Matter ....................... 51-56
Statistics 106, 108, 138, 141............... 16
Preparatory Subject Matter.............. 30-31
Mathematics 21A, 21B, 21C, 21D ........ 16
Mathematics 22A .................................. 3
Computer Science Engineering 30
and 40 ................................................ 8
Any one introductory statistics course except
Statistics 10 ........................................3-4
Depth Subject Matter ............................ 52
Statistics 106, 108, 141 ...................... 12
Statistics 131A, 131B ............................ 8
Two courses from: Statistics 104, 135, 137,
138, 142, 144, 145 ............................. 8
Programming, Data Management & Data
Technologies: Computer Science Engineering
130 or 145; and 165A or 166............... 8
Two courses on Scientific Computational
Algorithm and Visualization from: Computer
Science Engineering 122A, 129, 140A,
158, 163 ............................................. 8
Two courses from: Mathematics 124, 128A,
128B, 129, 145, 148, 160, 165, 167,
168 ..................................................... 8
Total Units for the Major .................. 82-83
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.
Minor Program Requirements:
The Department offers a minor program in Statistics
that consists of five upper division level courses
focusing on the fundamentals of mathematical statistics and of the most widely used applied statistical
methods.
UNITS
Statistics ............................................... 20
Statistics 106, 108, and 130A-130B or
131A-131B......................................... 16
One course from: Statistics 104, 135, 137,
138, 141, 142, 144, 145 ..................... 4
Preparation. Statistics 13 or 32 or 100 or
102.
Graduate Study. The Graduate Program in Statistics offers study and research leading to the M.S.
and Ph.D. degrees in Statistics, including a Ph.D. in
Statistics with an emphasis in Biostatistics. Detailed
information concerning these degree programs, as
well as information on admissions and on financial
support, is available from the Department of Statistics.
Graduate Adviser. D. Paul
Statistical Consulting. The Department provides
a consulting service for researchers on campus. For
more information, call the Statistical Laboratory
office 530-752-6096.
Integrated B.S./M.S. Degree
Program
The Department offers undergraduate majors a path
into the Statistics M.S. program through the Integrated Degree Program (I.D.P.). This program is
intended for students who seek to be employed as
statisticians in government or industry. The minimum
Quarter Offered: I=Fall, II=Winter, III=Spring, IV=Summer; 2015-2016 offering in parentheses
Pre-Fall 2011 General Education (GE): ArtHum=Arts and Humanities; SciEng=Science and Engineering; SocSci=Social Sciences; Div=Domestic Diversity; Wrt=Writing Experience
Fall 2011 and on Revised General Education (GE): AH=Arts and Humanities; SE=Science and Engineering; SS=Social Sciences;
ACGH=American Cultures; DD=Domestic Diversity; OL=Oral Skills; QL=Quantitative; SL=Scientific; VL=Visual; WC=World Cultures; WE=Writing Experience
Statistics
major GPA requirement is 3.200 at the end of the
junior year, although students with demonstrated
excellence in academic work (with a major GPA of
3.500 or above) are most likely to be admitted. Students with a major GPA of 3.500 or above may
waive the GRE requirement in the M.S. application.
Before moving into the graduate phase, I.D.P. students must satisfy all requirements of the B.S.
degree.
To apply for the I.D.P., undergraduate students must
submit the Statistics I.D.P. form along with supporting
documents during the last quarter of their junior
year, to enter the I.D.P. in the first quarter of their
senior year. In addition, applicants must submit an
application to the M.S. program during the senior
year, prior to the deadline of May 31st. Before
applying to the I.D.P., students are strongly advised
to consult with both the undergraduate and graduate
advisers.
Once a student enters the graduate phase of the
I.D.P., they follow the course requirements for the
Master's degree (36 units, 18 of which are graduate
level). A maximum of 12 units taken in the undergraduate phase can be transferred to the M.S. provided they have not been used to satisfy any
requirements of the B.S. degree.
Courses in Statistics (STA)
Lower Division
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.)
13Y. 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 for students
who have completed course 13, or higher. GE
credit: SciEng | QL, SE.—I. (I.) Utts
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
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.)
519
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: SciEng | 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, goodnessof-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: SciEng | 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: SciEng | 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:
SciEng | 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:
SciEng | 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:
SciEng | 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 infer-
Quarter Offered: I=Fall, II=Winter, III=Spring, IV=Summer; 2015-2016 offering in parentheses
Pre-Fall 2011 General Education (GE): ArtHum=Arts and Humanities; SciEng=Science and Engineering; SocSci=Social Sciences; Div=Domestic Diversity; Wrt=Writing Experience
Fall 2011 and on Revised General Education (GE): AH=Arts and Humanities; SE=Science and Engineering; SS=Social Sciences;
ACGH=American Cultures; DD=Domestic Diversity; OL=Oral Skills; QL=Quantitative; SL=Scientific; VL=Visual; WC=World Cultures; WE=Writing Experience
520
Statistics
ence; one-way MANOVA; discriminant analysis;
principal components; canonical correlation; factor
analysis. Intensive use of computer analyses and real
data sets. GE credit: SciEng | 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 statespace models; Applications to data from economics,
engineering, medicine environment using time series
software. GE credit: SciEng | 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:
SciEng | 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: SciEng | 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: SciEng | 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: SciEng | 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
201. SAS Programming for Statistical
Analysis (3)
Lecture—2 hours; discussion/laboratory—1 hour.
Prerequisite: introductory, upper-division Statistics
course; some knowledge of vectors and matrices;
courses 106 or 108 or the equivalent suggested.
Introductory SAS language, data management, statistical applications, methods. Includes basics,
graphics, summary statistics, data sets, variables
and functions, linear models, repetitive code, simple
macros, GLIM and GAM, formatting output, correspondence analysis, bootstrap. Prepare SAS base
programmer certification exam.—III. (III.)
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.)
206. Statistical Methods for Research—I (4)
Lecture—3 hours; laboratory/discussion—1 hour.
Prerequisite: introductory statistics course; some
knowledge of vectors and matrices. Focus on linear
statistical models. Emphasis on concepts, method
and data analysis; formal mathematics kept to minimum. Topics include simple and multiple linear
regression, polynomial regression, diagnostics,
model selection, factorial designs and analysis of
covariance. Use of professional level software.—I.
(I.)
207. Statistical Methods for Research—II (4)
Lecture—3 hours; laboratory/discussion—1 hour.
Prerequisite: course 206; knowledge of vectors and
matrices. Linear and nonlinear statistical models
emphasis on concepts, methods/data analysis using
professional level software; formal mathematics kept
to minimum. Topics include linear mixed models,
repeated measures, generalized linear models,
model selection, analysis of missing data, and multiple testing procedures.—I. (I.)
208. Statistical Methods in Machine
Learning (4)
Lecture—3 hours; laboratory/discussion—1 hour.
Prerequisite: course 206, 207 and 135, or their
equivalents. Focus on linear and nonlinear statistical
models. Emphasis on concepts, methods, and data
analysis; formal mathematics kept to minimum. Topics include resampling methods, regularization techniques in regression and modern classification,
cluster analysis and dimension reduction techniques.
Use professional level software.—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 mea-
surements 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 (4-44)
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
Quarter Offered: I=Fall, II=Winter, III=Spring, IV=Summer; 2015-2016 offering in parentheses
Pre-Fall 2011 General Education (GE): ArtHum=Arts and Humanities; SciEng=Science and Engineering; SocSci=Social Sciences; Div=Domestic Diversity; Wrt=Writing Experience
Fall 2011 and on Revised General Education (GE): AH=Arts and Humanities; SE=Science and Engineering; SS=Social Sciences;
ACGH=American Cultures; DD=Domestic Diversity; OL=Oral Skills; QL=Quantitative; SL=Scientific; VL=Visual; WC=World Cultures; WE=Writing Experience
Statistics (A Graduate Program)
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.
(II-III.)
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. Offered irregularly.—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, changepoint problems, asymptotics for parametric, nonparametric and semiparametric models, nonlinear
time series, robustness. May be repeated for credit
with consent of instructor. Offered irregularly.—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
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
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. Offered irregularly. (S/U grading only.)—I,
II, III. (I, II, III.)
521
Statistics
(A Graduate Program)
Hans-Georg Müller, Ph.D., Chairperson of the Program
Program Office. 4118 Mathematical Sciences
Building 530-692-5194;
http://www.stat.ucdavis.edu
Faculty
Ethan Anderes, Ph.D., Associate Professor (Statistics)
Alexander Aue, Ph.D., Associate Professor
(Statistics)
Paul Baines, Ph.D., Assistant Professor (Statistics)
Laurel Beckett, Ph.D., Professor
(Public Health Sciences)
Paul Baines, Ph.D., Assistant Professor (Statistics)
Prabir Burman, Ph.D., Professor (Statistics)
Colin Cameron, Ph.D., Professor (Economics)
Hao Chen, Ph.D., Assistant Professor (Statistics)
Christiana Drake, Ph.D., Professor (Statistics)
Thomas B. Farver, Ph.D., Professor
(Population Health and Reproduction)
Peter Hall, Ph.D., Professor (Statistics)
Fushing Hsieh, Ph.D., Professor (Statistics)
Jiming Jiang, Ph.D., Professor (Statistics)
Oscar Jorda, Ph.D., Professor (Economics)
Thomas Lee, Ph.D., Professor (Statistics)
Hans-Georg Müller, M.D., Ph.D., Professor
(Statistics)
Debashis Paul, Ph.D. Associate Professor (Statistics)
Jie Peng, Ph.D., Associate Professor (Statistics)
Wolfgang Polonik, Ph.D., Professor (Statistics)
David Rocke, Ph.D., Professor
(Public Health Sciences)
Naoki Saito, Ph.D., Professor (Mathematics)
Duncan Temple Lang, Ph.D., Professor (Statistics)
Chih-Ling Tsai, Ph.D., Professor
(Graduate School of Management)
Jane-Ling Wang, Ph.D., Professor (Statistics)
Emeriti Faculty
Rudolph Beran, Ph.D., Professor Emeritus
P.K. Bhattacharya, Ph.D., Professor Emeritus
Alan P. Fenech, Ph.D., Professor Emeritus
George G. Roussas, Ph.D., Professor Emeritus
Yue-Pok (Ed) Mack, Ph.D., Professor Emeritus
Francisco J. Samaniego, Ph.D., Professor Emeritus
Robert H. Shumway, Ph.D., Professor Emeritus
Alvin D. Wiggins, Ph.D., Professor Emeritus
Affiliated Faculty
Rahman Azari, Ph.D., Lecturer (Statistics)
Graduate Study. The Graduate Program in Statistics offers programs of study and research leading to
the M.S. and Ph.D. degrees. The M.S. gives students
a strong foundation in the theory of statistics as well
as substantial familiarity with the most widely used
statistical methods. Facility in computer programming is essential for some of the course work. The
supervised statistical consulting required of all M.S.
students has proven to be a valuable educational
experience. The Ph.D. program combines advanced
course work in statistics and probability with the
opportunity for in-depth concurrent study in an
applied field. For detailed information contact the
Chairperson of the Program or the Graduate
Adviser.
Preparation. Preparation for the graduate program requires a year of calculus, a course in linear
algebra, facility with a programming language and
upper division coursework in mathematics and/or
statistics. For admission to the Ph.D. program, course
work requirements for the master's degree, and at
least one semester/two quarters of advanced calculus must be completed.
Graduate Adviser. Debashis Paul (Statistics)
Quarter Offered: I=Fall, II=Winter, III=Spring, IV=Summer; 2015-2016 offering in parentheses
Pre-Fall 2011 General Education (GE): ArtHum=Arts and Humanities; SciEng=Science and Engineering; SocSci=Social Sciences; Div=Domestic Diversity; Wrt=Writing Experience
Fall 2011 and on Revised General Education (GE): AH=Arts and Humanities; SE=Science and Engineering; SS=Social Sciences;
ACGH=American Cultures; DD=Domestic Diversity; OL=Oral Skills; QL=Quantitative; SL=Scientific; VL=Visual; WC=World Cultures; WE=Writing Experience