Department of Statistics and Applied Probability
Division of Mathematical, Life, and Physical Sciences
South Hall 5607A
Telephone: (805) 893-2129
E-mail: info@pstat.ucsb.edu
Website: www.pstat.ucsb.edu (will
open in a new browser window)
Department Chair: Raisa Feldman
Contents:
- Faculty
- Undergraduate Program
- Graduate Program
- Master of Arts-Statistics-Mathematical Statistics Specialization
- Master of Arts-Statistics-Applied Statistics Specialization
- Doctor of Philosophy-Statistics and Applied Probability
- Optional Ph.D. Emphasis in Financial Mathematics and Statistics
- Optional Ph.D. Emphasis in Quantitative Methods in the Social Sciences
- Statistics and Applied Probability Courses
Guillaume Bonnet, Ph.D., University of North Carolina, Chapel Hill, Assistant Professor (probability, stochastic partial differential equations, mathematical models in population dynamics)
Andrew V. Carter, Ph.D., Yale University, Associate Professor (mathematical statistics)
János Englander, D.Sc., Technion (Haifa, Israel), Assistant Professor (probability, stochastic calculus, partial differential equations)
Raisa Feldman, Ph.D., Technion-IIT, Associate Professor (probability and stochastic processes)
Jean-Pierre Fouque, Ph.D. and D.Sc., Paris VI, Professor (stochastic processes, stochastic partial differential equations, financial mathematics)
David V. Hinkley, Ph.D., London University, Professor (statistical theory and methods)
Dawn E. Holmes, Ph.D., University of Bradford, U.K., Lecturer with Security of Employment (probabilistic reasoning, Bayesian networks)
John Hsu, Ph.D., University of Wisconsin, Associate Professor (Bayesian inference, linear models)
Sreenivasa R. Jammalamadaka, Ph.D., Indian Statistical Institute, Professor (mathematical statistics, nonparametric methods, directional data)
Wendy Meiring, Ph.D., University of Washington, Associate Professor (applied statistics, statistics of space-time processes)
Yuedong Wang, Ph.D., University of Wisconsin at Madison, Professor (biostatistics, smoothing splines)
Joseph Gani, Ph.D., Australian National University, D.Sc., University of London, Professor Emeritus (applied probability, biomathematics, stochastic processes)
Svetlozar Rachev, D.Sc., Steklov Mathematical Institute, Professor Emeritus (probability theory, stability, probability metrics, mathematical finance)
James B. Robertson, Ph.D., Indiana University, Professor Emeritus (probability, ergodic theory, stochastic processes)
Undergraduate Program
Statistics is basic to quantitative research in the biological, physical, and social sciences. Because its methods are based on mathematics, it requires a firm understanding of mathematical methods as well as an appreciation of scientific method, computation, and practical problems.
As preparation for entry into any of UCSB’s undergraduate statistics programs, students should have completed two years of algebra and courses in plane geometry and trigonometry in high school. In the first two years of university study, students should complete the preparation requirements outlined below. These include ten courses, many of which are sequential. Thus students should begin satisfying these requirements in the first quarter of the freshman year. At the end of the second year, students should decide which of the undergraduate degrees described below is best suited to their needs and should design an upper-division program in consultation with their faculty advisor. Recommended programs for each emphasis are available from the faculty advisor.
Bachelor of Arts - Statistical Science
The B.A. in statistical science is a basic degree intended for students interested in general training in statistics and the use of statistical methods in the social and decision sciences. It is suitable as a terminal baccalaureate degree, or as preparation for advanced training in business administration, management science, or operations research.
Preparation for the major. Students must complete each of Mathematics 3A-B-C, 5A-B, and 8. Note that prerequisites to these courses must be completed with a grade of C or above. In addition, students must complete Computer Science 10. (Students are advised to take Computer Science 5JA in preparation for 10.)
Upper-division requirements. Forty upper-division units in statistics and mathematics are required, excluding PSTAT 133A-B-C, and Mathematics 100A-B, 101A-B, 102A-B, 193. The 40 units must include PSTAT 120A-B-C, a minimum of 16 units from PSTAT 105, 122, 123, 126, 130, 140, 160A-B, 174, 175 and a minimum of 8 units from other PSTAT courses not used above or Mathematics 104A-B-C, 108A-B, 111A-B-C, 117, 118A-B-C, 132A-B, Economics 100A-B, 104A-B and 4 additional units of upper-division PSTAT or mathematics. (With an advisor’s approval, 4 of the 40 units may be courses in subjects other than statistics or mathematics, taken as part of a coherent statistics program.)
Bachelor of Science - Statistical Science
The B.S. in statistical science is a specialized statistics degree intended for students interested in the use of statistical theory and methods in the biological, physical, and technological sciences. It is suitable as a terminal baccalaureate degree, or as preparation for advanced training in actuarial statistics, applied statistics, biostatistics, or probability and statistics.
The B.S. in statistical science offers three possible areas of concentration: actuarial statistics, applied statistics, and probability and statistics. Completion of one of these concentrations will not be formally acknowledged on the student’s official transcript or diploma.
Preparation for the major. Students must complete each of Mathematics 3A-B-C, 5A-B, and 8. Note that prerequisites to these courses must be completed with a grade of C or above. In addition, students must complete Computer Science 10. (Students are advised to take Computer Science 5JA in preparation for 10.)
Upper-division requirements. Fifty-two upper-division units in statistics and mathematics are required, excluding PSTAT 133A-B-C and Mathematics 100A-B, 101A-B, 102A-B, 193. The 52 units must include PSTAT 120A-B-C, 122, 126; 8 units from PSTAT or Mathematics 104A-B-C, 108A-B, 111A-B-C, 117, 118A-B-C, 132A-B, Economics 100A-B or 104A-B, 134A-B. Students must also complete one of the following concentrations:
Actuarial statistics concentration. Twelve units from PSTAT 170, 171, 172A-B, 173, and 12 elective units of upper-division PSTAT courses. Up to 4 of the elective PSTAT units required may be chosen from courses in related departments, if approved by the major advisor as part of a coherent statistics program.
Applied statistics concentration. PSTAT 130; 8 units from PSTAT 123, 131,140, 174, 175; 12 units of upper-division elective PSTAT courses. Up to 4 of the elective PSTAT units required may be chosen from courses in related departments, if approved by the major advisor as part of a coherent statistics program.
Probability and statistics concentration. PSTAT 160A-B is required, with 16 elective units of upper-division PSTAT courses. Up to 4 of the elective PSTAT units required may be chosen from courses in related departments, if approved by the major advisor as part of a coherent statistics program.
Bachelor of Science - Financial Mathematics and Statistics
This is a joint major between the Department of Mathematics and the Department of Statistics and Applied Probability. This degree is intended for students who would like to learn how mathematics, probability, and statistics play a key role in pricing and hedging securities in the financial markets.
Pre-major requirements. In order to be admitted into the Financial Mathematics and Statistics major, students must complete all of the following pre-major courses with a grade-point average of 2.5 or higher. Mathematics 3A-B-C, 5A-B-C, 8, Economics 1 and 2. Also required is one course from: Computer Science 5AA-ZZ, 10, or Engineering 3. The computer science and engineering courses are excluded from the pre-major GPA calculation but will apply to the overall major GPA.
Entry into pre-major does not guarantee admission into full major status. Upon satisfactory completion of the pre-major requirements, and after meeting with a faculty advisor to discuss career opportunities and upper-division course electives, students may petition to be accepted to full major status.
Upper-division major. Fifty-two upper-division units in mathematics, statistics, and economics are required, excluding Mathematics 100A-B, 193, and 195A-B and PSTAT 133A-B-C. The 52 units must include Economics 104A, Mathematics 104A-B, 124A-B, PSTAT 120AB, PSTAT 120C, 130, PSTAT 160A, and either PSTAT 170 or Mathematics 170. The remaining 12 elective upper-division units can be chosen from: Economics 104B, 105, 134A-B, 140B; Mathematics 104C, 108A-B, 117, 126, 131; PSTAT 160B, 171, 173,174.
All courses to be applied to the minor must be completed on a letter-grade basis. This includes both courses offered in probability and statistics and those offered by other departments and applied to the minor.
Preparation for the minor. Mathematics 3A-B-C (12 units), 5A-B and 8 (13 units).
Upper-division minor. Twenty units, distributed as follows: PSTAT 120A, 120B-C or 160A-B; 8 units of upper-division PSTAT electives (up to 4 of the elective units may be in a related department, subject to the approval of the statistics and applied probability undergraduate advisor.) Note, however, that the following courses are not applicable to the minor: PSTAT 133A-B-C.
Note: Substitutions and waivers are subject to approval by the chair of the department. Please see "Academic Minors" for special conditions governing minors in the College of Letters and Science.
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Graduate Program
The following programs are available: M.A. in Statistics - Mathematical Statistics Specialization, or Applied Statistics Specialization; and Ph.D. in Statistics and Applied Probability, with two optional Ph.D. emphases (Financial Mathematics and Statistics and Quantitative Methods in the Social Sciences). Specializations are not listed on transcripts or diplomas.
In addition to departmental requirements, candidates for graduate degrees must meet the university degree requirements described in the section "Graduate Education at UCSB."
In addition to departmental admission requirements, applicants must also meet the university requirements for admission described in the section "Graduate Education at UCSB."
All courses required for the graduate degrees must be completed with a grade of B or better.
The Statistical Laboratory (Statlab) has been providing UCSB graduate students and faculty with statistical consulting advice since 1981. The Department of Statistics and Applied Probability is endeavoring to expand the activities of the laboratory and to establish it as a source point for statistical expertise on campus, organizing cross-disciplinary seminars on applied statistics and offering services related to statistical computing and data analysis. The Statlab offers graduate students practical experience in statistical consulting while providing the UCSB campus with professional statistical services. The Statlab may be reached at (805) 893-2007 or by email at statlab@pstat.ucsb.edu.
Admission
A candidate for admission must fulfill the scholarship requirements for graduate study and have had undergraduate coursework equivalent to PSTAT 120A-B-C, Math 108A (linear algebra) and a basic computer science course. Students may be admitted who do not satisfy all requirements, but they will be asked to take supplementary undergraduate courses which will not count toward the graduate degree unit course requirements described below.
Master of Arts - Statistics-Mathematical Statistics Specialization
Degree Requirements
Candidates must complete 42 units of approved upper-division or graduate work, including any two of the three basic graduate course sequences in statistics and probability: PSTAT 207A-B-C, 213A-B-C, and 220A-B-C.
Two plans are available for completing the degree: Plan 1 (thesis), and Plan 2 (examination). Candidates in both plans must complete 42 units of approved upper-division or graduate work.
Under Plan 1, students must pass a comprehensive examination in one statistics area requirement, described under the heading “Doctor of Philosophy” below, prepare a thesis under the supervision of a faculty member, and defend it before a faculty committee. A maximum of 6 of the 42 units may be in PSTAT 596.
Under Plan 2, students must pass a comprehensive examination in two statistics area requirements. For information on area requirements, please refer to Department's Graduate Brochure (http://www.pstat.ucsb.edu).
Master of Arts-Statistics - Applied Statistics Specialization
Degree Requirements
The requirements for the applied statistics track will be kept flexible so that joint programs of study with other departments and schools can be worked out to suit the needs of individual students. These individualized programs should form a coherent plan and are subject to the approval of the statistics faculty. Courses that have substantial overlap will not be allowed.
Candidates must complete 42 units of upper-division or graduate work approved by the graduate advisor in statistics. The 42 units must include at least 24 units of graduate courses in the 200 series and must include PSTAT 122, 220A-B-C and 230.The remaining 18 units of credit may be obtained by taking any upper-division or graduate courses from the Statistics and Applied Probability listing, excluding 120A-B-C and 133/233 A-B-C, or any of the approved courses from the other applied disciplines.
Students must pass a comprehensive written examination based on PSTAT 120A-B-C, 122, 126, and 220A-B-C, and must submit a project report on data analysis to the Applied Statistics Exam Committee.
Doctor of Philosophy - Statistics and Applied Probability
Degree Requirements
Area requirements. Ph.D. students in statistics will be required to fulfill two area requirements. For information on area requirements, please refer to Department’s Graduate Brochure (www.pstat.ucsb.edu). Each student has up to two attempts for each area exam and must successfully pass two area exams within three years after arrival to the PSTAT graduate program whether or not a master’s degree has already been completed.
Course requirements. Students must complete 72 units of PSTAT graduate courses or approved courses from other departments. At least 60 units are 200 level graduate courses (except PSTAT 263) offered by the department and must include PSTAT 207A-B-C, 213A-B-C, and 220A-B-C. Students doing the optional Ph.D. emphasis in mathematical and empirical finance and in quantitative methods in social sciences must refer to the descriptions below. Each required course must be completed with a grade of B or better. Graduate courses in statistics from other departments may be included, but should have prior approval from the graduate advisor in statistics and/or the thesis advisor. These advanced courses should form a coherent plan and facilitate the selection of an area for dissertation research.
The student advances to candidacy after satisfactorily completing two area requirements and passing the preliminary oral examination. The student is required to complete a dissertation representing an original contribution to knowledge; the thesis is defended before a faculty committee.
Optional Ph.D. emphases in Financial Mathematics and Statistics and in quantitative methods in the social sciences are also available. See below.
Specific details about degree requirements are found in the departmental graduate guide. Departmental requirements stated there are in addition to the minium university requirements stated in the General Catalog.
Optional Ph.D. Emphasis in Financial Mathematics and Statistics
Students pursuing a Ph.D. in this department may petition to add an emphasis in mathematical and empirical finance. Students are required to accumulate 72 graduate units, which must include PSTAT 207 A-B-C, 213 A-B-C, and 223 A-B-C, Math 201A-B and either Econ210A-B or Econ 235A-B. A grade of B or better must be obtained in these required courses. Twenty units of electives are required from: PSTAT 220 A-B-C, 221 A-B-C, 222 A-B-C, 262FM, Econ 235 A-B, Econ 210A-B-C, Math 201 A-B-C, 228A-B-C-D, 246 A-B-C, 206 A-B-C-D. With prior approval from the coordinating committee for the emphasis, other courses can be chosen as electives. Students must fulfill two area requirements: probability/stochastic processes and mathematical statistics. The student’s doctoral committee shall be appointed according to the same regulations governing other Ph.D. students in Statistics and Applied Probability, and must be approved by the coordinating committee for the emphasis. The topics of dissertations must focus on an area of Financial Mathematics and Statistics and be approved by the student’s doctoral committee.
Optional Ph.D. Emphasis in Quantitative Methods in the Social Sciences
Students pursuing a Ph.D. in political science may petition to add an interdisciplinary emphasis in quantitative methods in the social sciences (QMSS). QMSS emphasis is intended for students who wish to develop and use cutting-edge quantitative methods on social science research. Our curriculum is designed to provide students with the rigorousmathematical and statistical background necesssary for advanced quantitative work,while also providing a broad interdisciplanary perspective on the use of quantitave methods in social sciences. To that end, students who petition to add the QMSS emphasis, must complete two quarters of calculus, one quarter in linear algebra, and a one-year sequence of statistics. (These requirements can be waived if equivalent courses have already been completed.) QMSS students must also complete at least three quantitative social sciences methods courses (at least two of which are outside the student’s home department), enroll in the QMSS colloquia for at least three quarters, and present their own original quantitative social science research at the QMSS colloquia at least once.
Students that add the QMSS emphasis are expected to write a Ph.D dissertation that is focued on an issue that is appropriate to the QMSS emphasis. For instance, the dissertation could develop a quantitative method that could be applied to social science fields beyond the student’s discipline, or adapt a quantitative method used in a social science field outside the student’s discipline for researching a substantive problem within the student’s discipline. The dissertation committee must include at least one QMSS faculty member from outside the student’s home department.
For more information, please consult the QMSS website at www.qmss.ucsb.edu.
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Statistics and Applied Probability Courses
Lower Division
5A. Statistics
(5) Staff
Not open for credit to students who have completed PSTAT 5E, 5S, Economics 5, Psychology 5, Sociology 3, EEMB 30, Communications 87, or other introductory statistics courses.
Recommended preparation: high school algebra.
Random variables, sampling distribution, estimation hypothesis testing, correlation and regression, other topics from statistics.
5E. Statistics with Economics and Business Applications
(5) Staff
Not open for credit to students who have completed PSTAT 5A, 5S, Economics 5, Psychology 5, Sociology 3, EEMB 30, Communications 87, or other introductory statistics courses.
Recommended preparation: high school algebra.
Introduction to statistical methods applied to the analysis of economic data. Topics include basic probability, statistical inference and hypothesis testing, and regression.
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Upper Division
105. Introduction to Nonparametric Methods
(4) Staff
Prerequisites: PSTAT 120A and 120B (may be taken concurrently) or equivalent.
Statistical methods for model-free data analysis, including use of ranks in comparing means and assessing correlation, computer-based permutation and bootstrap calculations for significance tests and confidence intervals, estimation of lifetime survival curves. Emphasis on scientific applications.
120A. Probability and Statistics
(4) Staff
Prerequisite: Mathematics 3A-B-C.
Concepts of probability; random variables; combinatorial probability; discrete and continuous distributions; joint distributions, expected values; moment generating functions; law of large numbers and central limit theorems.
120B. Probability and Statistics
(4) Staff
Prerequisites: a grade of C or better in PSTAT 120A.
Distribution of sample mean and sample variance; t, x2 and F distributions; summarizing data by statistics and graphs; estimation theory for single samples: sufficiency, efficiency, consistency, method of moments, maximum likelihood; hypothesis testing: likelihood ratio, goodness of fit tests; confidence intervals.
120C. Probability and Statistics
(4) Staff
Prerequisites: a grade of C or better in PSTAT 120B.
Two-sample comparisons: t-test for means of independent samples, paired t-test; analysis of variance: one- and two-way models; analysis of categorical data using chi-squared tests; linear regression via least squares method.
122. Design and Analysis of Experiments
(4) Staff
Prerequisite: PSTAT 120A-B.
Linear models; least squares theory; one-way and two-way analysis of variance; multiple comparison procedures; fixed, random, and mixed effects models; basic designs including completely randomized design, randomized blocks design, incomplete block designs, latin squares, factorial and fractional factorial designs; analysis of covariance.
123. Sampling Techniques
(4) Staff
Prerequisite: a prior upper-division PSTAT course.
An elementary development of the statistical methods used to design and analyze sample surveys. Basic ideas: estimates, bias, variance, sampling and nonsampling errors; simple random sampling with and without replacement, ratio and regression estimates; stratified sampling; systematic sampling; cluster sampling; sampling with unequal probabilities, multistage sampling. Examples from various fields will be discussed to illustrate the concepts including sampling of biological populations, opinion polls, etc.
126. Regression Analysis
(4) Staff
Prerequisites: PSTAT 120A-B.
Linear and multiple regression, analysis of residuals, variable and model selection including stepwise regression, and analysis of covariance. Other topics may include logistic regression, probit analysis, nonlinear regression and nonparametric regression, and correlation methods.
130. SAS Base Programming
(4) Staff
Prerequisite: one upper division course in PSTAT, MATH, Computer Science or ECE.
Requires prior knowledge of at least one programming language.
Recommended preparation: Computer Science 10 or equivalent programming course.
Indepth SAS programming course. Topics include importing/exporting raw data files, manipulating/transforming data, combining SAS data sets, generating reports, handling syntax and logic errors. Course provides preparation for the SAS Institute Certified Professional (Base Programming) Examination.
131. Data Mining
(4) Staff
Prerequisites: PSTAT 120A-B, 130; and, PSTAT 120C or 126 (may be taken concurrently).
Introduction to data mining techniques. Model assessment and performance evaluation. Data preparation. Programming techniques for transforming raw data into a form suitable for predictive modeling. Extracting data to a form that predictive models can utilize. Incorporating non numeric data in predictive models. Techniques for managing exceptional and extreme data. Building predictive models using SAS Enterprise Miner 5 in SAS 9, including Decision Trees, Neutral Networks and Bayesian Networks.
140. Statistics in Industry
(4) Staff
Prerequisite: PSTAT 120A or 133A.
Review of basic probabilty distributions and concept in estimation and testing hypotheses; statistical quality control charts for the mean, standard deviation, the range, the fraction defective, and number of defects; sampling by attributes and variables; acceptance sampling, single,double, and multiple sampling plans, choice of acceptable quality level, average outgoing quality limit and lot tolerance percent defective values; Dodge-Romig and Mil-Std 105 plans; some aspects of life testing and reliability.
160A-B. Applied Stochastic Processes
(4-4) Staff
Prerequisites: Mathematics 5A and 8; and PSTAT 120A with a minimum grade of C.
Random walks, Markov chains, Poisson processes, Markov processes; second order processes, Wiener process stochastic differential equations, optimal prediction, spectral distributions; queueing theory, simulation and applications to mathematical finance.
170. Introduction to Mathematical Finance
(4) Staff
Prerequisites: PSTAT 120A-B and 160A.
Same course as Mathematics 170.
Recommended preparation: PSTAT 160B and 171.
Describes mathematical methods for estimating and evaluating asset pricing models, equilibrium and derivative pricing, options, bonds, and the term-structure of interest rates. Also introduces finance optimization models for risk management and financial engineering.
171. Mathematics of Compound Interest
(4) Staff
Prerequisites: Mathematics 3A-B.
Introduction to compound interest. Topics include: measurement of interest, annuities certain, varying annuities, amortization schedules, sinking funds, bonds and related securities, depreciation.
172A. Actuarial Statistics I
(4) Staff
Prerequisites: PSTAT 120A and 171.
Probabilistic and deterministic contingency mathematics in life and health insurance, annuities, and pensions. Topics include: survival distributions and life tables, life insurance, life annuities, net premiums, net premium reserves.
172B. Actuarial Statistics II
(4) Staff
Prerequisite: PSTAT 172A.
Net premium reserves, multiple life functions, multiple decrement models, valuation theory for pension plans, insurance models including expenses, nonforfeiture benefits and dividends.
173. Risk Theory
(4) Staff
Prerequisite: PSTAT 120A.
Utility theory and the economics of insurance, individual risk models for a short term, collective risk models for a single period and for an extended period, applications.
174. Time Series
(4) Staff
Prerequisites: PSTAT 120A-B.
Time series models: stationary and non-stationary models, seasonal time series, ARMA models: stationary, causality, calculation of ACF, PACF, Mean and ACF estimation. Barlett’s formula, model estimation: Yule-Walker estimates, ML method. Identification techniques, diagnostic checking, forecasting, spectral analysis, the periodogram.
175. Survival Analysis
(4) Staff
Prerequisite: PSTAT 120A-B.
Properties of survival models, including both parametric and tabular models; methods of estimating them from both complete and incomplete samples, including the actuarial, moment and maximum likelihood estimation techniques, and the estimation of life tables from general population data.
182T. Tutorial in Actuarial Statistics
(1) Staff
Prerequisites: upper-division standing and consent of instructor.
May be repeated for credit to a maximum of 3 units.
Problem solving sessions to prepare students for the first four actuarial examinations. Topics corresponding to these examinations (general mathematics, mathematical statistics, applied statistics and mathematics, and actuarial mathematics) will be offered in different quarters.
190AA-ZZ. Special Topics in Statistics
(4) Staff
Prerequisite: upper-division standing.
May be repeated up to 12 units provided letter designation is different. Only 8 units of credit allowed for the major.
Information about the special topics to be presented may be obtained from the office of the Statistics and Applied Probability Department.
193. Internship in Statistics
(1-4) Staff
Prerequisites: upper-division standing; consent of instructor.
May be repeated for credit to a maximum of 4 units.
Faculty sponsored academic internship in industrial or research firms.
195. Special Topics in Statistics
(1-4) Staff
Prerequisites: upper-division standing in statistics; consent of instructor.
Special topics of current importance in statistical sciences. Course content will vary.
199. Independent Studies in Statistics
(1-4) Staff
Prerequisites: upper-division standing; completion of two upper-division courses in statistics.
Students must have a minimum grade-point average of 3.0 for the preceding three quarters and are limited to 5 units per quarter and 30 units total in all 98/99/198/199/199AA-ZZ courses combined.
199RA. Independent Research Assistance
(1-4) Staff
Prerequisites: PSTAT 120A-B-C; a prior upper-division course in Probability and Statistics; upper-division standing; consent of instructor and department.
Students must have a minimum 3.0 grade-point average for the preceding three quarters and are limited to 5 units per quarter and 30 units total in all 98/99/198/199/199AA-ZZ courses combined.
Coursework shall consist of faculty supervised research assistance.
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Graduate Courses
Students enrolling in graduate courses will be expected to have completed PSTAT 120A-B-C or equivalents.
207A-B-C. Statistical Theory
(4-4-4) Staff
Prerequisites: PSTAT 120A-B-C.
Univariate and multivariate distribution theory; generating functions; inequalities in statistics; order statistics, estimation theory; likelihood, sufficiency, efficiency, maximum likelihood; testing hypotheses: likelihood ratio and score tests, power; confidence and prediction intervals; bavesian estimation and hypothesis testing; basic decision theory; linear regression; analysis of variance.
210. Measure Theory for Probability
(4) Staff
Prerequisite: PSTAT 120A.
Probability spaces: axioms, sigma-algebras, monotone class theorems, construction of probability measures on measurable spaces. Random variables. Expectations (integral Lebesgue). Product spaces and Fubini theorem. L2 spaces of random variables.
213A-B-C. Introduction to Probability Theory and Stochastic Processes
(4-4-4) Staff
Prerequisites: PSTAT 120 A-B (for PSTAT 213A): PSTAT 210 (for PSTAT 213B-C).
Recommended preparation: Mathematics
118A-B-C.
Markov chains, random walks, branching processes, convergence concepts, laws of large numbers, characteristic functions, weak convergence, central limit theorems, conditional expectations, martingale sequences, introduction to large deviations, ergodic theory, continuous time, stochastic processes and Brownian motion.
215A-B. Statistical Decision Theory
(4-4) Staff
Prerequisites: PSTAT 207A-B-C or equivalent.
A basic introductory mathematical statistics course in which statistical concepts and procedures are developed and examined from the point of view of game theory, optimization, and decision theory.
216. Multivariate Analysis
(4) Staff
Prerequisites: PSTAT 207A-B-C or equivalent.
Statistical theory associated with the multivariate normal, Wishart and related distributions, partial and multiple correlation, principal components. Hotelling’s T2-statistic, multivariate linear models, classification and discriminant analysis. Other topics may include invariance, admissibility, minimax, James-Stein estimates, multivariate probability inequalities, majorization, and Schur functions.
217. Design of Experiments
(4) Staff
Prerequisites: PSTAT 207A-B-C or equivalent.
Linear models and the analysis of variance; regression and least squares theory; contingency table analysis; method of steepest ascent; ridge regression.
220A. Advanced Statistical Methods
(4) Staff
Prerequisites: PSTAT 120A-B-C 122, 126 and Mathematics 108A or equivalents.
General linear models; regression; analysis of variance of fixed, random, and mixed effects models; analysis of covariance; and experimental design. Discussion of each technique includes graphical methods; estimation and inference; diagnostics; and model selection. Emphasis on application rather than theory.
220B. Advanced Statistical Methods
(4) Staff
Prerequisite: PSTAT 220A or equivalent.
Generalized linear models; log-linear models with application to categorical data; and nonlinear regression models. Discussion of each technique includes graphical methods; estimation and inference; diagnostics; and model selection. Emphasis on application rather than theory.
220C. Advanced Statistical Methods
(4) Staff
Prerequisites: PSTAT 220A and Mathematics 108 or equivalents.
Multivariate analysis. Topis selected from factor analysis; canonical correlation analysis; classification and discrimination; clustering; and data mining. Emphasis on application rather than theory.
221A-B-C. Advanced Probability Theory
(4-4-4) Staff
Prerequisites: PSTAT 213A-B-C.
May be repeated for credit provided topics are different.
Topics chosen from: Large deviations, random walks, weak convergence in metric spaces, empirical processes, point processes, Gaussian processes, random fields, branching processes, inference for stochastic processes. Applications.
222A-B-C. Advanced Stochastic Processes
(4-4-4) Staff
Prerequisites: PSTAT 213A-B-C.
May be repeated for credit provided topics are different.
Topics chosen from: Markov processes, continuous time martingales, theory of Brownian motion and diffusion processes, Lévy processes, stochastic calculus, stochastic differential equations and numerical methods, stochastic control, Applications to engineering, finance, biology, etc.
223A-B-C. Financial Modeling - An Engineering Approach
(4-4-4) Staff
Prerequisites: PSTAT 213A-B-C.
An introduction to stochastic models in finance. Stochastic models and applications to price determination for stocks, bonds, derivative securities, interest rate term structure. Portfolio issues, hedging, risk management and financial engineering. Numerical methods and computation.
225. Linear and Nonlinear Mixed Effects Models
(4) Staff
Prerequisite: PSTAT 220A or equivalent.
Linear and nonlinear mixed effects models. Topics include fixed effects, random effects, several size experimental units, design structure, treatment structure, randomized block design, nested design, split plot design, repeated measures, growth curves, longitudinal and spatial data, BLUP, ML, and REML estimates.
226. Nonparametric Regression and Classification Methods
(4) Staff
Prerequisites: PSTAT 207A-B and 220A or equivalents.
Introduction to some statistical regression and classification techniques including kernel smoothing, smoothing spline, local regression, generalized additive models, neural networks, wavelets, decision tree and nearest neighbor methods.
227. Bootstrap and Resampling Methodology
(4) Staff
Prerequisites: PSTAT 207A-B and 220A or equivalents.
Resampling methods: bootstrap and subsampling. Topics: parametric and nonparametric bootstrap simulation; confidence limit methods; resample significance tests, including Monte Carlo and bootstrap; resampling for improved regression model selection and prediction; diagnostics for bootstrap validity.
228. Spline Smoothing and Their Applications
(4) Staff
Prerequisites: PSTAT 207A-B-C and 220A.
Model building, multivariate function estimation and supervised learning using reproducing kernel Hilbert space, regularization and splines. Smoothing splines for Gaussian and non-Gaussian data. Bayesian models and data-driven tuning parameter selection. Emphasis on methodology, computation and application.
230. Seminar and Projects in Statistical Consulting
(4) Staff
Prerequisites: PSTAT 220A-B-C (may be taken concurrently).
Students participate in the discussions and consulting projects in the statistical laboratory. They are assigned project(s) to work on, and write a report on statistical aspects of the project.
231. Data Mining
(4) Staff
Prerequisites: PSTAT 120A-B and 130; and, PSTAT 120C or 126 (may be taken concurrently).
Introduction to data mining techniques. Model assessment and performance evaluation. Data preparation. Programming techniques for transforming raw data into a form suitable for predictive modeling. Extracting data to a form that predictive models can utilize. Incorporating non-numeric data in predictive models. Techniques for managing exceptional and extreme data. Building predictive models using SAS Enterprise Miner 5 in SAS 9, including Decision Trees, Neural Networks, and Bayesian Networks.
232. Computational Techniques in Statistics
(4) Staff
Prerequisites: PSTAT 120A-B-C, 160A-B-C or equivalent. Knowledge of at least one programming language.
Explores computationally-intensive methods in statistics. Topics covered include combinatorial optimization, EM optimization, Monte Carlo simulation, Markov Chain Monte Carlo methods and bootstrapping. Lab work is carried out using R or SAS.
233A. Introduction to Statistical Methods
(4) Staff
Prerequisite: not open to mathematics and statistics majors.
Statistical data analysis using S-Plus and SAS, minimum use of calculus. Exploratory data analysis, probability, significance tests and confidence intervals for means and variances. Correlation, multiple and nonlinear regression. Experimental designs, analysis of variance, contrasts. Nonparametric methods. Logistic and loglinear regression. Multivariate data methods. Spatial and temporal correlation.
233B. Introduction to Statistical Methods
(4) Staff
Prerequisite: not open to mathematics majors.
Students who have had PSTAT 33 may be admitted into PSTAT 233B with the consent of the instructor.
Considers basic ideas in probability and covers important topics in statistical methods with the minimum use of calculus; relies on the use of personal computers. Topics: probability, random variables and distributions, expectation and variance, binomial, normal, and other probability models. Statistical tests, correlation, and regression. Elementary design of experiments, analysis of variance, sampling, and nonparametric statistics.
250. Quantitative Methods in the Social Sciences Seminar
(2) Staff
Same course as Geography 201Q, Sociology 212Q, and ED 212. May be repeated for credit.
Required course for students in the interdisciplinary Quantitative Methods in the Social Sciences emphasis.
262AA-ZZ. Seminars in Probability and Statistics
(1-6) Staff
Prerequisites: PSTAT 120A-B-C; consent of instructor.
May be repeated for credit.
Topics of current research interest in probability and/or statistics, by means of lectures and informal conferences with members of staff. PSTAT 262FM is reserved for topics in financial mathematics and statistics.
263. Research Seminars in Probability and Statistics
(1) Staff
Prerequisite: graduate standing.
Maximum of 2 units total is allowed towards MA degree. May be repeated for credit.
Research seminars presented by faculty, visiting scholars, and invited speakers on current research topics.
274. Time Series
(4) Staff
Prerequisites: PSTAT 120A-B.
Time series models: stationary and non-stationary models, seasonal time series, ARMA models: stationary, causality, calculation of ACF, PACF, Mean and ACF estimation. Bartlett’s formula, Model estimation: Yule-Walker estimates, ML method. Identification techniques, diagnostic checking, forecasting, spectral analysis, the periodogram.
275. Survival Analysis
(4) Staff
Prerequisites: PSTAT 120A-B and 220A.
Basic concepts: survival functions, hazard functions, cumulative hazard functions and censoring types. Kaplan-Meier and Nelson-Fleming-Harrington estimates. Log-rank test. Exponential and Weibull models. Cox proportional hazards and accelerated failure time regression models. Current software and applications.
500. Teaching Assistant Practicum
(1-4) Staff
Prerequisite: appointment as teaching assistant.
No unit credit allowed toward advanced degree.
Supervised teaching of undergraduate probability and statistics courses.
501. Teaching Assistant Training
(1-2) Staff
Prerequisite: appointment as teaching assistant.
No unit credit allowed toward advanced degree.
Consideration of ideas about the process of learning mathematics and discussion of approaches to teaching.
502. Teaching Associate Practicum
(1-5) Staff
Prerequisite: appointment as associate.
No unit credit allowed toward advanced degree.
Supervised teaching of undergraduate courses.
510. Readings for Area Examinations
(2-6) Staff
Prerequisite: enrollment in M.A. or Ph.D. program.
596. Directed Reading and Research
(1-6) Staff
Prerequisites: graduate standing and consent of instructor.
May be repeated for credit as determined by the department chair up to half the graduate units required for the M.A. degree.
598. Master’s Thesis Research and Preparation
(1-6) Staff
Only for research underlying the thesis, writing the thesis. Instructor should be the chair of the student’s thesis committee.
599. Ph.D. Dissertation Preparation
(1-6) Staff
Prerequisites: graduate standing and consent of instructor. Maximum of 12 units total.
