UC Santa Barbara General CatalogUniversity of California, Santa Barbara

Statistics and Applied Probability

Department of Statistics and Applied Probability
Division of Mathematical, Life, and Physical Sciences
South Hall 5607A
Telephone: (805) 893-2129
Undergraduate E-mail: undergradinfo@pstat.ucsb.edu
Graduate E-mail: gradinfo@pstat.ucsb.edu
Website: www.pstat.ucsb.edu
Department Chair: John Hsu
Vice Chair: Michael Ludkovski


 

Some courses displayed may not be offered every year. For actual course offerings by quarter, please consult the Quarterly Class Search or GOLD (for current students). To see the historical record of when a particular course has been taught in the past, please visit the Course Enrollment Histories.

Statistics & Applied Probability
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Collapse Courses Lower Division 
PSTAT 5A. Statistics
(5) STAFF
Recommended Preparation: high school algebra.
Enrollment Comments: Not open for credit to students who have Advance Placement Exam credit for Statistics; or completed PSTAT 5LS, Psychology 5, Economics 5, Sociology 3, EEMB 30, Communications 87, or other introductory statistics courses. Students should not simultaneously enroll in any of these courses.
Repeat Comments: Partial credit of 2 units will be given to students who have received credit for PSTAT 109.
Random variables, sampling distribution, estimation hypothesis testing, correlation and regression, other topics from statistics. Computing labs required.
PSTAT 5H. Honors Seminar, Statistics
(1) STAFF
Prerequisite: Concurrent enrollment in Statistics 5A, 5LS or 109.
Recommended Preparation: High school algebra.
Enrollment Comments: Quarters usually offered: Winter, Spring, Fall.
Eligible students will be invited to enroll. A variety of statistics topics will be introduced based on weekly reading assignments. As well as preparation for discussion, a 15- minute group presentation or a short (2-3 pages) analytical essay will be required.
PSTAT 5LS. Statistics for Life Sciences
(5) STAFF
Recommended Preparation: High school algebra.
Enrollment Comments: Not open for credit to students who have who have Advance Placement Exam credit for Statistics; or completed PSTAT 5A, Psychology 5, Economics 5, Sociology 3, EEMB 30, Communications 87, or other introductory statistics courses. Students should not simultaneously enroll in any of these courses.
Repeat Comments: Partial credit of 2 units will be given to students who have received credit for PSTAT 109.
An introduction to statistics for students interested in the quantitative analysis of problems in the life sciences. The focus is on application; topics include probability, correlation and regression, sampling distributions, confidence intervals, and hypothesis testing.
PSTAT 10. Introduction to Computing for Data Science
(5) STAFF
Prerequisite: Math 2B or 3B with a minimum grade of C or better.
An overview of data analytic thinking through examples. Introduction to descriptive statistics and linear regression. Fundamentals of programming using R. Basic graphics in R. Relational database management systems and simple data manipulation using SQL.
PSTAT 99. Independent Studies in Statistics
(1-4) STAFF
Enrollment Comments: Students must have a minimum 3.0 GPA and are limited to 4 units per quarter and 30 units total in all 98/99/198/199/199AA-ZZ courses combined.
Independent study under the guidance of a faculty member in the department. Course offers exceptional students an opportunity to undertake independent study or work in a group.
Collapse Courses Upper Division 
PSTAT 105. Introduction to Nonparametric Methods
(4) STAFF
Prerequisite: PSTAT 10 and PSTAT 120B both with a minimum grade of C or better.
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.
PSTAT 109. Statistics for Economics
(5) STAFF
Prerequisite: Math 34A-B or Math 2A-B or 3A-B; Math 34B or 2B or 3B can be taken simultaneously. Course cannot be used to satisfy any Actuarial Science, FinancialMath & Statistics or Statistical Science major or minor requirements.
An introduction to probabilistic modeling and statistical inference for students with basic knowledge of calculus: probability, discrete and continuous random variables, probability distributions, mean, variance, correlation, sampling, parameter estimation, unbiasedness and efficiency, confidence intervals, hypothesis testing. Computing labs with Excel.
PSTAT 115. Introduction to Bayesian Data Analysis
(4) STAFF
Prerequisite: PSTAT 126 with a minimum grade of C.
An introduction to the Bayesian approach to statistical inference, its theoretical foundations and comparison to classical methods. Topics include parameter estimation, testing, prediction and computational methods (Markov Chain Monte Carlo simulation). Emphasis on concepts, methods and data analysis. Extensive use of the R programming language and examples from the social, biological and physical sciences to illustrate concepts.
PSTAT 120A. Probability and Statistics
(4) STAFF
Prerequisite: Math 3C or Math 4A or Math 4AI or Math 6A or Math 6AI completed with a minimum grade of C or better.
Recommended Preparation: Math 6A
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.
PSTAT 120B. Probability and Statistics
(4) STAFF
Prerequisite: PSTAT 120A with a grade of C or better.
Distribution of sample mean and sample variance; t, chi-squared 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 test; confidence intervals.
PSTAT 120C. Probability and Statistics
(4) STAFF
Prerequisite: PSTAT 120B with a grade C or better.
Hypothesis tests for means of independent samples and paired data; likelihood ratio tests; nonparametric hypothesis tests: sign, rank, and Mann-Whitney tests; chi-squared goodness-of-fit tests and contingency tables; Bayesian methods of estimating parameters and credible intervals.
PSTAT 122. Design and Analysis of Experiments
(4) STAFF
Prerequisite: PSTAT 10 and PSTAT 120B both with a minimum grade of C or better.
An introduction to statistical design and analysis of experiments. Covers: principles of randomization, blocking and replication; fixed, random and mixed effects models; block designs, factorial designs and nested designs; analysis of variance and multiple comparison.
PSTAT 123. Sampling Techniques
(4) STAFF
Prerequisite: PSTAT 10 and PSTAT 120B both with a minimum grade of C or better.
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.
PSTAT 126. Regression Analysis
(4) STAFF
Prerequisite: PSTAT 10 and PSTAT 120B both with a minimum grade of C or better.
Linear and multiple regression, analysis of residuals, transformations, variable and model selection including stepwise regression, and analysis of covariance. The course will stress the use of computer packages to solve real-world problems.
PSTAT 127. Advanced Statistical Models
(4) STAFF
Prerequisite: PSTAT 126 with a minimum grade of C or better.
Exponential family and generalized linear models including logistic and Poisson regression, nonparametric regression, including kernel, spline and local polynomials, and generalized additive models. Other topics as time allows: regularization, neural networks, and support vector machines. Emphasis will be on concepts and practical applications.
PSTAT 130. SAS Base Programming
(4) STAFF
Prerequisite: One upper division course in PSTAT, MATH, Computer Science or ECE.
Recommended Preparation: Computer Science 16 or equivalent programming class.
In depth SAS programming course. Topics include importing/exporting raw data files, manipulating/transforming data, combining SAS data sets, generating reports, handling syntax and logic errors. Provides preparation for the SAS Institute Certified Professional (Base Programming) Examination.
PSTAT 131. Introduction to Statistical Machine Learning
(4) STAFF
Prerequisite: PSTAT 120A-B and PSTAT 126 with a minimum grade of C or better.
Statistical Machine Learning is used to discover patterns and relationships in large data sets. Topics will include: data exploration, classification and regression tress, random forests, clustering and association rules. Building predictive models focusing on model selection, model comparison and performance evaluation. Emphasis will be on concepts, methods and data analysis; and students are expected to complete a significant class project, individual or team based, using real-world data.
PSTAT 132. Database Management for Data Analysis
(4) STAFF
Prerequisite: PSTAT 10 with a minimum grade of C or better.
Database systems concepts and architecture, data modeling by ER, relational model, Structured Query Language (SQL), functional dependencies, normalization, physical database design decisions, transaction processing concepts and theory. Introduction to the non-relational model, NoSQL and NewSQL.
PSTAT 134. Statistical Data Science
(4) STAFF
Prerequisite: PSTAT 120B and PSTAT 10 with a minimum grade of C or better, and one course from Computer Science 8, or 16 or Engineering 3.
Overview and use of data science tools in R and Python for data retrieval, analysis, visualization, reproducible research and automated report generation. Case studies will illustrate practical use of these tools.
PSTAT 135. Big Data Analytics
(4) STAFF
Prerequisite: PSTAT 134 and one of the following: PSTAT 131 or PSTAT 231 or Computer Science 165B. A minimum letter grade of C or better must be earned in each course
Basics in distributed data storage, retrieval, processing and cloud computing. Overview of methods for analyzing big data from both high dimensional statistics and machine learning - topics chosen from penalized regression, classification/clustering, dimension reduction, random projections, kernel methods, network clustering, graph analytics, supervised and unsupervised learning among others.
PSTAT 140. Statistical Process Control
(4) STAFF
Prerequisite: PSTAT 10 and PSTAT 120B both with a minimum grade of C or better.
Topics include, statistical quality control charts for mean, standard deviation, range, fraction defective, and number of defects; sampling by attributes and variables; acceptance sampling, choice of acceptable quality level, average outgoing quality limit and lot tolerance percent defective values.
PSTAT 160A. Applied Stochastic Processes
(4) STAFF
Prerequisite: Mathematics 4A or 4AI or 5A, Mathematics 8, and PSTAT 120A. A minimum letter grade of C or better must be earned in each course.
Discrete probability models. Review of discrete and continuous probability. Conditional expectations. Simulation techniques for random variables. Discrete time stochastic processes: random walks and Markov chains with applications to Monte Carlo simulation and mathematical finance. Introduction to Poisson process.
PSTAT 160B. Applied Stochastic Processes
(4) STAFF
Prerequisite: PSTAT 120B and PSTAT 160A, both a grade of C or better
Continuous models. Continuous time stochastic processes: Poisson process, Markov chains, Renewal process, Brownian motion, including simulation of these processes. Applications to Black-Scholes model, insurance and ruin problems and related topics.
PSTAT 170. Introduction to Mathematical Finance
(4) STAFF
Prerequisite: PSTAT 120A-B and 160A, all completed with a minimum grade of C or better.
Recommended Preparation: PSTAT 160B and 171.
Enrollment Comments: Same course as Mathematics 170.
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.
PSTAT 171. Mathematics of Fixed Income Markets
(4) STAFF
Prerequisite: Mathematics 2B or 3B with a minimum grade of C
Introduction to fixed Income Markets. Topics include: measurement of interest, annuities certain, varying annuities, amortization schedules, sinking funds, bonds and related securities, depreciation.
PSTAT 172A. Actuarial Statistics I
(4) STAFF
Prerequisite: 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.
PSTAT 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.
PSTAT 173. Risk Theory
(4) STAFF
Prerequisite: PSTAT 120B with a minimum grade of C or better.
Risk measures, individual and collective risk models, credibility theory; applications to actuarial and financial mathematics.
PSTAT 174. Time Series
(4) STAFF
Prerequisite: PSTAT 10 and PSTAT 120B both with a minimum grade of C or better.
Stationary and non-stationary models, seasonal time series, ARMA models: 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. Current software and applications.
PSTAT 175. Survival Analysis
(4) STAFF
Prerequisite: PSTAT 10 and PSTAT 120B both with a minimum grade of C or better.
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.
PSTAT 176. Advanced Mathematical Finance
(4) STAFF
Prerequisite: PSTAT 160A-B, PSTAT 170; PSTAT 160B may be taken concurrently. PSTAT 160A and PSTAT 170 must be completed with a B- or higher.
Enrollment Comments: Concurrently offered with PSTAT 276.
Advanced topics in asset pricing models, portfolio optimization, interest rate modeling and derivative pricing. Fundamental Theorem of Asset Pricing, Markowitz Mean-Variance Frontier, Capital Asset Pricing Theory, Monte Carlo methods and variance reduction techniques.
PSTAT 182T. Tutorial in Actuarial Statistics
(2) STAFF
Prerequisite: Statistics 120A
Enrollment Comments: May be repeated for credit to a maximum of six units.
Problem solving sessions to prepare students for the first four actuarial examinations. Topics corresponding to these examinations (probability, financial mathematics, statistical modeling, and risk management) will be offered in different quarters.
PSTAT 183. Fundamental Actuarial Concepts
(4) STAFF
Prerequisite: PSTAT 171
Introduces students to practical actuarial concepts and principles related to Property/Casualty Insurance (also known as General Insurance). Topics include pricing methods, reserving methods, insurance accounting, actuarial standards, and other subject matter students are likely to encounter early in their actuarial career. Examples expose students to Property Casualty Insurance; however, many of the concepts covered such as; frequency, severity, development, trend, deductibles and coinsurance, also apply to other practice areas (e.g., Life, Health, or Retirement).
PSTAT 193. Internship in Statistics
(1-4) STAFF
Prerequisite: Upper-division standing and consent of instructor.
Repeat Comments: May be repeated for credit to a maximum of 12 units. No units may be applied to a major.
Faculty sponsored academic internship in industrial or research firms.
PSTAT 194. Group Studies for Advanced Students
(1-4) STAFF
Prerequisite: Upper-division standing; consent of instructor.
Enrollment Comments: Enrollment normally limited to 12 or fewer students.
Lectures and discussions on special topics in probability and statistics.
PSTAT 195. Special Topics in Statistics
(1-4) STAFF
Prerequisite: Upper-division standing in statistics, actuarial science, and financial mathematics.
Special topics of current importance in statistical sciences, actuarial science, or financial mathematics and statistics. Course content will vary.
PSTAT 196. Undergraduate Research in Actuarial Science and Mathematical Finance
(2-4) STAFF
Enrollment Comments: Upper-division standing, consent of the instructor. Must have a minimum 3.2 grade-point average for the preceding three quarters. May be repeated for up to 12 units. No more than 4 units may be applied to departmental electives.
Research opportunities for undergraduate students. Presentation and discussion of current research and reviews of the literature. Students will be expected to give regular oral presentations, actively participate in a weekly seminar, and prepare at least one written report on their research.
PSTAT 199. Independent Studies in Statistics
(1-4) STAFF
Prerequisite: Upper-division standing; completion of 2 upper-division courses in PSTAT.
Enrollment Comments: Students must have a minimum 3.0 GPA for the preceding 3 quarters and are limited to 5 units per quarter and 30 units total in all 98/99/198/199/199AA-ZZ courses combined.
Independent studies in statistics.
PSTAT 199RA. Independent Research Assistance
(1-4) STAFF
Prerequisite: Upper-division standing; PSTAT 120A-B-C; an additional upper-division coursin PSTAT; consent of instuctor and department.
Enrollment Comments: Students must have a 3.0 GPA for the preceding 3 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.
Collapse Courses Graduate 
PSTAT 207A. Statistical Theory
(4) STAFF
Prerequisite: PSTAT 120A-B-C. Part of a three quarter sequence with 207B and 207C.
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; bayesian estimation and hypothesis testing; basic decision theory, linear regression; analysis of variance.
PSTAT 207B. Statistical Theory
(4) STAFF
Prerequisite: PSTAT 207A. Part of a three quarter sequence with 207A and 207C.
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; bayesian estimation and hypothesis testing; basic decision theory, linear regression; analysis of variance.
PSTAT 207C. Statistical Theory
(4) STAFF
Prerequisite: PSTAT 207B. Part of a three quarter sequence with 207A and 207B.
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; bayesian estimation and hypothesis testing; basic decision theory, linear regression; analysis of variance.
PSTAT 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 Lebesque). Product spaces and Fubini theorem. L2 spaces of random variables.
PSTAT 213A. Introduction To Probability Theory And Stochastic Processes
(4) STAFF
Prerequisite: PSTAT 120A-B.
Recommended Preparation: Students are advised to complete Mathematics 117 and PSTAT 160 A-B in preparation for this course.
Generating functions, discrete and continuous time Markov chains; random walks; branching processes; birth-death processes; Poisson processes, point processes.
PSTAT 213B. Introduction to Probability Theory and Stochastic Processes
(4) STAFF
Prerequisite: Prerequisites: PSTAT 213A, and either PSTAT 210 or Math 118 A-B-C
Convergence of random variables: different types of convergence; characteristic functions, continuity theorem, laws of large numbers, central limit theorem, large deviations, infinitely divisible and stable distributions, uniform integrability. Conditional expectation.
PSTAT 213C. Introduction To Probability Theory And Stochastic Processes
(4) STAFF
Prerequisite: PSTAT 213B
Martingales, martingale convergence, stopping times, optional sampling, optional stopping theorems and applications, maximal inequalities. Brownian motion, introduction to diffusions.
PSTAT 215A. Bayesian Inference
(4) STAFF
Prerequisite: PSTAT 207A or PSTAT 220A (may be taken concurrently).
Fundamentals of the Bayesian inference, including the likelihood principle, the discrete version of Bayes theorem, prior and posterior distributions, Bayesian point and interval estimations, and predictions. Bayesian computational methods such as Laplacian approximations and Markov Chain Monte Carlo (MCMC) simulation.
PSTAT 215B. Statistical Decision Theory
(4) STAFF
Prerequisite: PSTAT 207A-B-C.
Statistical inference including estimation, testing and multiple decision rules in decision theoretic framework, relationship to game theory, admissibility, optimality including Bayes and minimax rules, empirical and hierarchical Bayes, invariant decisions.
PSTAT 215C. Statistical Decision Theory
(4) STAFF
Prerequisite: PSTAT 207A-B-C.
Statistical inference including estimation, testing and multiple decision rules in decision theoretic framework, relationship to game theory, admissibility, optimality including Bayes and minimax rules, empirical and hierarchical Bayes, invariant decisions.
PSTAT 216. Multivariate Analysis
(4) STAFF
Prerequisite: 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.
PSTAT 217. Advanced Topics in Mathematical Statistics
(4) STAFF
Prerequisite: PSTAT 207A-B-C.
Repeat Comments: May be repeated for credit provided topics are different.
Topics in mathematical statistics and decision theory including: asymptotics, nonparametric function estimation, design of experiments and linear models, sequential analysis, multiple testing problems, semiparametric inference, directional statistics.
PSTAT 220A. Advanced Statistical Methods
(4) STAFF
Prerequisite: 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. R/SAS Computation.
PSTAT 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. R/SAS computation.
PSTAT 220C. Advanced Statistical Methods
(4) STAFF
Prerequisite: PSTAT 220A and Mathematics 108B or equivalents.
Multivariate analysis. Topics selected from factor analysis; canonical correlation analysis; classification and discrimination; clustering; and data mining. Emphasis on application rather than theory. R/SAS computation.
PSTAT 221A. Advanced Probability Theory
(4) STAFF
Prerequisite: PSTAT 213A-B-C.
Topics chosen from: large deviations; random walks; weak covergence in metric spaces; empirical processes; point processes; Gaussian processes; random fields; branching processes; inference for stochastic processes. Applications.
PSTAT 221B. Advanced Probability Theory
(4) STAFF
Prerequisite: PSTAT 213A-B-C.
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.
PSTAT 221C. Advanced Probability Theory
(4) STAFF
Prerequisite: PSTAT 213A-B-C.
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.
PSTAT 222A. Advanced Stochastic Processes
(4) STAFF
Prerequisite: PSTAT 213A-B-C.
Topics chosen from: Markov processes; continuous time matringales; theory of Brownian motion and diffusion processes; Levy processes stochastic calculus; stochastic differential equations and numerical methods; stochastic control. Applications to engineering, finance, biology, etc.
PSTAT 222C. Advanced Stochastic Processes
(4) STAFF
Prerequisite: PSTAT 213A-B-C.
Topics chosen from: Markov processes; continuous time matringales; theory of Brownian motion and diffusion processes; Levy processes stochastic calculus; stochastic differential equations and numerical methods; stochastic control. Applications to engineering, finance, biology, etc.
PSTAT 223A. STOCHASTIC CALCULUS AND APPLICATIONS
(4) STAFF
Prerequisite: PSTAT 213A-B-C (or equivalent first-year graduate course in Probability and Stochastic Processes).
An introduction to Brownian motion, stochastic calculus and stochastic differential equations. Diffusion processes, related partial differential equations and Feynman-Kac formula. Applications to filtering, stochastic control, mathematical finance and other areas of science and engineering.
PSTAT 223B. Financial Modeling
(4) STAFF
Prerequisite: PSTAT 223A
An introduction to stochastic models in finance with applications to valuation and hedging of derivatives in equity, fixed income, and credit markets, and to portfolio allocation.
PSTAT 223C. ADVANCED TOPICS IN FINANCIAL MODELING
(4) STAFF
Prerequisite: PSTAT 223A-B
Advanced topics in financial mathematics including: portfolio optimization, stochastic control, risk management, systemic risk, high frequency trading, numerical methods and computation.
PSTAT 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.
PSTAT 226. Nonparametric Regression and Classification Methods
(4) STAFF
Prerequisite: 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.
PSTAT 227. Bootstrap and Resampling Methodology
(4) STAFF
Prerequisite: PSTAT 207A-B and PSTAT 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.
PSTAT 228. Spline Smoothing and Applications
(4) STAFF
Prerequisite: Statistics & Applied Probability 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 turning parameter selection. Emphasis on methodology, computation and application.
PSTAT 230. Seminar and Projects in Statistical Consulting
(4) STAFF
Prerequisite: PSTAT 220A-B-C (may be taken concurrently)
Students participate in the discussions and consulting projects in the statistics laboratory. They are assigned project(s) to work on and write a report on statistical aspects of the project.
PSTAT 231. Introduction to Statistical Machine Learning
(4) STAFF
Prerequisite: PSTAT 120A-B; and PSTAT 126 with a minimum grade of C or better.
Enrollment Comments: Concurrently offered with PSTAT 131.
Statistical Machine Learning is used to discover patterns and relationships in large data sets. Topics will include: data exploration, classification and regression trees, random forests, clustering and association rules. Building predictive models focusing on model selection, model comparison and performance evaluation. Emphasis will be on concepts, methods and data analysis; and students are expected to complete a significant class project, individual or team based, using real world data.
PSTAT 232. Computational Techniques in Statistics
(4) STAFF
Prerequisite: PSTAT 120A-B-C, 160A-B or equivalent. Knowledge of at least one programminglanguage.
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.
PSTAT 234. Statistical Data Science
(4) STAFF
Prerequisite: PSTAT 126 with a minimum grade of C, and one course from CS 8, or CS 16, or Engineering 3, or equivalent.
Overview and use of data science tools in R and Python for data retrieval, analysis, visualization, reproducible research and automated report generation. Case studies will illustrate practical use of these tools.
PSTAT 235. Big Data Analytics
(4) STAFF
Prerequisite: PSTAT 126 and PSTAT 234, each with a minimum grade of C or better, and one course from CS 8, or CS 16, or Engineering 3, or equivalent.
Basics in distributed data storage, retrieval, processing and cloud computing. Overview of methods for analyzing big data from both high dimensional statistics and machine learning - topics chosen from penalized regression, classification/clustering, dimension reduction, random projections, kernel methods, network clustering, graph analytics, supervised and unsupervised learning among others.
PSTAT 250. Quantitative Methods in the Social Sciences Colloquium
(2) STAFF
Enrollment Comments: May be repeated for credit. Same course as Sociology 212Q, Geography 201Q, and ED 212.
Required colloquium course for students in the interdisciplinary Quantitative Methods in the Social Sciences emphasis.
PSTAT 262AAZZ. Seminars In Probability and Statistics
(1-6) STAFF
Prerequisite: PSTAT 120A-B-C; consent of instructor.
Enrollment Comments: 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.
PSTAT 262A. Seminars In Probability and Statistics
PSTAT 262AA. Seminars In Probability and Statistics
PSTAT 262AP. Seminars In Probability and Statistics
PSTAT 262AS. Seminars In Probability and Statistics
PSTAT 262AT. Seminars In Probability and Statistics
PSTAT 262B. Seminars In Probability and Statistics
PSTAT 262BN. Seminars In Probability and Statistics
PSTAT 262BT. Seminars In Probability and Statistics
PSTAT 262C. Seminars In Probability and Statistics
PSTAT 262D. Seminars In Probability and Statistics
PSTAT 262DH. Seminars In Probability and Statistics
PSTAT 262DS. Seminars In Probability and Statistics
PSTAT 262E. Seminars In Probability and Statistics
PSTAT 262ES. Seminars In Probability and Statistics
PSTAT 262F. Seminars In Probability and Statistics
PSTAT 262FD. Seminars In Probability and Statistics
PSTAT 262FM. Seminars In Probability and Statistics
PSTAT 262FR. Seminars In Probability and Statistics
PSTAT 262G. Seminars In Probability and Statistics
PSTAT 262GS. Seminars In Probability and Statistics
PSTAT 262GT. Seminars In Probability and Statistics
PSTAT 262JH. Seminars In Probability and Statistics
PSTAT 262JL. Seminars In Probability and Statistics
PSTAT 262MC. Seminars In Probability and Statistics
PSTAT 262RM. Seminars In Probability and Statistics
PSTAT 262S. Seminars In Probability and Statistics
PSTAT 262SP. Seminars In Probability and Statistics
PSTAT 262ST. Seminars In Probability and Statistics
PSTAT 262TL. Seminars In Probability and Statistics
PSTAT 262WL. Seminars In Probability and Statistics
PSTAT 262WM. Seminars In Probability and Statistics
PSTAT 262Y. Seminars In Probability and Statistics
PSTAT 262YS. Seminars In Probability and Statistics
PSTAT 262YY. Seminars In Probability and Statistics
PSTAT 262Z. Seminars In Probability and Statistics
PSTAT 263. Research Seminars in Probability and Statistics
(1) STAFF
Prerequisite: Graduate standing.
Enrollment Comments: Maximum of 2 units total is allowed toward MA degree. May be repeated for credit.
Research seminars presented by faculty, visiting scholars, and invited speakers on current research topics.
PSTAT 274. Time Series
(4) STAFF
Prerequisite: PSTAT 120A-B.
Stationary and non-stationary models, seasonal time series, ARMA models: 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. Current software and applications.
PSTAT 275. Survival Analysis
(4) STAFF
Prerequisite: PSTAT 120A-B-C and PSTAT 220A.
Basic concepts: survival functions, hazard functions, cumulative hazard functions, and censoring types. Kaplan-Meier and Nelson-Fleming-Harrington estimates. Log-rank tests. Exponential and Weibull models. Cox proportional hazards and accelerated failure time regression models. Current software and applications.
PSTAT 276. ADVANCED MATHEMATICAL FINANCE
(4) STAFF
Prerequisite: PSTAT 160A-B, PSTAT 170; PSTAT 160B may be taken concurrently. PSTAT 160A and PSTAT 170 must be completed with a B- or higher.
Enrollment Comments: Concurrently offered with PSTAT 176.
Advanced topics in asset pricing models, portfolio optimization, interest rate modeling and derivative pricing. Fundamental Theorem of Asset Pricing, Markowitz Mean-Variance Frontier, Capital Asset Pricing Theory, Monte Carlo methods and variance reduction techniques.
PSTAT 296A. Intro to Research in Actuarial Science
(4) STAFF
Introduction to research skills. Discussion of current research trends, writing literature reviews etc. Students will be required to present material reflecting their interests in actuarial science, which will be critically appraised for both content and presentation. Emphasis will be placed on aiding students to acquire a high-level of professionalism.
PSTAT 296B. Research Projects in Actuarial Science
(4) STAFF
Prerequisite: PSTAT 296A
Introduction to research opportunities. Planning, organizing and managing projects; quality and time management. Students will complete projects on topics of their interest in the areas of actuarial science and financial mathematics. A written report will be required.
PSTAT 500. Teaching Assistant Practicum
(1-4) STAFF
Prerequisite: Appointment as teaching assistant.
Supervised teaching of undergraduate Probability and Statistics courses.
PSTAT 501. Teaching Assistant Training
(1-2) STAFF
Prerequisite: Appointment as teaching assistant.
Consideration of ideas about the process of learning probability and statistics, and discussion of approaches to teaching.
PSTAT 502. Teaching Associate Practicum
(1-5) STAFF
Prerequisite: Appointment as associate.
Supervised teaching of undergraduate courses.
PSTAT 510. Readings for Area Examinations
(2-6) STAFF
Prerequisite: Enrollment in M.A. or Ph.D. program.
Readings for area examinations.
PSTAT 596. Directed Reading and Research
(1-6) STAFF
Prerequisite: Graduate standing and consent of instructor.
Enrollment Comments: May be repeated for credit as determined by the department chairman up to half the graduate units required for the M.A. degree.
Directed reading and research.
PSTAT 598. Master's Thesis Research and Preparation
(1-6) STAFF
Prerequisite: Consent of instructor.
Enrollment Comments: No unit credit allowed toward degree.
Only for research underlying the thesis, writing the thesis. Instructor should be the chair of the student's thesis committee.
PSTAT 599. Ph.D Dissertation Preparation
(1-6) STAFF
Prerequisite: Graduate standing and consent of instructor.
Enrollment Comments: May be repeated for credit.
Ph.D dissertation preparation.

 
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PSTATW 120A. Probability and Statistics
(4) STAFF
Prerequisite: Math 3C or Math 4A or Math 4AI or Math 6A or Math 6AI completed with a minimum grade of C or better.
Recommended Preparation: Math 6A
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.
PSTATW 182T. Tutorial in Actuarial Statistics
(2) STAFF
Prerequisite: Statistics 120A
Enrollment Comments: May be repeated for credit to a maximum of six units.
Problem solving sessions to prepare students for the first four actuarial examinations. Topics corresponding to these examinations (probability, financial mathematics, statistical modeling, and risk management) will be offered in different quarters.