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.
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 convergence 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 martingales; 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 martingales; 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 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.
PSTAT 234.
Statistical Data Science
(4)
STAFF
Prerequisite: PSTAT 120B and PSTAT 126 with a minimum grade of C, and one course from CS 8, or CS 16, or Engineering 3.
Overview and use of data science tools in R and/or 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, PSTAT 134 or 234, and one of the following: PSTAT 131 or 231, or Computer Science 165B. A minimum grade of C or better must be earned in each class.
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 236.
Spatial Statistics
(4)
STAFF
Prerequisite: PSTAT 120A-B or equivalent; MATH 108A or equivalent; knowledge of at least one statistical programming language; or consent of instructor.
Recommended Preparation: PSTAT 126 or equivalent; PSTAT 174/274 or equivalent.
Spatial Covariance Functions, Variograms, Kriging, Gaussion Processes, Estimation Methods and Uncertainty Quantification. Stationary and Non-Stationary Models, Selected Topics from Non-Gaussion Spatial Models, Spatial Point Processes, Areal Data Models, Spatial Networks, Hierarchical Models, Spatio-Temporal Models, and Recent Advances.
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 262LC.
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 262UQ.
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.