150. Stochastic Processes. (3) Three hours of lecture per week. Random walks, discrete time Markov chains, Poisson processes. Further topics such as: continuous time Markov chains, queueing theory, point processes, branching processes, renewal theory, stationary processes, Gaussian processes. Prerequisites: 101 or 134. (SP)
151A-151B. Linear Modeling: Theory and Applications. (4;4) Three hours of lecture and two hours of laboratory per week. A coordinated treatment of linear and generalized linear models and their application. Linear regression, analysis of variance and covariance, random effects, design and analysis of experiments, quality improvement, log-linear models for discrete multivariate data, model selection, robustness, graphical techniques, productive use of computers, in-depth case studies. Prerequisites: 102 or 135. (F,SP)
152. Sampling Surveys. (4) Three hours of lecture and two hours of laboratory per week. Theory and practice of sampling from finite populations. Simple random, stratified, cluster, and double sampling. Sampling and unequal probabilities. Properties of various estimators including ratio, regression, and difference estimators. Error estimation for complex samples. Prerequisites: 101 or 131A or 134. (F)
153. Introduction to Time Series. (4) Three hours of lecture and two hours of laboratory per week. An introduction to time series analysis in the time domain and spectral domain. Topics will include: estimation of trends and seasonal effects, autoregressive moving average models, forecasting, indicators, harmonic analysis, spectra. Prerequisites: 101 or 134 or consent of instructor. (SP)
155. Game Theory. (3) Three hours of lecture per week. General theory of zero-sum, two-person games, including games in extensive form and continuous games, and illustrated by detailed study of examples. Prerequisites: Two years of calculus. (F)
156. Statistical Inference. (4) Three hours of lecture per week. Fundamental concepts of parametric inference such as sufficiency, inference based on likelihood exponential family models, the Bayesian formulation and large sample approximations; fundamental aspects of nonparametric inference such as rank, permutation and goodness of fit tests and estimation of density functions and regression functions. The selection of topics may vary from year to year. Prerequisites: Math 50A-50B; Statistics 102 or 135. (F)
157. Seminar on Topics in Probability and Statistics. (3) Three hours of seminar per week. Substantial student participation required. The topics to be covered each semester that the course may be offered will be announced by the middle of the preceding semester, see departmental bulletins. Prerequisites: Math 50A-50B and consent of instructor.
200A-200B. Introduction to Probability and Statistics at an Advanced Level. (4;4) Three hours of lecture and two hours of laboratory per week. Probability spaces, random variables, distributions in probability and statistics, central limit theorem, Poisson processes, transformations involving random variables, estimation, confidence intervals, hypothesis testing, linear models, large sample theory, categorical models, decision theory. Prerequisites: Two years of calculus and one semester of linear algebra. (F,SP)
205A-205B. Probability Theory. (4;4) Three hours of lecture per week. Measure theory concepts needed for probability. Expectation, distributions. Laws of large numbers and central limit theorems for independent random variables. Characteristic function methods. Conditional expectations; martingales and theory convergence. Markov chains. Stationary processes. Prerequisites: Some knowledge of real analysis and metric spaces, including compactness, Riemann integral. Knowledge of Lebesgue integral and/or elementary probability is helpful, but not essential, given otherwise strong mathematical background. (F,SP)
206A-206B. Stochastic Processes. (3;3) The content of this course changes from year to year. Course topics will be selected from: the general theory of processes, sample function properties, weak convergence, Brownian motion, diffusions, Levy processes, Markov processes, martingales, Gaussian processes and further topics. Course may be repeated for credit with different instructor. (F,SP)
210A-210B. Theoretical Statistics. (4;4) Three hours of lecture per week. A survey of mathematical statistics: in particular both small and large sample theorems of hypothesis testing, point estimation, and confidence intervals with applications to topics such as exponential families, univariate and multivariate linear models and nonparametric inference. Prerequisites: A year of upper division probability and statistics. A course in linear algebra. (F,SP)
212A-212B. Topics in Theoretical Statistics. (3;3) Three hours of lecture per week. This course introduces the student to topics of current research interest in theoretical statistics. Typical topics, which change from year to year, include the following: parametric, semiparametric and nonparametric modeling; time series and survival analysis; model selection; empirical and point processes; asymptotic behavior of bootstrap, stochastic search and Monte Carlo integration; convergence of experiments; minimum distance methods. Course may be repeated for credit with different instructor. Prerequisites: 210 or 205 and 215. (F,SP)
215A-215B. Statistical Models: Theory and Application. (4;4) Three hours of lecture and two hours of laboratory per week. The techniques of applied statistics. Data types and structures. Model formulation, fitting and validation. The principal models. Planning and design. Difficulties that arise. Usage of statistical computer packages. Presentation of conclusions. (F,SP)
230A-230B. Linear Models. (4;4) Three hours of lecture and two hours of laboratory per week. Theory of least squares estimation, interval estimation, and tests under the general linear fixed effects model with normally distributed errors. Large sample theory for non-normal linear models. Two and higher way layouts, residual analysis. Effects of departures from the underlying assumptions. Robust alternatives to least squares. Prerequisites: Matrix algebra, a year of calculus, two semesters of upper division or graduate probability and statistics. (F)
232. Experimental Design. (4) Three hours of lecture and two hours of laboratory per week. Randomization, blocking, factorial design, confounding, fractional replication, response surface methodology, optimal design.. Applications. Prerequisites: 200B or equivalent. (SP)
235. Large Sample Theory for Applied Statistics. (3) Two hours of lecture and one hour of laboratory per week. An introduction, with the use of advanced mathematics, to asymptotics. Emphasis is on intuitive understanding rather than proofs. Topics include: Limits, order comparisons, convergence in probability and in law, with applications to: approximate variances, normal and other approximations to distributions, sample size determination, variance stabilizing transformations. There will be particular emphasis on robustness and asymptotic efficiency. Prerequisites: Calculus (at least one year, preferably three semesters) one year of probability and statistics at the undergraduate level.
236. Analysis of Discrete Observations. (4) Three hours of lecture and two hours of laboratory per week. Discrete stochastic models, generating functions, birth-death processes. Contingency tables: sources, models, sampling schemes, analysis, exact tests. Linear, log linear, logistics models. Search for models. Power. Chi-square. Quantal response; probit, logit. Asymptotics. Cluster analysis. Prerequisites: 102, or 200B. (F,SP)
238 Bayesian Statistics (4) Three hours of lecture and two hours of laboratory per week. Bayesian methods: conditional probability, one-parameter and multiparameter models, hierarchical models, predictive checking and sensitivity analysis, linear and generalized linear models, mixtures, time series, spatial models. Simulation of probability distributions. Experimental design. Case studies of applied modeling. Bayes theory; asymptotics, decision theory, randomization. The selection of topics may vary from year to year. Prerequisites: Calculus, linear algebra, basic probability and statistics. (F,SP)
240. Nonparametric and Robust Methods. (4) Three hours of lecture and two hours of laboratory per week. Standard nonparametric test and confidence intervals for continuous and categorical data; nonparametric estimation of quantiles; robust estimation of location and scale parameters. Efficiency comparison with the classical procedures. Prerequisites: A year of upper division probability and statistics. (F)
242A-242B. Analysis of Multidimensional Data. (4;4) Three hours of lecture and two hours of laboratory per week. Graphical exploration and representation of multivariate data. Model based and model free dimensionality reduction. Analysis of variance, multiple regression, and discrimination methods. Variable selection and transformation techniques. Model fitting and checking. Robustness. Computational aspects. Prerequisites: A graduate course in statistics. (F,SP)
243. Introduction to Statistical Computing. (4) Three hours of lecture and two hours of laboratory per week. The structure and use of statistical languages and packages. Use of graphical displays in data analysis. Statistical data base management. Course may be repeated for credit. Prerequisites: Graduate standing (F)
244. Statistical Computing. (4) Three hours of lecture and two hours of laboratory per week. Algorithms in statistical computing: random number generation, generating other distributions, random sampling and permutations. Matrix computations in linear models. Non-linear optimization with applications to statistical procedures. Other topics of current interest, such as issues of efficiency, and use of graphics. Prerequisites: Knowledge of a higher level of programming language. (SP)
248. Analysis of Time Series. (4) Three hours of lecture and two hours of laboratory per week. Frequency-based techniques of time series analysis, spectral theory, linear filters, estimation of spectra, estimation of transfer functions, design, system identification, vector-valued stationary processes, model building. Prerequisites: 102 or equivalent. (F)
250. Applied Stochastic Processes. (3) Three hours of lecture per week. Various aspects of applied stochastic processes. Offered according to student demand and faculty availability. Course may be repeated for credit. (F)
260. Topics in Probability and Statistics. (3) Three hours of lecture per week. Special topics in probability and statistics offered according to student demand and faculty availability. Course may be repeated for credit. (F,SP)
261 Quantitative/ Statistical Research Methods in Social Sciences. (3) Two hours of lecture per week. Selected topics in quantitative/statistical methods of research in the social sciences and particularly in sociology. Possible topics include analysis of qualitative/categorical data; loglinear models and latent-structure analysis; the analysis of cross-classified data having ordered and un-ordered categories; measures, models, and graphical displays in the analysis of cross-classified data; correspondence analysis, association analysis, and related methods of data analysis. Also listed as Sociology 271D and Interdepartmental Studies 224. Prerequisites: Consent of Instructor.
272. Statistical Consulting. (3) Two hours of class per week and individual meetings as necessary. Must be taken on a satisfactory/unsatisfactory basis. To be taken concurrently with service as a consultant in the department's drop-in consulting service. Participants will work on problems arising in the service and will discuss general ways of handling such problems. There will be working sessions with researchers in substantive fields and occasional lectures on consulting. Course may be repeated for credit. Prerequisites: Some course work in applied statistics and permission of instructor. (F,SP)
278B. Statistical Research Seminar. (1-4) Two or more hours of seminar per week. Special topics, by means of lectures and informational conferences. Course may be repeated for credit. (F,SP)
298. Directed Study for Graduate Students. (1-12) Special tutorial or seminar on selected topics. Course may be repeated for credit. Prerequisites: Consent of instructor. (F,SP)
299. Individual Study Leading to Higher Degrees. (2-12) Course may be repeated for credit. (F,SP)
601. Individual Study for Master's Candidates. (1-8) By appointment. Must be taken on a satisfactory/unsatisfactory basis. Individual study in consultation with graduate adviser, intended to provide an opportunity for qualified students to prepare themselves for the master's comprehensive examinations. Units may not be used to meet either unit or residence requirement for a master's degree. Course may be repeated for credit for a maximum of 16 units. (F,SP)
602. Individual Study for Doctoral Candidates. (1-8) Course does not satisfy unit of residence requirements for doctoral degree. Must be taken on a satisfactory/unsatisfactory basis. Individual study in consultation with the graduate adviser, intended to provide an opportunity for qualified students to prepare themselves for certain examinations required of candidates for the Ph.D. degree. Course may be repeated for credit for a maximum of 16 units. Prerequisites: One year of full-time graduate study and permission of the graduate adviser. (F,SP)
300. Professional Preparation: Teaching of Probability and Statistics. (2-4) One to two hours of lecture and two to four hours of laboratory per week. Must be taken on a satisfactory/unsatisfactory basis. Discussion, problem review and development, guidance of laboratory classes, course development, supervised practice teaching. Course may be repeated for credit. Prerequisites: Graduate standing and appointment as a graduate student instructor. (F,SP)
Last Modified: Sep 14, 1995