STATS 42Q:
Undergraduate Admissions to Selective Universities - a Statistical Perspective
The goal is the building of a statistical model, based on applicant data, for predicting admission to selective universities. The model will consider factors such as gender, ethnicity, legacy status, public-private schooling, test scores, effects of early action, and athletics. Common misconceptions and statistical pitfalls are investigated. The applicant data are not those associated with any specific university.
Terms: Aut
| Units: 2
STATS 50:
Mathematics of Sports (MCS 100)
The use of mathematics, statistics, and probability in the analysis of sports performance, sports records, and strategy. Topics include mathematical analysis of the physics of sports and the determinations of optimal strategies. New diagnostic statistics and strategies for each sport. Corequisite: STATS 116.
| Units: 3
| UG Reqs: GER:DB-Math
STATS 60:
Introduction to Statistical Methods: Precalculus (PSYCH 10, STATS 160)
Techniques for organizing data, computing, and interpreting measures of central tendency, variability, and association. Estimation, confidence intervals, tests of hypotheses, t-tests, correlation, and regression. Possible topics: analysis of variance and chi-square tests, computer statistical packages.
Terms: Aut, Win, Spr, Sum
| Units: 5
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR
STATS 110:
Statistical Methods in Engineering and the Physical Sciences
Introduction to statistics for engineers and physical scientists. Topics: descriptive statistics, probability, interval estimation, tests of hypotheses, nonparametric methods, linear regression, analysis of variance, elementary experimental design. Prerequisite: one year of calculus.
Terms: Aut, Sum
| Units: 4-5
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR
STATS 116:
Theory of Probability
Probability spaces as models for phenomena with statistical regularity. Discrete spaces (binomial, hypergeometric, Poisson). Continuous spaces (normal, exponential) and densities. Random variables, expectation, independence, conditional probability. Introduction to the laws of large numbers and central limit theorem. Prerequisites: MATH 52 and familiarity with infinite series, or equivalent.
Terms: Aut, Spr, Sum
| Units: 3-5
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR
STATS 141:
Biostatistics (BIO 141)
Introductory statistical methods for biological data: describing data (numerical and graphical summaries); introduction to probability; and statistical inference (hypothesis tests and confidence intervals). Intermediate statistical methods: comparing groups (analysis of variance); analyzing associations (linear and logistic regression); and methods for categorical data (contingency tables and odds ratio). Course content integrated with statistical computing in R.
Terms: Aut, Win
| Units: 4-5
| UG Reqs: GER:DB-Math, WAY-AQR
STATS 160:
Introduction to Statistical Methods: Precalculus (PSYCH 10, STATS 60)
Techniques for organizing data, computing, and interpreting measures of central tendency, variability, and association. Estimation, confidence intervals, tests of hypotheses, t-tests, correlation, and regression. Possible topics: analysis of variance and chi-square tests, computer statistical packages.
Terms: Aut, Win, Spr, Sum
| Units: 5
STATS 166:
Computational Biology (BIOMEDIN 366, STATS 366)
Course is designed to introduce students from the mathematical, physical and engineering sciences to selected current issues in computational biology and bioinformatics. Topics: principles of gene expression measurement by microarrays and sequencing, methods to measure locations of protein-DNA interaction, the application of these techniques in the study of gene regulation, approaches to the mapping of genes by association studies. Emphasis is on the statistical and computational issues in these studies. Assignments: weekly reading of papers and a final project.
Terms: Spr
| Units: 2-3
STATS 167:
Probability: Ten Great Ideas About Chance (PHIL 166, PHIL 266, STATS 267)
Foundational approaches to thinking about chance in matters such as gambling, the law, and everyday affairs. Topics include: chance and decisions; the mathematics of chance; frequencies, symmetry, and chance; Bayes great idea; chance and psychology; misuses of chance; and harnessing chance. Emphasis is on the philosophical underpinnings and problems. Prerequisite: exposure to probability or a first course in statistics at the level of STATS 60 or 116.
Last offered: Spring 2010
| Units: 4
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR
STATS 191:
Introduction to Applied Statistics
Statistical tools for modern data analysis. Topics include regression and prediction, elements of the analysis of variance, bootstrap, and cross-validation. Emphasis is on conceptual rather than theoretical understanding. Applications to social/biological sciences. Student assignments/projects require use of the software package R. Recommended: 60, 110, or 141.
Terms: Win
| Units: 3-4
| UG Reqs: GER:DB-Math, WAY-AQR
STATS 198:
Practical Training
For students majoring in Mathematical and Computational Science only. Students obtain employment in a relevant industrial or research activity to enhance their professional experience.
Terms: Sum
| Units: 1-3
| Repeatable
2 times
(up to 6 units total)
STATS 199:
Independent Study
For undergraduates.
Terms: Aut, Win, Spr, Sum
| Units: 1-15
| Repeatable
for credit
Instructors: ;
Candes, E. (PI);
Cover, T. (PI);
Dembo, A. (PI);
Diaconis, P. (PI);
Donoho, D. (PI);
Efron, B. (PI);
Friedman, J. (PI);
Hastie, T. (PI);
Holmes, S. (PI);
Johnstone, I. (PI);
Lai, T. (PI);
Montanari, A. (PI);
Olkin, I. (PI);
Olshen, R. (PI);
Owen, A. (PI);
Rajaratnam, B. (PI);
Rogosa, D. (PI);
Romano, J. (PI);
Siegmund, D. (PI);
Switzer, P. (PI);
Taylor, J. (PI);
Tibshirani, R. (PI);
Walther, G. (PI);
Wong, W. (PI);
Zhang, N. (PI)
STATS 200:
Introduction to Statistical Inference
Modern statistical concepts and procedures derived from a mathematical framework. Statistical inference, decision theory; point and interval estimation, tests of hypotheses; Neyman-Pearson theory. Bayesian analysis; maximum likelihood, large sample theory. Prerequisite: 116.
Terms: Win, Sum
| Units: 3
STATS 202:
Data Mining and Analysis
Data mining is used to discover patterns and relationships in data. Emphasis is on large complex data sets such as those in very large databases or through web mining. Topics: decision trees, association rules, clustering, case based methods, and data visualization.
Terms: Aut, Sum
| Units: 3
STATS 203:
Introduction to Regression Models and Analysis of Variance
Modeling and interpretation of observational and experimental data using linear and nonlinear regression methods. Model building and selection methods. Multivariable analysis. Fixed and random effects models. Experimental design. Pre- or corequisite: 200.
Terms: Win
| Units: 3
STATS 206:
Applied Multivariate Analysis
Introduction to the statistical analysis of several quantitative measurements on each observational unit. Emphasis is on concepts, computer-intensive methods. Examples from economics, education, geology, psychology. Topics: multiple regression, multivariate analysis of variance, principal components, factor analysis, canonical correlations, multidimensional scaling, clustering. Pre- or corequisite: 200.
Last offered: Autumn 2009
| Units: 3
STATS 207:
Introduction to Time Series Analysis
Time series models used in economics and engineering. Trend fitting, autoregressive and moving average models and spectral analysis, Kalman filtering, and state-space models. Seasonality, transformations, and introduction to financial time series. Prerequisite: basic course in Statistics at the level of 200.
Terms: Spr
| Units: 3
STATS 208:
Introduction to the Bootstrap
The bootstrap is a computer-based method for assigning measures of accuracy to statistical estimates. By substituting computation in place of mathematical formulas, it permits the statistical analysis of complicated estimators. Topics: nonparametric assessment of standard errors, biases, and confidence intervals; related resampling methods including the jackknife, cross-validation, and permutation tests. Theory and applications. Prerequisite: course in statistics or probability.
Terms: Win
| Units: 3
STATS 209:
Understanding Statistical Models and their Social Science Applications (EDUC 260X, HRP 239)
Critical examination of statistical methods in social science applications, especially for cause and effect determinations. Topics: path analysis, multilevel models, matching and propensity score methods, analysis of covariance, instrumental variables, compliance, longitudinal data, mediating and moderating variables. See http://www-stat.stanford.edu/~rag/stat209. Prerequisite: intermediate-level statistical methods
Terms: Win
| Units: 3
STATS 211:
Meta-research: Appraising Research Findings, Bias, and Meta-analysis (HRP 206, MED 206)
Open to graduate, medical, and undergraduate students. Appraisal of the quality and credibility of research findings; evaluation of sources of bias. Meta-analysis as a quantitative (statistical) method for combining results of independent studies. Examples from medicine, epidemiology, genomics, ecology, social/behavioral sciences, education. Collaborative analyses. Project involving generation of a meta-research project or reworking and evaluation of an existing published meta-analysis. Prerequisite: knowledge of basic statistics.
Terms: Win
| Units: 3
STATS 212:
Applied Statistics with SAS
Data analysis and implementation of statistical tools in SAS. Topics: reading in and describing data, categorical data, dates and longitudinal data, correlation and regression, nonparametric comparisons, ANOVA, multiple regression, multivariate data analysis, using arrays and macros in SAS. Prerequisite: statistical techniques at the level of STATS 191 or 203; knowledge of SAS not required.
Terms: Sum
| Units: 3
STATS 215:
Statistical Models in Biology
Poisson and renewal processes, Markov chains in discrete and continuous time, branching processes, diffusion. Applications to models of nucleotide evolution, recombination, the Wright-Fisher process, coalescence, genetic mapping, sequence analysis. Theoretical material approximately the same as in STATS 217, but emphasis is on examples drawn from applications in biology, especially genetics. Prerequisite: 116 or equivalent.
Terms: Aut
| Units: 3
STATS 217:
Introduction to Stochastic Processes
Discrete and continuous time Markov chains, poisson processes, random walks, branching processes, first passage times, recurrence and transience, stationary distributions. Non-Statistics masters students may want to consider taking STATS 215 instead. Prerequisite: STATS 116 or consent of instructor.
Terms: Win, Sum
| Units: 3
STATS 218:
Introduction to Stochastic Processes
Renewal theory, Brownian motion, Gaussian processes, second order processes, martingales.
Terms: Spr, Sum
| Units: 3
STATS 219:
Stochastic Processes (MATH 136)
Introduction to measure theory, Lp spaces and Hilbert spaces. Random variables, expectation, conditional expectation, conditional distribution. Uniform integrability, almost sure and Lp convergence. Stochastic processes: definition, stationarity, sample path continuity. Examples: random walk, Markov chains, Gaussian processes, Poisson processes, Martingales. Construction and basic properties of Brownian motion. Prerequisite: STATS 116 or MATH 151 or equivalent. Recommended: MATH 115 or equivalent.
Terms: Aut
| Units: 3
STATS 237:
Time Series Modeling and Forecasting
Box-Jenkins and Bayesian approaches. State-space and change-point models. Application to revenue prediction, forecasting product demand, and other real world problems. Development and assessment of models and forecasts in practical applications. Hands-on experience with real data.
Last offered: Summer 2010
| Units: 3
STATS 240:
Statistical Methods in Finance
(SCPD students register for 240P.) Regression analysis and applications to investment models. Principal components and multivariate analysis. Likelihood inference and Bayesian methods. Financial time series. Estimation and modeling of volatilities. Statistical methods for portfolio management. Prerequisite: STATS 200 or equivalent.
Terms: Aut
| Units: 3-4
STATS 240P:
Statistical Methods in Finance
For SCPD students; see 240.
Terms: Aut
| Units: 3
STATS 241:
Financial Modeling Methodology and Applications
(SCPD students register for 241P.) Substantive and empirical modeling approaches. Statistical trading strategies and their evaluation. Nonparametric regression. Advanced time series modeling and forecasting. Options and interest rate markets. Credit markets and default risk modeling. Prerequisite: 240 or equivalent.
Terms: Win
| Units: 3-4
STATS 241P:
Financial Modeling Methodology and Applications
For SCPD students; see 241.
Terms: Win
| Units: 3
STATS 242:
Algorithmic Trading and Quantitative Strategies
An introduction to financial trading strategies based on methods of statistical arbitrage that can be automated. Methodologies related to high frequency data and stylized facts on asset returns; models of order book dynamics and order placement, dynamic trade planning with feedback; momentum strategies, pairs trading. Emphasis on developing and implementing models that reflect the market and behavioral patterns. Prerequisite: STATS 240 or equivalent.
Terms: Sum
| Units: 3
STATS 243:
Statistical Models and Methods for Risk Management and Surveillance
(SCPD students register for 243P.) Banking and bank regulation. Market risk and credit risk, asset and liability management. Logistic regression, generalized linear models and generalized mixed models. Censored data and survival analysis, loan prepayment and default as competing risks. Back testing, stress testing and Monte Carlo methods. Risk surveillance, early warning and adaptive risk control methodologies. Prerequisite: STATS 240 or equivalent.
| Units: 3-4
STATS 250:
Mathematical Finance (MATH 238)
Stochastic models of financial markets. Forward and futures contracts. European options and equivalent martingale measures. Hedging strategies and management of risk. Term structure models and interest rate derivatives. Optimal stopping and American options. Corequisites: MATH 236 and 227 or equivalent.
Terms: Win
| Units: 3
STATS 253:
Spatial Statistics (STATS 352)
Statistical descriptions of spatial variability, spatial random functions, grid models, spatial partitions, spatial sampling, linear and nonlinear interpolation and smoothing with error estimation, Bayes methods and pattern simulation from posterior distributions, multivariate spatial statistics, spatial classification, nonstationary spatial statistics, space-time statistics and estimation of time trends from monitoring data, spatial point patterns, models of attraction and repulsion. Applications to earth and environmental sciences, meteorology, astronomy, remote-sensing, ecology, materials.
Last offered: Spring 2009
| Units: 3
STATS 260A:
Workshop in Biostatistics (HRP 260A)
Applications of statistical techniques to current problems in medical science.
Terms: Aut
| Units: 1-2
| Repeatable
for credit
STATS 260B:
Workshop in Biostatistics (HRP 260B)
Applications of statistical techniques to current problems in medical science.
Terms: Win
| Units: 1-2
| Repeatable
for credit
STATS 260C:
Workshop in Biostatistics (HRP 260C)
Applications of statistical techniques to current problems in medical science.
Terms: Spr
| Units: 1-2
| Repeatable
for credit
STATS 261:
Intermediate Biostatistics: Analysis of Discrete Data (BIOMEDIN 233, HRP 261)
Methods for analyzing data from case-control and cross-sectional studies: the 2x2 table, chi-square test, Fisher's exact test, odds ratios, Mantel-Haenzel methods, stratification, tests for matched data, logistic regression, conditional logistic regression. Emphasis is on data analysis in SAS. Special topics: cross-fold validation and bootstrap inference.
Terms: Win
| Units: 3
STATS 262:
Intermediate Biostatistics: Regression, Prediction, Survival Analysis (HRP 262)
Methods for analyzing longitudinal data. Topics include Kaplan-Meier methods, Cox regression, hazard ratios, time-dependent variables, longitudinal data structures, profile plots, missing data, modeling change, MANOVA, repeated-measures ANOVA, GEE, and mixed models. Emphasis is on practical applications. Prerequisites: basic ANOVA and linear regression.
Terms: Spr
| Units: 3
STATS 267:
Probability: Ten Great Ideas About Chance (PHIL 166, PHIL 266, STATS 167)
Foundational approaches to thinking about chance in matters such as gambling, the law, and everyday affairs. Topics include: chance and decisions; the mathematics of chance; frequencies, symmetry, and chance; Bayes great idea; chance and psychology; misuses of chance; and harnessing chance. Emphasis is on the philosophical underpinnings and problems. Prerequisite: exposure to probability or a first course in statistics at the level of STATS 60 or 116.
Last offered: Spring 2010
| Units: 4
STATS 290:
Paradigms for Computing with Data
For Statistics graduate students and others whose research involves data analysis and development of associated computational software. Programming and computing techniques to support projects in data analysis and related research. Prerequisites: CS 106, and STATS 110 or 141, or equivalent background.
Terms: Win
| Units: 3
STATS 297:
Practical Training
For students in the M.S. program in Financial Mathematics only. Students obtain employment in a relevant industrial or research activity to enhance their professional experience. May be repeated for credit once. Prerequisite: consent of adviser.
Terms: Aut, Win, Spr, Sum
| Units: 1-3
| Repeatable
2 times
(up to 6 units total)
STATS 298:
Industrial Research for Statisticians
Masters-level research as in 299, but must be conducted for an off-campus employer. Final report required. Prerequisite: enrollment in Statistics M.S. or Ph.D. program, prior to candidacy.
Terms: Aut, Win, Spr, Sum
| Units: 1-9
| Repeatable
2 times
(up to 18 units total)
Instructors: ;
Candes, E. (PI);
Cover, T. (PI);
Dembo, A. (PI);
Diaconis, P. (PI);
Donoho, D. (PI);
Efron, B. (PI);
Friedman, J. (PI);
Hastie, T. (PI);
Holmes, S. (PI);
Johnstone, I. (PI);
Lai, T. (PI);
Montanari, A. (PI);
Olkin, I. (PI);
Olshen, R. (PI);
Owen, A. (PI);
Rajaratnam, B. (PI);
Rogosa, D. (PI);
Romano, J. (PI);
Siegmund, D. (PI);
Switzer, P. (PI);
Taylor, J. (PI);
Tibshirani, R. (PI);
Walther, G. (PI);
Wong, W. (PI);
Zhang, N. (PI)
STATS 299:
Independent Study
For Statistics M.S. students only. Reading or research program under the supervision of a Statistics faculty member. May be repeated for credit.
Terms: Aut, Win, Spr, Sum
| Units: 1-10
| Repeatable
for credit
Instructors: ;
Candes, E. (PI);
Cover, T. (PI);
Dembo, A. (PI);
Diaconis, P. (PI);
Donoho, D. (PI);
Efron, B. (PI);
Friedman, J. (PI);
Hastie, T. (PI);
Holmes, S. (PI);
Johnstone, I. (PI);
Lai, T. (PI);
Montanari, A. (PI);
Olkin, I. (PI);
Olshen, R. (PI);
Owen, A. (PI);
Rajaratnam, B. (PI);
Rogosa, D. (PI);
Romano, J. (PI);
Ross, K. (PI);
Siegmund, D. (PI);
Switzer, P. (PI);
Taylor, J. (PI);
Tibshirani, R. (PI);
Walther, G. (PI);
Wong, W. (PI);
Zhang, N. (PI)
STATS 300:
Advanced Topics in Statistics
May be repeated for credit.
Terms: Sum
| Units: 3
| Repeatable
for credit
STATS 300A:
Theory of Statistics
Elementary decision theory; loss and risk functions, Bayes estimation; UMVU estimator, minimax estimators, shrinkage estimators. Hypothesis testing and confidence intervals: Neyman-Pearson theory; UMP tests and uniformly most accurate confidence intervals; use of unbiasedness and invariance to eliminate nuisance parameters. Large sample theory: basic convergence concepts; robustness; efficiency; contiguity, locally asymptotically normal experiments; convolution theorem; asymptotically UMP and maximin tests. Asymptotic theory of likelihood ratio and score tests. Rank permutation and randomization tests; jackknife, bootstrap, subsampling and other resampling methods. Further topics: sequential analysis, optimal experimental design, empirical processes with applications to statistics, Edgeworth expansions, density estimation, time series.
Terms: Aut
| Units: 2-4
STATS 300B:
Theory of Statistics
Elementary decision theory; loss and risk functions, Bayes estimation; UMVU estimator, minimax estimators, shrinkage estimators. Hypothesis testing and confidence intervals: Neyman-Pearson theory; UMP tests and uniformly most accurate confidence intervals; use of unbiasedness and invariance to eliminate nuisance parameters. Large sample theory: basic convergence concepts; robustness; efficiency; contiguity, locally asymptotically normal experiments; convolution theorem; asymptotically UMP and maximin tests. Asymptotic theory of likelihood ratio and score tests. Rank permutation and randomization tests; jackknife, bootstrap, subsampling and other resampling methods. Further topics: sequential analysis, optimal experimental design, empirical processes with applications to statistics, Edgeworth expansions, density estimation, time series.
Terms: Win
| Units: 2-4
STATS 300C:
Theory of Statistics
Decision theory formulation of statistical problems. Minimax, admissible procedures. Complete class theorems ("all" minimax or admissible procedures are "Bayes"), Bayes procedures, conjugate priors, hierarchical models. Bayesian non parametrics: diaichlet, tail free, polya trees, bayesian sieves. Inconsistency of bayes rules.
Terms: Spr
| Units: 2-4
STATS 302:
Qualifying Exams Workshop
Prepares Statistics Ph.D. students for the qualifying exams by reviewing relevantnncourse topics and problem solving strategies.
Terms: Sum
| Units: 3
STATS 305:
Introduction to Statistical Modeling
Review of univariate regression. Multiple regression. Geometry, subspaces, orthogonality, projections, normal equations, rank deficiency, estimable functions and Gauss-Markov theorem. Computation via QR decomposition, Gramm-Schmidt orthogonalization and the SVD. Interpreting coefficients, collinearity, graphical displays. Fits and the Hat matrix, leverage & influence, diagnostics, weighted least squares and resistance. Model selection, Cp/Aic and crossvalidation, stepwise, lasso. Basis expansions, splines. Multivariate normal distribution theory. ANOVA: Sources of measurements, fixed and random effects, randomization. Emphasis on problem sets involving substantive computations with data sets. Prerequisites: consent of instructor, 116, 200, applied statistics course, CS 106A, MATH 114.
Terms: Aut
| Units: 2-4
STATS 306A:
Methods for Applied Statistics
Regression modeling extended to categorical data. Logistic regression. Loglinear models. Generalized linear models. Discriminant analysis. Categorical data models from information retrieval and Internet modeling. Prerequisite: 305 or equivalent.
Terms: Win
| Units: 2-4
STATS 306B:
Methods for Applied Statistics: Unsupervised Learning
Unsupervised learning techniques in statistics, machine learning, and data mining.
Terms: Spr
| Units: 2-4
STATS 310A:
Theory of Probability (MATH 230A)
Mathematical tools: asymptotics, metric spaces; measure and integration; Lp spaces; some Hilbert spaces theory. Probability: independence, Borel-Cantelli lemmas, almost sure and Lp convergence, weak and strong laws of large numbers. Weak convergence and characteristic functions; central limit theorems; local limit theorems; Poisson convergence. Prerequisites: 116, MATH 171.
Terms: Aut
| Units: 2-4
STATS 310B:
Theory of Probability (MATH 230B)
Stopping times, 0-1 laws, Kolmogorov consistency theorem. Uniform integrability. Radon-Nikodym theorem, branching processes, conditional expectation, discrete time martingales. Exchangeability. Large deviations. Laws of the iterated logarithm. Birkhoff's and Kingman's ergodic theorems. Recurrence, entropy. Prerequisite: 310A or MATH 230A.
Terms: Win
| Units: 2-4
STATS 310C:
Theory of Probability (MATH 230C)
Continuous time stochastic processes: martingales, Brownian motion, stationary independent increments, Markov jump processes and Gaussian processes. Invariance principle, random walks, LIL and functional CLT. Markov and strong Markov property. Infinitely divisible laws. Some ergodic theory. Prerequisite: 310B or MATH 230B.
Terms: Spr
| Units: 2-4
STATS 315A:
Modern Applied Statistics: Learning
Overview of supervised learning. Linear regression and related methods. Model selection, least angle regression and the lasso, stepwise methods. Classification. Linear discriminant analysis, logistic regression, and support vector machines (SVMs). Basis expansions, splines and regularization. Kernel methods. Generalized additive models. Kernel smoothing. Gaussian mixtures and the EM algorithm. Model assessment and selection: crossvalidation and the bootstrap. Pathwise coordinate descent. Sparse graphical models. Prerequisites: STATS 305, 306A,B or consent of instructor.
Terms: Win
| Units: 2-3
STATS 315B:
Modern Applied Statistics: Data Mining
Two-part sequence. New techniques for predictive and descriptive learning using ideas that bridge gaps among statistics, computer science, and artificial intelligence. Emphasis is on statistical aspects of their application and integration with more standard statistical methodology. Predictive learning refers to estimating models from data with the goal of predicting future outcomes, in particular, regression and classification models. Descriptive learning is used to discover general patterns and relationships in data without a predictive goal, viewed from a statistical perspective as computer automated exploratory analysis of large complex data sets.
Terms: Spr
| Units: 2-3
STATS 318:
Modern Markov Chains
Tools for understanding Markov chains as they arise in applications. Random walk on graphs, reversible Markov chains, Metropolis algorithm, Gibbs sampler, hybrid Monte Carlo, auxiliary variables, hit and run, Swedson-Wong algorithms, geometric theory, Poincare-Nash-Cheger-Log-Sobolov inequalities. Comparison techniques, coupling, stationary times, Harris recurrence, central limit theorems, and large deviations.
Terms: Aut
| Units: 2-3
STATS 319:
Literature of Statistics
Literature study of topics in statistics and probability culminating in oral and written reports. May be repeated for credit.
Terms: Aut, Win, Spr
| Units: 1-3
| Repeatable
for credit
STATS 320:
Heterogeneous Data with Kernels
Mathematical and computational methods necessary to understanding analysis of heterogeneous data using generalized inner products and Kernels. For areas that need to integrate data from various sources, biology, environmental and chemical engineering, molecular biology, bioinformatics. Topics: Distances, inner products and duality. Multivariate projections. Complex heterogeneous data structures (networks, trees, categorical as well as multivariate continuous data). Canonical correlation analysis, canonical correspondence analysis. Kernel methods in Statistics. Representer theorem. Kernels on graphs. Kernel versions of standard statistical procedures. Data cubes and tensor methods.
Terms: Spr
| Units: 3
STATS 322:
Function Estimation in White Noise
Gaussian white noise model sequence space form. Hyperrectangles, quadratic convexity, and Pinsker's theorem. Minimax estimation on Lp balls and Besov spaces. Role of wavelets and unconditional bases. Linear and threshold estimators. Oracle inequalities. Optimal recovery and universal thresholding. Stein's unbiased risk estimator and threshold choice. Complexity penalized model selection. Connecting fast wavelet algorithms and theory. Beyond orthogonal bases.
Terms: Aut
| Units: 2-3
STATS 324:
Multivariate Analysis
Classic multivariate statistics: properties of the multivariate normal distribution, determinants, volumes, projections, matrix square roots, the singular value decomposition; Wishart distributions, Hotelling's T-square; principal components, canonical correlations, Fisher's discriminant, the Cauchy projection formula.
| Units: 2-3
STATS 345:
Computational Algorithms for Statistical Genetics (GENE 245)
Computational algorithms for human genetics research. Topics include: permutation, bootstrap, expectation maximization, hidden Markov model, and Markov chain Monte Carlo. Rationales and techniques illustrated with existing implementations commonly used in population genetics research, disease association studies, and genomics analysis. Prerequisite: GENE 244 or consent of instructor.
Last offered: Spring 2009
| Units: 2-3
STATS 362:
Monte Carlo
Random numbers and vectors: inversion, acceptance-rejection, copulas. Variance reduction: antithetics, stratification, control variates, importance sampling. MCMC: Markov chains, detailed balance, Metropolis-Hastings, random walk Metropolis,nnindependence sampler, Gibbs sampling, slice sampler, hybrids of Gibbs and Metropolis, tempering. Sequential Monte Carlo. Quasi-Monte Carlo. Randomized quasi-Monte Carlo. Examples, problems and motivation from Bayesian statistics,nnmachine learning, computational finance and graphics.
Terms: Aut
| Units: 2-3
STATS 366:
Computational Biology (BIOMEDIN 366, STATS 166)
Course is designed to introduce students from the mathematical, physical and engineering sciences to selected current issues in computational biology and bioinformatics. Topics: principles of gene expression measurement by microarrays and sequencing, methods to measure locations of protein-DNA interaction, the application of these techniques in the study of gene regulation, approaches to the mapping of genes by association studies. Emphasis is on the statistical and computational issues in these studies. Assignments: weekly reading of papers and a final project.
Terms: Spr
| Units: 2-3
STATS 367:
Statistical Models in Genetics
Statistical problems in association and linkage analysis of qualitative and quantitative traits in human and experimental populations; sequence alignment and analysis; population genetics/evolution (Wright-Fisher model, Kingman coalescent, models of nucleotide substitution); related computational algorithms. Prerequisites: knowledge of probability through elementary stochastic processes and statistics through likelihood theory.
Terms: Win
| Units: 2-3
STATS 375:
Inference in Graphical Models
Graphical models as a unifying framework for describing the statistical relationships between large sets of variables; computing the marginal distribution of one or a few such variables. Focus is on sparse graphical structures, low-complexity algorithms, and their analysis. Topics include: variational inference; message passing algorithms; belief propagation; generalized belief propagation; survey propagation. Analysis techniques: correlation decay; distributional recursions. Applications from engineering, computer science, and statistics. Prerequisite: EE 278, STATS 116, or CS 228. Recommended: EE 376A or STATS 217.
Terms: Win
| Units: 3
STATS 376A:
Information Theory (EE 376A)
The fundamental ideas of information theory. Entropy and intrinsic randomness. Data compression to the entropy limit. Huffman coding. Arithmetic coding. Channel capacity, the communication limit. Gaussian channels. Kolmogorov complexity. Asymptotic equipartition property. Information theory and Kelly gambling. Applications to communication and data compression. Prerequisite: EE178 or EE278 or STATS 116, or equivalent.
Terms: Win
| Units: 3
STATS 376B:
Information Theory (EE 376B)
Rate distortion theory and Kolmogorov complexity. Information theory and statistics. Method of types. Stein's lemma. AEP. Information capacity of networks. Slepian-Wolf theorem. Optimal investment and information theory. Universal portfolios and universal data compression. Maximum entropy and Burg's theorem. Prerequisite: EE376A.
Terms: Spr
| Units: 3
STATS 390:
Consulting Workshop
Skills required of practicing statistical consultants, including exposure to statistical applications. Students participate as consultants in the department's drop-in consulting service, analyze client data, and prepare formal written reports. Seminar provides supervised experience in short term consulting. May be repeated for credit. Prerequisites: course work in applied statistics or data analysis, and consent of instructor.
Terms: Aut, Win, Spr, Sum
| Units: 1-3
| Repeatable
for credit
STATS 398:
Industrial Research for Statisticians
Doctoral research as in 298, but must be conducted for an off-campus employer. Final report required. May be repeated for credit. Prerequisite: Statistics Ph.D. candidate.
Terms: Aut, Win, Spr, Sum
| Units: 1-9
| Repeatable
for credit
Instructors: ;
Candes, E. (PI);
Cover, T. (PI);
Dembo, A. (PI);
Diaconis, P. (PI);
Donoho, D. (PI);
Efron, B. (PI);
Friedman, J. (PI);
Hastie, T. (PI);
Holmes, S. (PI);
Johnstone, I. (PI);
Lai, T. (PI);
Montanari, A. (PI);
Olkin, I. (PI);
Olshen, R. (PI);
Owen, A. (PI);
Rajaratnam, B. (PI);
Rogosa, D. (PI);
Romano, J. (PI);
Siegmund, D. (PI);
Switzer, P. (PI);
Taylor, J. (PI);
Tibshirani, R. (PI);
Walther, G. (PI);
Wong, W. (PI);
Zhang, N. (PI)
STATS 399:
Research
Research work as distinguished from independent study of nonresearch character listed in 199. May be repeated for credit.
Terms: Aut, Win, Spr, Sum
| Units: 1-10
| Repeatable
for credit
Instructors: ;
Candes, E. (PI);
Cover, T. (PI);
Dembo, A. (PI);
Diaconis, P. (PI);
Donoho, D. (PI);
Efron, B. (PI);
Friedman, J. (PI);
Hastie, T. (PI);
Holmes, S. (PI);
Johnstone, I. (PI);
Lai, T. (PI);
Montanari, A. (PI);
Olkin, I. (PI);
Olshen, R. (PI);
Owen, A. (PI);
Rajaratnam, B. (PI);
Rogosa, D. (PI);
Romano, J. (PI);
Siegmund, D. (PI);
Switzer, P. (PI);
Taylor, J. (PI);
Tibshirani, R. (PI);
Walther, G. (PI);
Wong, W. (PI);
Zhang, N. (PI)
STATS 47N:
Breaking the Code?
Preference to freshmen. Cryptography and its counterpart, cryptanalysis or code breaking. How the earliest cryptanalysts used statistical tools to decrypt messages by uncovering recurring patterns. How such frequency-analysis tools have been used to analyze biblical texts to produce a Bible code, and to detect genes in the human genome. Overview of codes and ciphers. Statistical tools useful for code breaking. Students use simple computer programs to apply these tools to break codes and explore applications to various kinds of data.
| Units: 3
| UG Reqs: GER:DB-Math
Terms: Aut, Win, Spr, Sum
| Units: 0
| Repeatable
for credit
Instructors: ;
Candes, E. (PI);
Cover, T. (PI);
Dembo, A. (PI);
Diaconis, P. (PI);
Donoho, D. (PI);
Efron, B. (PI);
Friedman, J. (PI);
Hastie, T. (PI);
Holmes, S. (PI);
Johnstone, I. (PI);
Lai, T. (PI);
Montanari, A. (PI);
Olkin, I. (PI);
Olshen, R. (PI);
Owen, A. (PI);
Rajaratnam, B. (PI);
Rogosa, D. (PI);
Romano, J. (PI);
Siegmund, D. (PI);
Switzer, P. (PI);
Taylor, J. (PI);
Tibshirani, R. (PI);
Walther, G. (PI);
Wong, W. (PI);
Zhang, N. (PI)
STATS 802:
TGR Dissertation
Terms: Aut, Win, Spr, Sum
| Units: 0
| Repeatable
for credit
Instructors: ;
Candes, E. (PI);
Cover, T. (PI);
Dembo, A. (PI);
Diaconis, P. (PI);
Donoho, D. (PI);
Efron, B. (PI);
Friedman, J. (PI);
Hastie, T. (PI);
Holmes, S. (PI);
Johnstone, I. (PI);
Lai, T. (PI);
Montanari, A. (PI);
Olkin, I. (PI);
Olshen, R. (PI);
Owen, A. (PI);
Rajaratnam, B. (PI);
Rogosa, D. (PI);
Romano, J. (PI);
Siegmund, D. (PI);
Switzer, P. (PI);
Taylor, J. (PI);
Tibshirani, R. (PI);
Walther, G. (PI);
Wong, W. (PI);
Zhang, N. (PI)
STATS 205:
Introduction to Nonparametric Statistics
Nonparametric analogs of the one- and two-sample t-tests and analysis of variance; the sign test, median test, Wilcoxon's tests, and the Kruskal-Wallis and Friedman tests, tests of independence. Nonparametric regression and nonparametric density estimation, modern nonparametric techniques, nonparametric confidence interval estimates.
| Units: 3
STATS 214:
Randomness in the Physical World
Topics include: random numbers, and their generation and application; disordered systems, quenching, and annealing; percolation and fractal structures; universality, the renormalization group, and limit theorems; path integrals, partition functions, and Wiener measure; random matrices; and optical estimation. Prerequisite: introductory course in statistical mechanics or analysis.
| Units: 3
STATS 221:
Introduction to Mathematical Finance
Interest rate and discounted value. Financial derivatives, hedging, and risk management. Stochastic models of financial markets, introduction to Ito calculus and stochastic differential equations. Black-Scholes pricing of European options. Optimal stopping and American options. Prerequisites: MATH 53, STATS 116, or equivalents.
| Units: 3-4
STATS 239A:
Workshop in Quantitative Finance
Topics of current interest.
| Units: 1
| Repeatable
for credit
STATS 239B:
Workshop in Quantitative Finance
Topics of current interest. May be repeated for credit.
| Units: 1
| Repeatable
for credit
STATS 243P:
Statistical Models and Methods for Risk Management and Surveillance
For SCPD students; see 243.
| Units: 3
STATS 270:
A Course in Bayesian Statistics (STATS 370)
Advanced-level Bayesian statistics. Topics: Discussion of the mathematical and theoretical foundation for Bayesian inferential procedures. Examination of the construction of priors and the asymptotic properties of likelihoods and posterior densities. Discussion including but not limited to the case of finite dimensional parameter space. Prerequisite: familiarity with standard probability and multivariate distribution theory.
| Units: 3
STATS 314:
Advanced Statistical Methods
Topic this year is multiple hypothesis testing. The demand for new methodology for the simultaneous testing of many hypotheses as driven by modern applications in genomics, imaging, astronomy, and finance. High dimensionality: how tests of many hypotheses may be considered simultaneously. Classical techniques, and recent developments. Stepwise methods, generalized error rates such as the false discovery rate, and the role of resampling. May be repeated for credit.
| Units: 2-3
| Repeatable
for credit
STATS 316:
Stochastic Processes on Graphs
Local weak convergence, Gibbs measures on trees, cavity method, and replica symmetry breaking. Examples include random k-satisfiability, the assignment problem, spin glasses, and neural networks. Prerequisite: 310A or equivalent.
| Units: 1-3
STATS 317:
Stochastic Processes
Semimartingales, stochastic integration, Ito's formula, Girsanov's theorem. Gaussian and related processes. Stationary/isotropic processes. Integral geometry and geometric probability. Maxima of random fields and applications to spatial statistics and imaging.
| Units: 2-3
STATS 329:
Large-Scale Simultaneous Inference
Estimation, testing, and prediction for microarray-like data. Modern scientific technologies, typified by microarrays and imaging devices, produce inference problems with thousands of parallel cases to consider simultaneously. Topics: empirical Bayes techniques, James-Stein estimation, large-scale simultaneous testing, false discovery rates, local fdr, proper choice of null hypothesis (theoretical, permutation, empirical nulls), power, effects of correlation on tests and estimation accuracy, prediction methods, related sets of cases ("enrichment"), effect size estimation. Theory and methods illustrated on a variety of large-scale data sets.
| Units: 1-3
STATS 330:
An Introduction to Compressed Sensing (CME 362)
Compressed sensing is a new data acquisition theory asserting that onencan design nonadaptive sampling techniques that condense theninformation in a compressible signal into a small amount of data.nThis revelation may change the way engineers think about signalnacquisition. Course covers fundamental theoretical ideas, numericalnmethods in large-scale convex optimization, hardware implementations,nconnections with statistical estimation in high dimensions, andnextensions such as recovery of data matrices from few entries (famousnNetflix Prize).
| Units: 2-3
STATS 338:
Topics in Biostatistics
Data monitoring and interim analysis of clinical trials. Design of Phase I, II, III trials. Survival analysis. Longitudinal data analysis.
| Units: 3
STATS 351A:
An Introduction to Random Matrix Theory (MATH 231A)
Patterns in the eigenvalue distribution of typical large matrices, which also show up in physics (energy distribution in scattering experiments), combinatorics (length of longest increasing subsequence), first passage percolation and number theory (zeros of the zeta function). Classical compact ensembles (random orthogonal matrices). The tools of determinental point processes.
| Units: 3
STATS 352:
Spatial Statistics (STATS 253)
Statistical descriptions of spatial variability, spatial random functions, grid models, spatial partitions, spatial sampling, linear and nonlinear interpolation and smoothing with error estimation, Bayes methods and pattern simulation from posterior distributions, multivariate spatial statistics, spatial classification, nonstationary spatial statistics, space-time statistics and estimation of time trends from monitoring data, spatial point patterns, models of attraction and repulsion. Applications to earth and environmental sciences, meteorology, astronomy, remote-sensing, ecology, materials.
| Units: 3
STATS 370:
A Course in Bayesian Statistics (STATS 270)
Advanced-level Bayesian statistics. Topics: Discussion of the mathematical and theoretical foundation for Bayesian inferential procedures. Examination of the construction of priors and the asymptotic properties of likelihoods and posterior densities. Discussion including but not limited to the case of finite dimensional parameter space. Prerequisite: familiarity with standard probability and multivariate distribution theory.
| Units: 3
