Graduate courses in Statistics

(Same as 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.

5 units, Aut (Thomas, E), Win (Walther, G), Spr (Boik, J), Sum (Staff)

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.

3 units, Win (Romano, J), Sum (Staff)

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, neural networks, association rules, clustering, case based methods, and data visualization.

3 units, Aut (Walther, G)

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.

3 units, Win (Zhang, N)

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.

3 units, Aut (Khalessi, S), Sum (Staff)

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.

3 units, Spr (Holmes, S)

STATS 209. Understanding Statistical Models and their Social Science Applications

(Same as EDUC 260X, HRP 239.) Statistical modeling in experimental and non-experimental settings, including misconceptions in social science applications such as causal models. Text is Statistical Models: Theory and Practice, by David Freedman. See http://www-stat.stanford.edu/~rag/stat209. Prerequisite: intermediate-level statistical methods including multiple regression, logistic regression, and log-linear models.

3 units, Win (Rogosa, D)

STATS 211. Topics in Quantitative Methods: Meta-Analysis

Meta-analysis as a quantitative method for combining the results of independent studies enabling researchers to evaluate available evidence. Examples of meta-analysis in medicine, education, and social and behavioral sciences. Statistical methods include nonparametric methods, contingency tables, regression and analysis of variance, and Bayesian methods. Project involving an existing published meta-analysis. Prerequisite: basic sequence in statistics.

1-3 units, Win (Olkin, I)

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.

3 units, Sum (Staff)

STATS 214. Randomness in the Physical World

(Same as APPPHYS 214.) 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.

3 units, Spr (Diaconis, P; Fisher, D; Holmes, S), alternate years, not given next year

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.

3 units, Win (Zhang, N)

STATS 217. Introduction to Stochastic Processes

Discrete and continuous time Markov chains, point processes, random walks, branching processes, first passage times, recurrence and transience, stationary distributions. Prerequisite: STATS 116 or consent of instructor.

3 units, Win (Rajaratnam, B), Sum (Staff)

STATS 218. Introduction to Stochastic Processes

Renewal theory, Brownian motion, Gaussian processes, second order processes, martingales.

3 units, Spr (Staff), Sum (Staff)

STATS 219. Stochastic Processes

(Same as 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.

3 units, Aut (Ross, K)

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.

3 units, Sum (Staff)

STATS 239A. Workshop in Quantitative Finance

Topics of current interest.

1 unit, Aut (Lai, T)

STATS 239B. Workshop in Quantitative Finance

Topics of current interest. May be repeated for credit.

1 unit, Spr (Lai, T)

STATS 240. Statistical Methods in Finance

(SCPD students register for 240P.) Regression analysis and applications to pricing and investment models. Principal components and multivariate analysis. Parametric influence. Financial time series. Estimation and modeling of volatilities. Statistical methods for portfolio management. Hands-on experience with financial data.

3-4 units, Aut (Lai, T)

STATS 240P. Statistical Methods in Finance

For SCPD students; see 240.

3 units, Aut (Lai, T)

STATS 241. Statistical Modeling in Financial Markets

(SCPD students register for 241P.) Nonparametric regression and yield curve smoothing. Advanced time series modeling and forecasting. Market risk measures. Substantive and empirical modeling approaches in financial markets. Statistical trading strategies. Prerequisite: 240 or equivalent.

3-4 units, Spr (Lai, T)

STATS 241P. Statistical Modeling in Financial Markets

For SCPD students; see 241.

3 units, Spr (Lai, T)

STATS 243. 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.

3-4 units, Sum (Staff)

STATS 250. Mathematical Finance

(Same as 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.

3 units, Win (Papanicolaou, G)

STATS 252. Data Mining and Electronic Business

The Internet and related technologies have caused the cost of communication and transactions to plummet, and consequently the amount of potentially relevant data to explode. The underlying principles, statistical issues, and algorithmic approaches to data mining and e-business, with real world examples.

3 units, Spr (Weigend, A)

STATS 253. Spatial Statistics

(Same as 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. GER:DB-Math

3 units, Spr (Taylor, J)

STATS 254. Correspondence Analysis and Related Methods

Use of correspondence analysis (CA) method for dimension-reduction based on the singular-value decomposition, aimed at frequency data or raw multivariate categorical observations. Comprehensive treatment of simple and multiple CA and related methods, using R packages and including 2- and 3-dimensional graphics.

3 units, Aut (Staff)

STATS 260A. Workshop in Biostatistics

(Same as HRP 260A.) Applications of statistical techniques to current problems in medical science.

1-2 units, Aut (Olshen, R)

STATS 260B. Workshop in Biostatistics

(Same as HRP 260B.) Applications of statistical techniques to current problems in medical science.

1-2 units, Win (Olshen, R)

STATS 260C. Workshop in Biostatistics

(Same as HRP 260C.) Applications of statistical techniques to current problems in medical science.

1-2 units, Spr (Olshen, R)

STATS 261. Intermediate Biostatistics: Analysis of Discrete Data

(Same as 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.

3 units, Win (Sainani, K)

STATS 262. Intermediate Biostatistics: Regression, Prediction, Survival Analysis

(Same as 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.

3 units, Spr (Sainani, K)

STATS 270. A Course in Bayesian Statistics

(Same as STATS 370.) Bayesian statistics including theory, applications, and computational tools. Topics: history of Bayesian methods, foundational problems (what is probability), subjective probability and coherence, exchangeability and deFinetti's theorem. Conjugate priors, Laplace approximations, Gibbs sampling, hierarchical and empirical Bayes, nonparametric methods, Dirichlet and Polya tree priors. Bayes robustness, asymptotic properties of Bayes procedures.

3 units, Win (Wong, W)

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.

3 units, Win (Narasimhan, B; Chambers, J)

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.

1-3 units, Aut (Lai, T), Win (Lai, T), Spr (Lai, T), Sum (Lai, T)

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.

1-9 units, Aut (Staff), Win (Staff), Spr (Staff), Sum (Staff)

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.

1-10 units, Aut (Staff), Win (Staff), Spr (Staff), Sum (Staff)

STATS 300. Advanced Topics in Statistics

May be repeated for credit.

3 units, Sum (Staff)

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.

2-4 units, Aut (Walther, G)

STATS 300B. Theory of Statistics

2-4 units, Win (Siegmund, D)

STATS 300C. Theory of Statistics

2-4 units, Spr (Siegmund, D)

STATS 305. Introduction to Statistical Modeling

The linear model: simple linear regression, polynomial regression, multiple regression, anova models; and with some extensions, orthogonal series regression, wavelets, radial basis functions, and MARS. Topics: normal theory inference (tests, confidence intervals, power), related distributions (t, chi-square, F), numerical methods (QR, SVD), model selection/regularization (Cp, AIC, BIC), diagnostics of model inadequacy, and remedies including bootstrap inference, and cross-validation. Emphasis is on problem sets involving substantial computations with data sets, including developing extensions of existing methods. Prerequisites: consent of instructor, 116, 200, applied statistics course, CS 106A, MATH 114.

2-4 units, Aut (Owen, A)

STATS 306A. Methods for Applied Statistics

Extension of modeling techniques of 305: binary and discrete response data and nonlinear least squares. Topics include regression, Poisson loglinear models, classification methods, clustering. May be repeated for credit. Prerequisite: 305 or equivalent.

2-4 units, Win (Efron, B)

STATS 306B. Methods for Applied Statistics

Unsupervised learning techniques in statistics, machine learning, and data mining.

2-4 units, Spr (Hastie, T)

STATS 310A. Theory of Probability

(Same as 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.

2-4 units, Aut (Diaconis, P)

STATS 310B. Theory of Probability

(Same as 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.

2-4 units, Win (Dembo, A)

STATS 310C. Theory of Probability

(Same as MATH 230C.) Infinitely divisible laws. Continuous time martingales, random walks and Brownian motion. Invariance principle. Markov and strong Markov property. Processes with stationary independent increments. Prerequisite: 310B or MATH 230B.

2-4 units, Spr (Dembo, A)

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.

2-3 units, not given this year

STATS 315A. Modern Applied Statistics: Learning

Topics: clustering, biclustering, and spectral clustering. Data analysis using the singular value decomposition, nonnegative decomposition, and generalizations. Plaid model, aspect model, and additive clustering. Correspondence analysis, Rasch model, and independent component analysis. Page rank, hubs, and authorities. Probabilistic latent semantic indexing. Recommender systems. Applications to genomics and information retrieval. Prerequisite: 315A,B, 305, 306A,B, or consent of instructor.

2-3 units, Aut (Tibshirani, R)

STATS 315B. Modern Applied Statistics: Data Mining

Three-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.

2-3 units, Win (Friedman, J)

STATS 315C. Modern Applied Statistics: Transposable data

2-3 units, Spr (Owen, A)

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.

1-3 units, not given this year

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.

2-3 units, Spr (Siegmund, D)

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.

2-3 units, not given this year

STATS 319. Literature of Statistics

Literature study of topics in statistics and probability culminating in oral and written reports. May be repeated for credit.

1-3 units, Aut (Taylor, J), Win (Montanari, A)

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.

2-3 units, Spr (Johnstone, I)

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.

2-3 units, not given this year

STATS 345. Computational Algorithms for Statistical Genetics

(Same as 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.

2-3 units, Spr (Tang, H; Zhang, N)

STATS 351A. An Introduction to Random Matrix Theory

(Same as 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.

3 units, Aut (Diaconis, P)

STATS 352. Spatial Statistics

(Same as 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.

3 units, Spr (Taylor, J)

STATS 362. Monte Carlo Sampling

Fundamentals of Monte Carlo methods. Generating uniform and nonuniform variables, random vectors and processes. Monte Carlo integration and variance reduction. Quasi-Monte Carlo sampling. Markov chain Monte Carlo, including Gibbs sampling and Metropolis-Hastings. Examples, problems and motivations from Bayesian statistics, computational finance, computer graphics, physics.

2-3 units, Aut (Owen, A)

STATS 366. Computational Biology

(Same as BIOMEDIN 366, STATS 166.) Methods to understand sequence alignments and phylogenetic trees built from molecular data, and general genetic data. Phylogenetic trees, median networks, microarray analysis, Bayesian statistics. Binary labeled trees as combinatorial objects, graphs, and networks. Distances between trees. Multivariate methods (PCA, CA, multidimensional scaling). Combining data, nonparametric inference. Algorithms used: branch and bound, dynamic programming, Markov chain approach to combinatorial optimization (simulated annealing, Markov chain Monte Carlo, approximate counting, exact tests). Software such as Matlab, Phylip, Seq-gen, Arlequin, Puzzle, Splitstree, XGobi.

2-3 units, Spr (Wong, W)

STATS 370. A Course in Bayesian Statistics

(Same as STATS 270.) Bayesian statistics including theory, applications, and computational tools. Topics: history of Bayesian methods, foundational problems (what is probability), subjective probability and coherence, exchangeability and deFinetti's theorem. Conjugate priors, Laplace approximations, Gibbs sampling, hierarchical and empirical Bayes, nonparametric methods, Dirichlet and Polya tree priors. Bayes robustness, asymptotic properties of Bayes procedures.

3 units, Win (Wong, W)

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.

3 units, Win (Montanari, A)

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.

1-3 units, Aut (Olshen, R), Win (Tibshirani, R), Spr (Owen, A), Sum (Staff)

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.

1-9 units, Aut (Staff), Win (Staff), Spr (Staff), Sum (Staff)

STATS 399. Research

Research work as distinguished from independent study of nonresearch character listed in 199. May be repeated for credit.

1-10 units, Aut (Staff), Win (Staff), Spr (Staff), Sum (Staff)

Registrar's Office

Stanford Bulletin, Archive 2008-09

Stanford Bulletin, Archive 2008-09

Alphabetical Index

Bulletin Archive

Graduate courses in Statistics