Results for STATS

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.

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.

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.

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.

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.

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.

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.

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 and taxa abundance measurements by microarrays and sequencing. Kernel methods for graph gene intereaction graph construction. Phylogenetic trees and their uses in microbiome studies. Computational nonparametric statistics for the analyses of real genomic studies. Assignments: weekly reading of papers and a final project.

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.

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.

For students majoring in Mathematical and Computational Science only. Students obtain employment in a relevant industrial or research activity to enhance their professional experience.

For undergraduates.

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.

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.

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.

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.

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.

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

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.

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.

Multivariate Normal Distribution and Inference, Wishart distributions, graph theory, probabilistic Markov models, pairwise and global Markov property, decomposable graph, Markov equivalence, MLE for DAG models and undirected graphical models, Bayesian inference for DAG models and undirected graphical models. Prerequisites: STATS 116, MATH 104 or equivalent class in linear algebra.

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.

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.

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

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.

Research designs and statistical procedures for time-ordered (repeated-measures) data. The analysis of longitudinal panel data is central to empirical research on learning and development. Topics: measurement of change, growth curve models, analysis of durations including survival analysis, experimental and non-experimental group comparisons, reciprocal effects, stability. See http://www-stat.stanford.edu/~rag/stat222/ . Prerequisite: intermediate statistical methods.

Asset returns and their volatilities. Markowitz¿s portfolio theory, capital asset pricing model, multifactor pricing models. Measures of market risk. Financial derivatives and hedging. Black¿Scholes pricing of European options. Valuation of American options. Implied volatility and the Greeks. Prerequisite: STATS 116 or equivalent

Topics of current interest.

(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.

For SCPD students; see 240.

(SCPD students register for 241P.) Substantive and empirical modeling approaches in options and interest rate markets. Nonlinear least squares and nonparametric regression. Multivariate time series modeling and forecasting. Applications of canonical correlation analysis and cointegration. Statistical trading strategies and their evaluation. Prerequisite: 240 or equivalent.

For SCPD students; see 241.

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.

(SCPD students register for 243P.) Market risk and credit risk, credit markets. Back testing, stress testing and Monte Carlo methods. Logistic regression, generalized linear models and generalized mixed models. Loan prepayment and default as competing risks. Survival and hazard functions, correlated default intensities, frailty and contagion. Risk surveillance, early warning andnadaptive control methodologies. Banking and bank regulation, asset and liability management. Prerequisite: STATS 240 or equivalent.

For SCPD students; see 243.

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.

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.

Applications of statistical techniques to current problems in medical science.

Applications of statistical techniques to current problems in medical science.

Applications of statistical techniques to current problems in medical science.

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.

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.

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.

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.

Advanced programming and computing techniques to support projects in data analysis and related research. For Statistics graduate students and others whose research involves data analysis and development of associated computational software. Prerequisites: Programming experience including familiarity with R; computing at least at the level of CS 106; statistics at the level of STATS 110 or 141.

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.

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.

For Statistics M.S. students only. Reading or research program under the supervision of a Statistics faculty member. May be repeated for credit.

May be repeated for credit.

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.

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.

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.

Prepares Statistics Ph.D. students for the qualifying exams by reviewing relevantnncourse topics and problem solving strategies.

For Statistics First Year PhD students only. Discussion of relevant topics in first year student courses, consultation with PhD advisor.

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.

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.

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

Mathematical tools: sigma algebras, measure theory, connections between coin tossing and Lebesgue measure, basic convergence theorems. Probability: independence, Borel-Cantelli lemmas, almost sure and Lp convergence, weak and strong laws of large numbers. Large deviations. Weak convergence; central limit theorems; Poisson convergence; Stein's method. Prerequisites: 116, MATH 171.

Conditional expectations, discrete time martingales, stopping times, uniform integrability, applications to 0-1 laws, Radon-Nikodym Theorem, ruin problems, etc. Other topics as time allows selected from (i) local limit theorems, (ii) renewal theory, (iii) discrete time Markov chains, (iv) random walk theory,nn(v) ergodic theory. Prerequisite: 310A or MATH 230A.

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.

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.

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.

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.

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.

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

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. Prerequisites: 315A,B, 305/306A,B, or consent of instructor.

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.

Compressed sensing is a new data acquisition theory asserting that onenncan design nonadaptive sampling techniques that condense thenninformation in a compressible signal into a small amount of data.nnThis revelation may change the way engineers think about signalnnacquisition. Course covers fundamental theoretical ideas, numericalnnmethods in large-scale convex optimization, hardware implementations,nnconnections with statistical estimation in high dimensions, andnnextensions such as recovery of data matrices from few entries (famousnnNetflix Prize).

We follow the change from concern about simultaneous inference on multiple parameters to concern about the selection effect, in areas where the multiplicity is high: Genomics, Brain Imaging and Medical Statistics. We review: (i) Basic principles for constructing simultaneous inference (ii) The introduction of the false discovery rate (iii) Variations on the false discovery rate. We emphasize (iv) selective inference, as a goal that merits its own terms and treatment, and present open challenges regarding concepts and methods.

Theory, computational aspects, and practice of a variety of important multivariate statistical tools for data analysis. Topics include classicalnnmultivariate Gaussian and undirected graphical models, graphical displays. PCA, SVD and generalizations including canonical correlation analysis, linear discriminant analysis, correspondence analysis, with focus on recent variants. Factor analysis and independent component analysis. Multidimensional scalingnnand its variants (e.g. Isomap, spectral clustering). Students are expected to program in R. Prerequisite: STATS 305 or equivalent.

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.

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.

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 and taxa abundance measurements by microarrays and sequencing. Kernel methods for graph gene intereaction graph construction. Phylogenetic trees and their uses in microbiome studies. Computational nonparametric statistics for the analyses of real genomic studies. Assignments: weekly reading of papers and a final project.

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.

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.

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.

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: EE178/278A or STATS 116, or equivalent.

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.

Applications of Computational Statistics and Data Mining to Biological Data. Attendance mandatory. Instructor approval required.

For Statistics PhD students defending their dissertation.

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.

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

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.

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.

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.

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.

(Same as LAW 564). This is a non-technical course that will focus on a series of case studies each designed to illuminate a serious public policy issue raised by the evolution of modern financial engineering. These will include discussions of Freddie Mac, Fannie Mae, sub-prime and Alt-A mortgages and the flaws of AAA CDOs; the spectacular losses by Orange County and the Florida Local Government Investment Pool and the challenges posed by unregulated investment pools; how credit default swaps are likely to change with central clearing using the PIIGS (Portugal/ Ireland/ Iceland/ Greece/ Spain), the monolines, AIG, Lehman and MF Global as examples; views of rogue trading using the similarities and disparities of Askin, Madoff, Barings, Soc Gen and UBS for discussion; and Risk Management 101 : the why/ how/ where/ when firms went wrong plus what to keep and what to throw out in the next phase of risk programs among other case studies. The subject matter, by necessity, is multi-disciplinary and so the course is particularly suited to those students having an interest in public policy and the evolution of modern financial markets. This includes students from the law or business schools, or the public policy, economics, EES, political science, or financial math and engineering programs among others. Several themes will tie the case studies, reading and discussions together:-Is this an example of an innovation that got too far ahead of existing operations, risk management, legal, accounting, regulatory or supervisory oversight?-How might temporary infrastructure be implemented without stifling innovation or growth?-How might losses be avoided by requiring permanent infrastructure sooner? Will Dodd-Frank, Basel III, etc., help to prevent such problems? What are the potential unintended consequences?-Is this an example of improperly viewing exposures that are subject to uncertainty or incorrectly modeling risk or both? Guest speakers will be invited to share their experiences. This course will aim to provide a practitioner(s) view of financial engineering over the past 3 ½ decades as well as a broad understanding of what went right and what went wrong plus cutting edge views of the future of financial engineering. Prerequisite: STATS 237 or equivalent and consent of instructor.

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.

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.

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.

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.

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.

Data monitoring and interim analysis of clinical trials. Design of Phase I, II, III trials. Survival analysis. Longitudinal data analysis.

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.

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.