printer friendly pageSTATS 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
Instructors:
Siegmund, D. (PI)
STATS 310C: Theory of Probability (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.
Terms: Spr
| Units: 2-4
Instructors:
Dembo, A. (PI)
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.
Terms: Aut
| Units: 2-3
| Repeatable
for credit
Instructors:
Romano, J. (PI)
STATS 315A: Modern Applied Statistics: Learning
Overview of supervised learning. Linear regression and related methods. Least angle regression and the lasso. Classification. Support vector machines (SVMs). Kernels and string kernels. Basic expansions and regularization. Generalized additive models. Kernel smoothing. Gaussian mixtures and EM algorithm. Model assessment and selection: cross-validation and the bootstrap. Pathwise coordinate descent and the fused lasso. Sparse graphical models. Discrete graphical models. Prerequisite:
STATS 305, 306A,B or consent of instructor
Terms: Win
| Units: 2-3
Instructors:
Tibshirani, R. (PI)
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.
Terms: Spr
| Units: 2-3
Instructors:
Friedman, J. (PI)
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.
Terms: Spr
| Units: 1-3
Instructors:
Dembo, A. (PI)
;
Montanari, A. (PI)
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, Spr
| Units: 1-3
| Repeatable
for credit
Instructors:
Donoho, D. (PI)
;
Taylor, J. (PI)
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.
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.
Terms: Win
| Units: 1-3
Instructors:
Efron, B. (PI)
STATS 330: An Introduction to Compressed Sensing (CME 362)
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).
Terms: Spr
| Units: 2-3
Instructors:
Candes, E. (PI)
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