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Course Criteria
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3.00 Credits
(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)
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3.00 Credits
(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)
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2.00 - 3.00 Credits
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
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3.00 Credits
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)
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2.00 - 3.00 Credits
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)
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3.00 Credits
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, Spr (Owen, A)
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3.00 Credits
Local weak convergence, Gibbs measures on trees, cavity method, and replica symmetry breaking. Examples include random ksatisfiability, the assignment problem, spin glasses, and neural networks. Prerequisite: 310A or equivalent. 1-3 units, not given this year
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2.00 - 3.00 Credits
Semimartingales, stochastic integration, Ito's formula, Girsanov'stheorem. 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)
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2.00 - 3.00 Credits
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
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1.00 - 3.00 Credits
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)
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