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.
Last offered: Autumn 2014
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.
Last offered: Spring 2015
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.
Last offered: Spring 2013
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.
Last offered: Spring 2011
STATS 321: Modern Applied Statistics: Transposable Data
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.
Last offered: Spring 2012
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.
Last offered: Autumn 2015
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.
Last offered: Winter 2008
STATS 325: Multivariate Analysis and Random Matrices in Statistics
Topics on Multivariate Analysis and Random Matrices in Statistics (full description TBA)
Last offered: Spring 2016
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.
Last offered: Winter 2010
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