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Course Criteria
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2.00 - 3.00 Credits
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)
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2.00 - 3.00 Credits
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
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3.00 Credits
(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)
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3.00 Credits
(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)
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3.00 Credits
(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, remotesensing, ecology, materials. 3 units, Spr (Taylor, J)
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2.00 - 3.00 Credits
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)
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2.00 - 3.00 Credits
(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)
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3.00 Credits
(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)
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3.00 Credits
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)
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3.00 Credits
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)
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