printer friendly pageSTATS 351: Random Walks, Networks and Environment
Selected material about probability on trees and networks, random walk in random and non-random environments, percolation and related interacting particle systems. Prerequisite: Exposure to measure theoretic probability and to stochastic processes.
Terms: Spr
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Units: 3
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Grading: Letter or Credit/No Credit
Instructors:
Dembo, A. (PI)
STATS 351A: An Introduction to Random Matrix Theory (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.
Terms: not given this year
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Units: 3
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Grading: Letter (ABCD/NP)
STATS 355: Observational Studies (HRP 255)
This course will cover statistical methods for the design and analysis of observational studies. Topics for the course will include the potential outcomes framework for causal inference; randomized experiments; methods for controlling for observed confounders in observational studies; sensitivity analysis for hidden bias; instrumental variables; tests of hidden bias; coherence; and design of observational studies.
Terms: not given this year
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Units: 2-3
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Grading: Letter or Credit/No Credit
STATS 360: Advanced Statistical Methods for Earth System Analysis (EESS 260)
Introduction for graduate students to important issues in data analysis relevant to earth system studies. Emphasis on concepts and implementation (in R), rather than formal proofs. Likely topics include the bootstrap, non-parametric methods, regression in the presence of spatial and temporal correlation, measurement errors, extreme value distributions, and high-dimensional regressions. Topics subject to change each year. Prerequisites:
STATS 110 or equivalent,
EESS 211.
Terms: Win
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Units: 3
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Grading: Letter or Credit/No Credit
Instructors:
Rajaratnam, B. (PI)
STATS 362: Topic in Bayesian nonparametrics
Bayesian analysis of infinite-dimensional models including the Dirichlet Process, species sampling models, neutral to the right processes, completely random measures, Gaussian Processes, and the Polya tree. Review of hierarchical constructions, inference algorithms, posterior asymptotics, and successful applications in the literature. Prerequisites:
Stats 310A and basic understanding of Bayesian analysis at the level of
Stats 270.
Terms: Spr
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Units: 2-3
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Repeatable for credit
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Grading: Letter or Credit/No Credit
Instructors:
Bacallado, S. (PI)
STATS 366: Modern Statistics for Modern Biology (BIOS 221)
Application based course in nonparametric statistics. Modern toolbox of visualization and statistical methods for the analysis of data, examples drawn from immunology, microbiology, cancer research and ecology. Methods covered include multivariate methods (PCA and extensions), sparse representations (trees, networks, contingency tables) as well as nonparametric testing (Bootstrap, permutation and Monte Carlo methods). Hands on, use R and cover many Bioconductor packages. Prerequisite: Minimal familiarity with computers. Instructor consent.
Terms: Sum
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Units: 3
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Grading: Letter or Credit/No Credit
Instructors:
Holmes, S. (PI)
;
Martin, T. (PI)
STATS 370: A Course in Bayesian Statistics (STATS 270)
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.
Terms: Win
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Units: 3
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Grading: Letter or Credit/No Credit
Instructors:
Wong, W. (PI)
STATS 374: Large Deviations Theory (MATH 234)
Combinatorial estimates and the method of types. Large deviation probabilities for partial sums and for empirical distributions, Cramer's and Sanov's theorems and their Markov extensions. Applications in statistics, information theory, and statistical mechanics. Prerequisite:
MATH 230A or
STATS 310.
Terms: not given this year
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Units: 3
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Grading: Letter or Credit/No Credit
STATS 375: Inference in Graphical Models
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.
Terms: not given this year
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Units: 3
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Grading: Letter or Credit/No Credit
STATS 376A: Information Theory (EE 376A)
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.
Terms: Win
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Units: 3
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Grading: Letter or Credit/No Credit
Instructors:
Weissman, T. (PI)
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