STATS 300A: Theory of Statistics
Finite sample optimality of statistical procedures; Decision theory: loss, risk, admissibility; Principles of data reduction: sufficiency, ancillarity, completeness; Statistical models: exponential families, group families, nonparametric families; Point estimation: optimal unbiased and equivariant estimation, Bayes estimation, minimax estimation; Hypothesis testing and confidence intervals: uniformly most powerful tests, uniformly most accurate confidence intervals, optimal unbiased and invariant tests. Prerequisites: Real analysis, introductory probability (at the level of
STATS 116), and introductory statistics.
Terms: Aut
| Units: 2-3
STATS 300B: Theory of Statistics
Elementary decision theory; loss and risk functions, Bayes estimation; UMVU estimator, minimax estimators, shrinkage estimators. Hypothesis testing and confidence intervals: Neyman-Pearson theory; UMP tests and uniformly most accurate confidence intervals; use of unbiasedness and invariance to eliminate nuisance parameters. Large sample theory: basic convergence concepts; robustness; efficiency; contiguity, locally asymptotically normal experiments; convolution theorem; asymptotically UMP and maximin tests. Asymptotic theory of likelihood ratio and score tests. Rank permutation and randomization tests; jackknife, bootstrap, subsampling and other resampling methods. Further topics: sequential analysis, optimal experimental design, empirical processes with applications to statistics, Edgeworth expansions, density estimation, time series.
Terms: Win
| Units: 2-4
STATS 300C: Theory of Statistics
Decision theory formulation of statistical problems. Minimax, admissible procedures. Complete class theorems ("all" minimax or admissible procedures are "Bayes"), Bayes procedures, conjugate priors, hierarchical models. Bayesian non parametrics: diaichlet, tail free, polya trees, bayesian sieves. Inconsistency of bayes rules.
Terms: Spr
| Units: 2-4
STATS 302: Qualifying Exams Workshop
Prepares Statistics Ph.D. students for the qualifying exams by reviewing relevant course topics and problem solving strategies.
Terms: Sum
| Units: 3
STATS 303: PhD First Year Student Workshop
For Statistics First Year PhD students only. Discussion of relevant topics in first year student courses, consultation with PhD advisor.
Terms: Aut, Win, Spr, Sum
| Units: 1
| Repeatable
4 times
(up to 4 units total)
Instructors:
Candes, E. (PI)
;
Holmes, S. (PI)
STATS 305: Introduction to Statistical Modeling
Review of univariate regression. Multiple regression. Geometry, subspaces, orthogonality, projections, normal equations, rank deficiency, estimable functions and Gauss-Markov theorem. Computation via QR decomposition, Gramm-Schmidt orthogonalization and the SVD. Interpreting coefficients, collinearity, graphical displays. Fits and the Hat matrix, leverage & influence, diagnostics, weighted least squares and resistance. Model selection, Cp/Aic and crossvalidation, stepwise, lasso. Basis expansions, splines. Multivariate normal distribution theory. ANOVA: Sources of measurements, fixed and random effects, randomization. Emphasis on problem sets involving substantive computations with data sets. Prerequisites: consent of instructor, 116, 200, applied statistics course,
CS 106A,
MATH 114.
Terms: Aut
| Units: 3
Instructors:
Tibshirani, R. (PI)
;
Achanta, R. (TA)
;
Markovic, J. (TA)
...
more instructors for STATS 305 »
Instructors:
Tibshirani, R. (PI)
;
Achanta, R. (TA)
;
Markovic, J. (TA)
;
Wang, J. (TA)
;
YANG, J. (TA)
STATS 306A: Methods for Applied Statistics
Regression modeling extended to categorical data. Logistic regression. Loglinear models. Generalized linear models. Discriminant analysis. Categorical data models from information retrieval and Internet modeling. Prerequisite: 305 or equivalent.
Terms: Win
| Units: 3
STATS 306B: Methods for Applied Statistics: Empirical Bayes Methods
Empirical Bayes procedures for estimation, testing, and prediction, especially as applied to large-scale problems.
Terms: Spr
| Units: 2-3
STATS 310A: Theory of Probability (MATH 230A)
Mathematical tools: sigma algebras, measure theory, connections between coin tossing and Lebesgue measure, basic convergence theorems. Probability: independence, Borel-Cantelli lemmas, almost sure and Lp convergence, weak and strong laws of large numbers. Large deviations. Weak convergence; central limit theorems; Poisson convergence; Stein's method. Prerequisites: 116,
MATH 171.
Terms: Aut
| Units: 2-4
STATS 310B: Theory of Probability (MATH 230B)
Conditional expectations, discrete time martingales, stopping times, uniform integrability, applications to 0-1 laws, Radon-Nikodym Theorem, ruin problems, etc. Other topics as time allows selected from (i) local limit theorems, (ii) renewal theory, (iii) discrete time Markov chains, (iv) random walk theory,nn(v) ergodic theory. Prerequisite: 310A or
MATH 230A.
Terms: Win
| Units: 2-3
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