printer friendly pageSTATS 300A: Theory of Statistics I
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: 3
STATS 300B: Theory of Statistics II
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: 3
STATS 300C: Theory of Statistics III
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: 3
Instructors:
Candes, E. (PI)
;
Salerno, M. (TA)
STATS 301: Statistics Teaching Practicum
Ordinarily for Statistics first year PhD students. Discussion of effective teaching, assessment, and course design. Students practice teaching in a guided environment. There will be a total of 10 course meetings spread out across autumn, winter, and spring quarters, but students enroll in spring quarter.
Terms: Spr
| Units: 1
| Repeatable
3 times
(up to 3 units total)
Instructors:
Sun, D. (PI)
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: 5-10
STATS 303: Statistics Faculty Research Presentations
For Statistics first and second year PhD students only. Discussion of statistics topics and research areas; consultation with PhD advisors.
Terms: Aut
| Units: 1
| Repeatable
2 times
(up to 2 units total)
Instructors:
Taylor, J. (PI)
STATS 305A: Applied Statistics I
Statistics of real valued responses. Review of multivariate normal distribution theory. Univariate regression. Multiple regression. Constructing features from predictors. Geometry and algebra of least squares: subspaces, projections, normal equations, orthogonality, rank deficiency, Gauss-Markov. Gram-Schmidt, the QR decomposition and the SVD. Interpreting coefficients. Collinearity. Dependence and heteroscedasticity. Fits and the hat matrix. Model diagnostics. Model selection, Cp/AIC and crossvalidation, stepwise, lasso. Multiple comparisons. ANOVA, fixed and random effects. Use of bootstrap and permutations. 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
STATS 305B: Applied Statistics II
This course uses exponential family structure to motivate generalized linear models and other useful applied techniques including survival analysis methods and Bayes and empirical Bayes analyses. The lectures are based on a forthcoming book whose notes will be distributed. Prerequisites: 305A or consent of the instructor.
Terms: Win
| Units: 3
STATS 305C: Applied Statistics III
Methods for multivariate responses. Theory, computation, and practice for multivariate statistical tools. Topics may include multivariate Gaussian models, probabilistic graphical models, MCMC and variational Bayesian inference, dimensionality reduction, principal components, factor analysis, independent components analysis, canonical correlations, linear discriminant analysis, hierarchical clustering, bi-clustering, multidimensional scaling and variants (e.g., Isomap, spectral clustering, t-SNE), matrix completion, topic modeling, and state space models. Extensive work with data involving programming, ideally in Python and/or R. Prerequisites:
Stats 305A and
Stats 305B or consent of the instructor.
Terms: Spr
| Units: 3
STATS 307: Introduction to Time Series Analysis (STATS 207)
Time series models used in economics and engineering. Trend fitting, autoregressive and moving average models and spectral analysis, Kalman filtering, and state-space models. Seasonality, transformations, and introduction to financial time series. Prerequisite: basic course in Statistics at the level of 200.
Terms: Spr
| Units: 3
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