## STATS 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: 2-3

## 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 for credit

Instructors:
Candes, E. (PI)

## STATS 305A: 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. (NB: prior to 2016-17 the 305ABC series was numbered as 305, 306A and 306B).

Terms: Aut
| Units: 3

Instructors:
Palacios, J. (PI)
;
Chin, A. (TA)
;
Greaves, D. (TA)
...
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Instructors:
Palacios, J. (PI)
;
Chin, A. (TA)
;
Greaves, D. (TA)
;
Ignatiadis, N. (TA)
;
Rosenman, E. (TA)
;
Sohn, Y. (TA)

## STATS 310A: Theory of Probability I (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 314A: Advanced Statistical Theory

Covers a range of topics, including: empirical processes, asymptotic efficiency, uniform convergence of measures, contiguity, resampling methods, Edgeworth expansions.

Terms: Aut
| Units: 3
| Repeatable for credit

## 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.
https://web.stanford.edu/~montanar/TEACHING/Stat316/stat316.html

Terms: Aut
| Units: 1-3

Instructors:
Dembo, A. (PI)
;
Montanari, A. (PI)

## 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 350: Topics in Probability Theory

See
http://statweb.stanford.edu/~adembo/stat-350/concentration/ Selected topics of contemporary research interest in probability theory. May be repeated once for credit. Prerequisite: 310A or equivalent.

Terms: Aut
| Units: 1-3
| Repeatable for credit

Instructors:
Dembo, A. (PI)

## STATS 385: Theories of Deep Learning

The spectacular recent successes of deep learning are purely empirical. Nevertheless intellectuals always try to explain important developments theoretically. In this literature course we will review recent work of Burna and Mallat, Mhaskar and Poggio, Papyan and Elad, Bolsckei and co-authors, Baraniuk and co-authors, and others, seeking to build theoretical frameworks deriving deep networks as consequences. After initial background lectures, we will have some of the authors presenting lectures on specific papers.

Terms: Aut
| Units: 1

## STATS 390: Consulting Workshop

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.

Terms: Aut, Win, Spr, Sum
| Units: 1-3
| Repeatable for credit

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