## MATH 230A: Theory of Probability I (STATS 310A)

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:
STATS 116,
MATH 171.

Terms: Aut
| Units: 3

## STATS 116: Theory of Probability

Probability spaces as models for phenomena with statistical regularity. Discrete spaces (binomial, hypergeometric, Poisson). Continuous spaces (normal, exponential) and densities. Random variables, expectation, independence, conditional probability. Introduction to the laws of large numbers and central limit theorem. Prerequisites:
MATH 52 and familiarity with infinite series, or equivalent.

Terms: Aut, Spr, Sum
| Units: 4
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR

Instructors:
Donoho, D. (PI)
;
Tirlea, M. (PI)
;
Wong, W. (PI)
;
GAO, Z. (TA)
;
Han, K. (TA)
;
Jang, J. (TA)
;
Kunnasagaran, A. (TA)
;
Misiakiewicz, T. (TA)
;
Tirlea, M. (TA)
;
Wu, H. (TA)

## 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: 3

## 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:
STATS 116,
MATH 171.

Terms: Aut
| Units: 3

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