Multi-arm bandits: Distribution Estimation

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Probabilistic Models for Linear Regression

Covers the probabilistic model for linear regression and its applications in nuclear magnetic resonance and X-ray imaging.

The Stein Phenomenon and Superefficiency

Explores the Stein Phenomenon, showcasing the benefits of bias in high-dimensional statistics and the superiority of the James-Stein Estimator over the Maximum Likelihood Estimator.

Estimators and Bias

Explores estimators, bias, and efficiency in statistics, emphasizing the trade-off between bias and variability.

Optimality in Decision Theory: Unbiased Estimation

Explores optimality in decision theory and unbiased estimation, emphasizing sufficiency, completeness, and lower bounds for risk.

Statistical Theory: Cramér-Rao Bound & Hypothesis Testing

Explores the Cramér-Rao bound, hypothesis testing, and optimality in statistical theory.

Basic Principles of Point Estimation

Explores the Method of Moments, Bias-Variance tradeoff, Consistency, Plug-In Principle, and Likelihood Principle in point estimation.

Implicit Generative Models

Explores implicit generative models, covering topics like method of moments, kernel choice, and robustness of estimators.

L-Moment Estimation: Probability-Weighted Moments

Covers L-moment estimation, probability-weighted moments, and maximum likelihood inference basics.

Property Testing: Uniform Distributions

Covers property testing against uniform distributions using the plug-in approach.

Distribution Estimation

Explores distribution estimation, constraints in estimators, and competitive analysis for robust estimation.