Maximum Likelihood, MSE, Fisher Information, Cramér-Rao Bound

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Related lectures (32)

Page 2 of 4

Covers Maximum Likelihood Estimation in statistical inference, discussing MLE properties, examples, and uniqueness in exponential families.

Statistical Theory: Inference and Optimality

Explores constructing confidence regions, inverting hypothesis tests, and the pivotal method, emphasizing the importance of likelihood methods in statistical inference.

Bias and Variance in Estimation

Discusses bias and variance in statistical estimation, exploring the trade-off between accuracy and variability.

Statistical Theory: Cramér-Rao Bound & Hypothesis Testing

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

Spin Glasses and Bayesian Estimation

Covers the concepts of spin glasses and Bayesian estimation, focusing on observing and inferring information from a system closely.

Confidence Intervals: Gaussian Estimation

Explores confidence intervals, Gaussian estimation, Cramér-Rao inequality, and Maximum Likelihood Estimators.

Bayesian Estimation: Unsupervised Learning & MCMC

Explores Bayesian estimation for unsupervised learning and MCMC, using a Spin Glass Card game example.

Statistical Estimation: Maximum Likelihood

Explores Maximum Likelihood Estimation properties, challenges, and alternative methods in statistical inference.

Consistency of Maximum Likelihood Estimation

Explores the mathematical reasoning behind the consistency of maximum likelihood estimation.

Estimation and Confidence Intervals

Explores parameter estimation, standard errors, and confidence intervals using the central limit theorem and practical examples.