Monte Carlo Method: Simulation and Inference

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Estimation Methods in Probability and Statistics

Discusses estimation methods in probability and statistics, focusing on maximum likelihood estimation and confidence intervals.

Confidence Intervals: Definition and Estimation

Explains confidence intervals, parameter estimation methods, and the central limit theorem in statistical inference.

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.

Probabilistic Models for Linear Regression

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

Confidence Intervals: Gaussian Estimation

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

Monte Carlo Estimation: Error Analysis

Covers the Monte Carlo method for generating realizations and unbiased estimators.

Statistical Inference

Covers likelihood ratio statistic, confidence intervals, and hypothesis testing concepts.

Optimality in Decision Theory: Unbiased Estimation

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

Estimators and Confidence Intervals

Explores bias, variance, unbiased estimators, and confidence intervals in statistical estimation.

Interval Estimation

Covers the construction of confidence intervals for a normal distribution with unknown mean and variance.