Statistical Theory: Inference and Optimality

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Statistical Significance: Maximum Likelihood Estimation and Confidence Intervals

Explores type I and type II errors, critical values, and confidence intervals in statistical significance.

Probabilities and Statistics

Covers fundamental concepts in probabilities and statistics, including linear regression, exploratory statistics, and the analysis of probabilities.

Probability Distributions in Environmental Studies

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.

Interval Estimation: Method of Moments

Covers the method of moments for estimating parameters and constructing confidence intervals based on empirical moments matching distribution moments.

Hypothesis Testing and Confidence Intervals: An Overview

Covers hypothesis testing, confidence intervals, and their applications in statistics.

Optimality in Decision Theory: Unbiased Estimation

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

Statistical Hypothesis Testing: Concepts and Applications

Provides an overview of statistical hypothesis testing, including its purpose, formulation, and significance in data analysis.

Estimation and Confidence Intervals

Explores bias, variance, and confidence intervals in parameter estimation using examples and distributions.

Estimation and Confidence Intervals

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

Confidence Intervals: Gaussian Estimation

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