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Lecture
Confidence Intervals: Margins, Coverage, Pivots
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Estimation and Confidence Intervals
Explores parameter estimation, standard errors, and confidence intervals using the central limit theorem and practical examples.
Hypothesis Testing: Wilks' Theorem
Explores hypothesis testing using Wilks' Theorem, likelihood ratio statistics, p-values, interval estimation, and confidence regions.
Confidence Intervals and MLE Limit Theorems
Explores constructing confidence intervals and MLE limit theorems for large samples.
Statistical Inference: Approximate Critical Values and Confidence Intervals
Covers the construction of confidence intervals and approximate critical values in statistical inference.
Uncertainty and Significant Figures
Explains confidence intervals, margin of error, pivots, and significant figures in statistical estimation.
Assessing Significance and Fit
Covers confidence intervals, R2, and examples on cement heat evolution and car horsepower-MPG relationships.
Monte Carlo Estimation: Error Analysis
Covers the Monte Carlo method for generating realizations and unbiased estimators.
Stochastic Simulation: Computation and Estimation
Covers computation and estimation in stochastic simulation, focusing on generating iid replicas and optimal importance sampling.
Statistical Tests: T-Tests and ANOVA
Covers the calculation of paired t-tests, advantages/disadvantages of different t-tests, and the concept of ANOVA.
Numerical Simulation of SDEs: Monte Carlo & Optimal Control
Covers Monte Carlo methods, variance reduction, and stochastic optimal control, exploring simulation techniques, efficiency, and investment dynamics.