Lectures related to Dynamic Model Simulation: EPFL Racing Team

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.

Probabilistic Models for Linear Regression

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

Intro to Quantum Sensing: Parameter Estimation and Fisher Information

Introduces Fisher Information for parameter estimation based on collected data.

Statistical Theory: Maximum Likelihood Estimation

Explores the consistency and asymptotic properties of the Maximum Likelihood Estimator, including challenges in proving its consistency and constructing MLE-like estimators.

Statistical Models and Parameter Estimation

Explores statistical models, parameter estimation, and sampling distributions in probability and statistics.

Bayes Estimator: Definition and Application

Introduces the Bayes estimator, explaining its definition, application in quadratic cost scenarios, and importance in probabilistic reasoning.

Optimality in Decision Theory: Unbiased Estimation

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

Bayes Estimator, Simulated Annealing and EM

Covers Bayes estimator, Simulated Annealing, and EM for parameter estimation.

Statistical Estimation: Gaussian Linear Model

Delves into statistical estimation, highlighting the Gaussian linear model and the limitations of ML estimators.

Basic Principles of Point Estimation

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

Sampling Distributions: Theory and Applications

Explores sampling distributions, estimators' properties, and statistical measures for data science applications.

Optimal Estimation and Bias in Statistics

Delves into optimal estimation, bias role in finite samples, and the delicate tradeoff between bias and variance in statistical estimation.

Distribution Estimation

Covers the estimation of distributions using samples and probability models.

Estimators and Bias

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

Statistical Theory: Cramér-Rao Bound & Hypothesis Testing

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

Maximum Likelihood Estimation

Delves into maximum likelihood estimators, their properties, and asymptotic behavior, emphasizing consistency and asymptotic normality.

Observers References

Explores the addition of a reference input to controllers and the design of autonomous and tracking-error estimators.

Empirical Estimation: Distribution Estimation

Covers methods to estimate probability distributions from samples.

Spectral & Parametric Estimation: Time Series

Covers spectral estimation techniques like tapering and parametric estimation, emphasizing the importance of AR models and Whittle likelihood in time series analysis.

Distribution Estimation

Covers the estimation of distributions using various methods such as minimum loss and expectation.