Lectures related to Intro to Quantum Sensing: Parameter Estimation and Fisher Information

Basic Principles of Point Estimation

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

Estimation and Confidence Intervals

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

Parameter Estimation: Detection & Estimation

Covers the concepts of parameter estimation, including unbiased estimators and Fisher information.

Statistical Models and Parameter Estimation

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

Sampling Distributions: Estimators and Variance

Covers estimation of parameters, MSE, Fisher information, and the Rao-Blackwell Theorem.

Estimators and Confidence Intervals

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

Confidence Intervals: Gaussian Estimation

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

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.

Optimality in Decision Theory: Unbiased Estimation

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

Maximum Likelihood: Estimation and Inference

Introduces maximum likelihood estimation, discussing its properties and applications in statistical analysis.

Statistical Estimation

Explores statistical estimation, comparing estimators based on mean and variance, and delving into mean squared error and Cramér-Rao bound.

Bias, Variance, Consistency, EMV

Covers bias, variance, mean squared error, consistency, and maximum likelihood estimation in the Poisson model.

Probabilistic Models for Linear Regression

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

Estimation: Linear Estimator

Explores linear estimation, optimal criteria, and the orthogonality principle for good choices in estimation.

Sampling Distributions: Estimation

Explores sampling distributions, estimation methods, and consistency in parameter estimation.

Fisher Information, Cramér-Rao Inequality, MLE

Explains Fisher information, Cramér-Rao inequality, and MLE properties, including invariance and asymptotics.

Estimation: Measures of Performance

Explores estimation measures of performance, including the Cramér-Rao bound and maximum likelihood estimation.

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.

Sampling Distributions: Theory and Applications

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