Lectures related to Path Integral Molecular Dynamics

Sampling Distributions: Theory and Applications

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

Parameter Estimation: Detection & Estimation

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

Probabilistic Models for Linear Regression

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

Linear Regression: Statistical Inference Perspective

Explores linear regression from a statistical inference perspective, covering probabilistic models, ground truth, labels, and maximum likelihood estimators.

Frequency Moments: Estimators and Algorithms

Covers the concept of frequency moments and introduces algorithms for estimating them efficiently.

Point Estimation in Statistics

Explores point estimation in statistics, discussing bias, variance, mean squared error, and consistency of estimators.

Statistics for Data Science: Introduction to Statistical Methods

Covers the fundamental concepts of statistics and their application in data science.

Risk and Return Measures

Covers risk and return measures, unbiasedness, and consistency of estimators.

Parameter Estimation & Fisher Information

Covers parameter estimation, Fisher information, unbiased estimator, and exponential distributions.

Generalization Error

Discusses mutual information, data processing inequality, and properties related to leakage in discrete systems.

Numerical Analysis: Implicit Schemes

Covers implicit schemes in numerical analysis for solving partial differential equations.

Path Integral Methods: Advanced Momentum Estimators

Covers the derivation of path integral estimators for momentum-dependent operators and discusses improvements for statistical convergence in multi-particle systems.

Generalized Integrals and Convergence Criteria

Covers generalized integrals, convergence criteria, series convergence, and harmonic series in analysis.

Statistical Estimation

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

Covariance Cleaning and Estimators

Explores covariance matrix cleaning, optimal estimators, and rotationally invariant methods for portfolio optimization.

Intro to Quantum Sensing: Parameter Estimation and Fisher Information

Introduces Fisher Information for parameter estimation based on collected data.

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Observers References

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

Statistical Learning Models: Risk and Empirical Risk Minimization

Covers statistical learning models, risk minimization, and empirical risk minimization with examples of maximum-likelihood estimators.

Stochastic Simulations: Ergodicity and Estimators Log in to Mediaspace to watch this video

Explores geometric ergodicity in Markov chains and estimators' bias and variance, highlighting efficiency loss quantification.