Lectures related to Fluctuation-dissipation relations for reversible diffusions

Explores the generation of multivariate Gaussian distributions and the challenges of factorizing covariance matrices.

Multivariate Statistics: Normal Distribution

Covers the multivariate normal distribution, properties, and sampling methods.

Principal Components: Properties & Applications

Explores principal components, covariance, correlation, choice, and applications in data analysis.

Explores dependence in random vectors, covering joint density, conditional independence, covariance, and moment generating functions.

Quantifying Statistical Dependence: Covariance and Correlation

Explores covariance, correlation, and mutual information in quantifying statistical dependence between random variables.

Multivariate Statistics: Wishart and Hotelling T²

Explores the Wishart distribution, properties of Wishart matrices, and the Hotelling T² distribution, including the two-sample Hotelling T² statistic.

Elements of Statistics: Probability, Distributions, and Estimation

Covers probability theory, distributions, and estimation in statistics, emphasizing accuracy, precision, and resolution of measurements.

Linear Response: Self-Consistent Transfer Operators

Discusses linear response for self-consistent transfer operators, exploring rigorous results and applications in theoretical frameworks.

Maximum Likelihood Estimation: Theory

Covers the theory behind Maximum Likelihood Estimation, discussing properties and applications in binary choice and ordered multiresponse models.

Elements of Statistics: Estimation & Distributions

Covers fundamental statistics concepts, including estimation theory, distributions, and the law of large numbers, with practical examples.

Non-Negative Definite Matrices and Covariance Matrices

Covers non-negative definite matrices, covariance matrices, and Principal Component Analysis for optimal dimension reduction.

Max-Stable Models: Smith and Schlather

Covers the Smith and Schlather max-stable models, exploring their validity and interpretation.

Maximum Likelihood Theory & Applications

Covers maximum likelihood theory, applications, and hypothesis testing principles in econometrics.

MLE Applications: Binary Choice Models

Explores the application of Maximum Likelihood Estimation in binary choice models, covering probit and logit models, latent variable representation, and specification tests.

Multivariate Statistics: Normal Distribution

Introduces multivariate statistics, covering normal distribution properties and characteristic functions.

Variance and Covariance: Properties and Examples

Explores variance, covariance, and practical applications in statistics and probability.

Linear Request Problem: Rigorous Results

Delves into the linear request problem, infinitesimal perturbations, transport plans, and the main theorem from 2018.

Dependence and Correlation

Explores dependence, correlation, and conditional expectations in probability and statistics, highlighting their significance and limitations.

Central Limit Theorem: Properties and Applications

Explores the Central Limit Theorem, covariance, correlation, joint random variables, quantiles, and the law of large numbers.

Optimization in Statistics and Machine Learning: Maximum Likelihood Estimation

Explores maximum likelihood estimation, logistic regression, covariance estimation, and support vector machines for classification problems.