Lectures related to Wishart distribution

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.

Mach-Zehnder Interferometer

Explores the Mach-Zehnder interferometer, density matrices, and detection probabilities in quantum systems.

Evolution of Density Matrices

Explores the evolution of density matrices in quantum optics, emphasizing super-operators and completely positive maps.

Evolution of Density Matrices

Covers the evolution of density matrices in quantum optics, focusing on quantum channels and amplitude damping.

Multivariate Statistics: Introduction and Methods

Introduces multivariate statistics, focusing on uncovering associations between components in data in vector form.

Shrinkage Estimation of Large Covariance Matrices

Explores shrinkage estimation of high-dimensional covariance matrices, comparing linear and nonlinear approaches for improved accuracy.

Gaussian Random Vectors: Conditional Generation

Explores generating Gaussian random vectors with specific components based on observed values and explains the concept of positive definite covariance functions in Gaussian processes.

Reduced Density Matrices: System+Environment

Covers the concept of density matrices and the system-environment interaction.

Classification with GMM and kNN

Covers classification using GMM and kNN, exploring boundaries, errors, and practical exercises.

Gaussian Correlation Conjecture

Explores the proof of the Gaussian correlation conjecture and its implications on random vectors and covariance matrices.

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Time Series: Estimation and Spectral Representation

Explores time series estimation, spectral representation, and p-variate analysis in depth.

Principal Component Analysis: Theory and Applications

Covers the theory and applications of Principal Component Analysis, focusing on dimension reduction and eigenvectors.

Market Response Functions

Explores market response functions, flash crashes, correlation estimation, and noise filtering in finance.

Non-Negative Definite Matrices and Covariance Matrices

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

Maximum Likelihood Theory & Applications

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

Extended Kalman Filter

Covers the Extended Kalman Filter algorithm with a focus on time-correlated observations and practical implementations.

Kalman Filtering: State Estimation and Prediction

Explores the Kalman filter for state estimation and prediction in a linear Gaussian setting, emphasizing the optimality of the predictor and filter.

Gaussian Mixture Regression: Theory and Applications

Explores Gaussian mixture regression and overfitting with multiple Gauss functions.

Bipartite systems - Entanglement

Covers the concept of entanglement in bipartite systems, focusing on entropy and Schmidt decomposition.