Lectures related to Extended Kalman Filter

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.

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.

Shrinkage Estimation of Large Covariance Matrices

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

Structural Modelling and the Kalman Filter: Time Series

Explores structural modelling in time series and introduces the Kalman filter for prediction and estimation.

Kalman Filter: Time Series

Covers structural modeling, state space models, and the Kalman filter in time series analysis.

Principal Components: Properties & Applications

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

Multivariate Statistics: Introduction and Methods

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

Non-Negative Definite Matrices and Covariance Matrices

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

ARCH and GARCH Models

Explores ARCH and GARCH models, volatility clustering, time series, estimation, and filtering steps in financial and macroeconomic contexts.

Market Response Functions

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

Gaussian Correlation Conjecture

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

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.

Maximum Likelihood Theory & Applications

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

Principal Component Analysis: Theory and Applications

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

Basics of Mobile Robotics: Uncertainties

Explores the fundamentals of mobile robotics, emphasizing uncertainties in localization, sensor fusion, and the Extended Kalman Filter.

Multivariate Statistics: Normal Distribution

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

Classification with GMM and kNN

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

Principal Component Analysis: Dimension Reduction

Covers Principal Component Analysis for dimension reduction in biological data, focusing on visualization and pattern identification.

Multivariate Statistics: Normal Distribution

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

Common Distributions: Moments and MGFs

Covers common distributions, moment generating functions, and covariance matrices in statistics for data science.