Lectures related to Principal Component Analysis: Introduction

Principal Components: Properties & Applications

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

Multivariate Statistics: Normal Distribution

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

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.

Dependence Concepts and Copulas

Explores dependence concepts, copulas, correlation fallacies, and rank correlations in statistics.

Copulas: Properties and Applications

Explores copulas in multivariate statistics, covering properties, fallacies, and applications in modeling dependence structures.

Principal Component Analysis: Properties and Applications

Explores Principal Component Analysis theory, properties, applications, and hypothesis testing in multivariate statistics.

Canonical Correlation Analysis: Overview

Covers Canonical Correlation Analysis, a method to find relationships between two sets of variables.

Maximum Likelihood Estimation: Multivariate Statistics

Explores maximum likelihood estimation and multivariate hypothesis testing, including challenges and strategies for testing multiple hypotheses.

Multivariate Statistics: Normal Distribution

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

Discriminant Analysis: Bayes Rule

Covers the Bayes discriminant rule for allocating individuals to populations based on measurements and prior probabilities.

Quantitative Risk Management: Distributions and Techniques

Covers distributions and techniques in Quantitative Risk Management for financial modeling.

Principal Component Analysis: Dimensionality Reduction

Covers Principal Component Analysis for dimensionality reduction, exploring its applications, limitations, and importance of choosing the right components.

Multivariate Statistics: Introduction and Methods

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

PCA: Directions of Largest Variance

Covers PCA, finding directions of largest variance, data dimensionality reduction, and limitations of PCA.

Elements of Statistics: Probability, Distributions, and Estimation

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

Multivariate Normal Distribution: Correlation and Covariance

Covers correlation, covariance, empirical estimates, eigenvalues, normality testing, and factor models.

Multivariate Methods I

Explores multivariate methods like PCA, SVD, PLS, and ICA for dimensionality reduction in functional brain imaging.

Multivariate Statistics: Introduction and Methods

Introduces major statistical methodologies for uncovering associations between vector components in multivariate data.

Clustering & Density Estimation

Covers clustering, PCA, LDA, K-means, GMM, KDE, and Mean Shift algorithms for density estimation and clustering.

Estimation Methods in Probability and Statistics

Discusses estimation methods in probability and statistics, focusing on maximum likelihood estimation and confidence intervals.