Linear Independence: Covariance and Statistical Dependence

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Independence and Covariance

Explores independence and covariance between random variables, discussing their implications and calculation methods.

Dependence Concepts and Copulas

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

Principal Component Analysis: Introduction

Introduces Principal Component Analysis, focusing on maximizing variance in linear combinations to summarize data effectively.

Probabilistic Linear Regression

Explores probabilistic linear regression, covering joint and conditional probability, ridge regression, and overfitting mitigation.

Causal Systems & Transforms: Delay Operator Interpretation

Covers z Variable as a Delay Operator, realizable systems, probability theory, stochastic processes, and Hilbert Spaces.

Maximum Likelihood Estimation: Multivariate Statistics

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

Multivariate Gaussian Laws

Explores multivariate Gaussian laws, covering probabilities, correlations, and conditional distributions in bivariate cases.

Understanding Statistics & Experimental Design

Explores t-tests, confidence intervals, ANOVA, and hypothesis testing in statistics, emphasizing the importance of avoiding false discoveries and understanding the logic behind statistical tests.

Propagation of Uncertainty: Estimation and Distribution

Discusses estimation and propagation of uncertainty in random variables and the importance of managing uncertainty in statistical analysis.

Multivariate Statistics: Conditional Distributions

Covers conditional distributions and correlations in multivariate statistics, including partial variance and covariance, with applications to non-normal distributions.