A deep dive into the seemingly contradictory behavior of Gaussian copulas: elevated density near corners versus zero asymptotic tail dependence.
A comprehensive guide to the Inverse Transform Sampling method and how to generate random samples from any distribution using uniform random numbers.
Learn about Gaussian copulas, vine copulas, and their applications in multivariate modeling with practical examples and implementation details.
Learn how copulas allow you to model dependence structures independently from marginal distributions, with detailed explanations of Gaussian and t-copulas.
Exploring how scDesign3 uses Gaussian and vine copulas to model complex dependencies between genes in single-cell RNA sequencing data.
A comprehensive mathematical exploration of how copulas connect marginal distributions to create joint densities, with rigorous proofs and practical examples.
Learn how the Clayton copula conditional sampling formula works, why it has that specific form, and see it in action with step-by-step numeric examples.
Understanding the relationship between copula fitting and batch effects in scDesign3, and why the order of operations is critical for meaningful simulation.
Understanding the difference between multivariate normal distributions and Gaussian copulas, with practical Python implementations.
A step-by-step mathematical derivation of Kendall's Tau correlation coefficient, showing how concordant and discordant pairs lead to the elegant sgn function formula.