Deriving the Poisson Log-Likelihood and MLEs for Single-Cell RNA-seq
A step-by-step derivation of the Poisson log-likelihood and maximum likelihood estimators for gene expression counts in single-cell data.
Nov 17, 2025
Understanding edgeR: A Deep Dive into Statistical Methods for RNA-seq Differential Expression Analysis
A comprehensive technical guide to edgeR's statistical framework, covering dispersion estimation, differential expression testing, and quasi-likelihood F-tests with detailed numeric examples.
May 27, 2025
Why Gaussian Copulas Look Dense at Corners but Have Zero Tail Dependence
A deep dive into the seemingly contradictory behavior of Gaussian copulas: elevated density near corners versus zero asymptotic tail dependence.
Mar 22, 2025
Understanding Inverse Transform Sampling: From Theory to Practice
A comprehensive guide to the Inverse Transform Sampling method and how to generate random samples from any distribution using uniform random numbers.
Mar 22, 2025
Understanding Gaussian Copulas and Vine Copulas
Learn about Gaussian copulas, vine copulas, and their applications in multivariate modeling with practical examples and implementation details.
Mar 22, 2025
Understanding Copulas: Separating Dependence from Marginal Distributions
Learn how copulas allow you to model dependence structures independently from marginal distributions, with detailed explanations of Gaussian and t-copulas.
Mar 22, 2025
Understanding Copulas in scDesign3: From Gaussian to Vine Copulas
Exploring how scDesign3 uses Gaussian and vine copulas to model complex dependencies between genes in single-cell RNA sequencing data.
Mar 22, 2025
Understanding Copulas and Joint Densities: From Theory to Practice
A comprehensive mathematical exploration of how copulas connect marginal distributions to create joint densities, with rigorous proofs and practical examples.
Mar 22, 2025
Understanding Clayton Copula Conditional Sampling: From Theory to Practice
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.
Mar 22, 2025
Is the Copula Independent of Batch Effects in scDesign3?
Understanding the relationship between copula fitting and batch effects in scDesign3, and why the order of operations is critical for meaningful simulation.
Mar 22, 2025