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Mathematical Models of Inequality: Understanding Lorenz Curves and Gini Coefficients
This article delves into mathematical models of inequality, focusing on the Lorenz curve and Gini coefficient to measure and interpret economic disparities.
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Statistics and Machine Learning: Where the Boundary Actually Lies
Statistics and machine learning overlap heavily, but neither is simply a subset of the other. The useful distinction is in the questions, loss functions, ass...
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Multiple Imputation: What It Gets Right, What Can Go Wrong
Multiple imputation is neither a universal cure for missing data nor an indefensible fiction. Its validity depends on the missingness assumptions, the imputa...
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ROC and Precision-Recall Under Class Imbalance
ROC and precision-recall curves answer different questions under class imbalance. ROC AUC does not become invalid when prevalence is low, but precision expos...
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Understanding Splines: What They Are and How They Are Used in Data Analysis
Splines are powerful tools for modeling complex, nonlinear relationships in data. In this article, we'll explore what splines are, how they work, and how the...
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Shapiro-Wilk vs. Anderson-Darling: What Normality Tests Can and Cannot Tell You
Shapiro-Wilk and Anderson-Darling are useful diagnostics for normality, but choosing between them by sample-size thresholds is misleading. The real question ...
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Hypatia of Alexandria: Mathematics, Teaching, and Historical Evidence
Hypatia of Alexandria was a mathematician, astronomer, and Neoplatonist teacher whose surviving historical record points more clearly to commentary, teaching...
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Calculus: Understanding Derivatives and Integrals
Dive into the world of calculus, where derivatives and integrals are used to analyze change and calculate areas under curves. Learn about these fundamental t...
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Kurt Gödel: Completeness, Incompleteness, and Formal Systems
Kurt Gödel transformed mathematical logic through the completeness theorem, incompleteness theorems, consistency results for set theory, and a surprising sol...
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David Hilbert: Problems, Axioms, and Mathematical Foundations
David Hilbert reshaped algebra, geometry, analysis, mathematical logic, and the research agenda of twentieth-century mathematics through his axiomatic method...
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