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Traffic Crash KDE: Density Is Not Risk
Kernel density estimation can map concentrations of traffic crashes, but crash density is not crash risk unless exposure and road-network geometry are accoun...
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Bayesian Workflow: From Priors to Posterior Predictive Checks
A practical Bayesian workflow begins before posterior sampling: specify the generative model, test priors with simulated data, inspect computation, check pos...
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Julia Robinson: Diophantine Equations and Hilbert's Tenth Problem
Julia Robinson's work on definability and Diophantine equations was central to the Davis-Putnam-Robinson-Matiyasevich theorem that resolved Hilbert's Tenth P...
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PDEs for Data Scientists: Forward Models, Inverse Problems, and Physics
Partial differential equations matter in data science when data are observations of a spatial-temporal physical system. The key problems are forward simulati...
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Ordinal Regression: Proportional Odds and Marginal Effects
Ordinal regression models cumulative probabilities without pretending ordered categories have equal spacing. This article derives the proportional-odds model...
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Katherine Johnson: Trajectories, Orbital Mechanics, and NASA
Katherine Johnson was a NASA research mathematician whose trajectory analysis, orbital calculations, and verification work supported Project Mercury, Apollo,...
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Predictive Maintenance in Practice: Data, Validation, and Deployment
Predictive-maintenance projects fail as often in data construction and deployment as in modeling. This companion article focuses on labels, censoring, featur...
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Data Visualization Best Practices
Discover best practices for creating clear and compelling data visualizations that communicate insights effectively.
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Applying Hypothesis Testing in the Real World
See how hypothesis testing helps draw meaningful conclusions from data in practical scenarios.
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Bayesian Inference Explained
Explore the fundamentals of Bayesian inference and how prior beliefs combine with data to form posterior conclusions.
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