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Chi-Square Tests: Expected Counts, Association, and Effect Size
Pearson's chi-square statistic compares observed counts with counts expected under a null model. The approximation depends on the sampling design and expecte...
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Heteroskedasticity: What Changes and What Does Not
Heteroskedasticity changes the conditional variance of regression errors. It does not by itself bias OLS coefficients when the conditional mean is correctly ...
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Machine Learning in Climate Science: Where It Helps and Where It Fails
Machine learning can emulate expensive climate-model components, extract structure from observations, and improve some forecasts, but it does not replace phy...
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Predictive Maintenance: From Sensors to Decisions
Predictive maintenance is a decision problem built on condition monitoring, diagnostics, prognostics, and maintenance economics. Model accuracy alone does no...
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One-Way vs Two-Way ANOVA: The Linear-Model View
One-way and two-way ANOVA are linear models with categorical predictors. Two-way ANOVA adds a second factor and, crucially, an interaction term whose interpr...
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Multiple Testing: Bonferroni, Holm, and False Discovery Rate
Multiple testing is not one problem with one correction. Bonferroni and Holm control family-wise error, while Benjamini-Hochberg controls false discovery rat...
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Kolmogorov-Smirnov Goodness-of-Fit: What the Test Actually Assumes
The Kolmogorov-Smirnov statistic measures the largest gap between cumulative distributions, but its null distribution changes when model parameters are estim...
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Maximum Likelihood Estimation: What It Guarantees and What It Does Not
Maximum likelihood is an estimation principle, not a guarantee of truth. Its properties depend on identifiability, regularity, model specification, and the g...
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Causality Beyond Correlation: Identification, DAGs, and Bias
Correlation is not causation, but the deeper question is how a causal effect becomes identifiable from a combination of design, assumptions, and data.
Read articleModel Drift in Production: Case Studies
Machine learning models degrade over time due to model drift, which includes data drift, concept drift, and feature drift. Learn how to detect, measure, and ...
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