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Customer Lifetime Value: Expected Future Contribution
Customer lifetime value is an expected discounted future contribution under assumptions about activity, retention, margin, censoring, and intervention.
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Monte Carlo Methods: Sampling, Error, and Variance Reduction
Monte Carlo methods approximate expectations with random samples. MCMC is one important special case, not a synonym for Monte Carlo.
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Probabilistic Programming and MCMC
Probabilistic programming separates model specification from inference, but inference still depends on diagnostics, geometry, and numerical stability.
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The Normal Distribution: Why the Bell Curve Appears
The normal distribution is important because of Gaussian models, additive noise, asymptotic approximations, and the central limit theorem—not because real da...
Read articleMarina Viazovska and the E8 Sphere-Packing Proof
Marina Viazovska solved the eight-dimensional sphere-packing problem by constructing the exact auxiliary function needed to prove optimality of the E8 lattice.
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Text Preprocessing in NLP: When Cleaning Helps and Hurts
Text preprocessing is model-dependent. Lowercasing, stemming, stop-word removal, normalization, and tokenization can help some pipelines and damage others.
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Mathematics of Machine Learning: Risk and Generalization
The mathematics of machine learning is a study of risk, approximation, optimization, and generalization under finite data.
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Data Engineering: Reliable Data Systems
Data engineering is the design of reliable data systems: ingestion, storage, contracts, transformations, orchestration, lineage, quality, and serving.
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Value at Risk and Expected Shortfall: Quantiles and Tail Risk
Value at Risk is a quantile of a loss distribution. Expected Shortfall averages the tail beyond that quantile. Both are model-dependent and require careful h...
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Data Science for Carbon Reduction: Measurement Before Optimization
Data science can support decarbonization, but credible carbon analysis starts with system boundaries, attribution, baselines, life-cycle accounting, and unce...
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