Bayes' theorem in the form that actually matters day to day: why a 99%-accurate test on a rare condition is still usually wrong, why doctors and juries fall for the same reasoning error, and how the same math runs underneath spam filters and alert triage. Priors, likelihoods, and posteriors made concrete with natural-frequency arithmetic instead of symbol-pushing.
Statistics
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Bayes' Theorem for Engineers: The Base-Rate Trap That Fools Doctors, Juries, and Alert Dashboards -
Bayesian Statistics for Engineers Bayesian and frequentist statistics answer different questions, and engineers benefit from knowing which question they are actually asking. This post walks through priors, conjugate posteriors, a worked Bayesian A/B test, MCMC at a working level, and where Bayesian reasoning genuinely beats classical inference.
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Monte Carlo Methods: Simulating Your Way Out of Hard Math When a closed-form solution does not exist or is not worth finding, random sampling is the most practical path forward. This post covers the core theory of Monte Carlo estimation — convergence, variance reduction, PRNG discipline — and applies it to portfolio Value at Risk, infrastructure reliability, and capacity planning, with a full Python walkthrough using numpy.
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Portfolio Optimization in Python: Mean-Variance, Risk Parity, and the Covariance Problem Markowitz's mean-variance framework is mathematically elegant and practically treacherous. This post works through the geometry of the efficient frontier, the statistical nightmare of covariance estimation at scale, risk parity as the practitioner's escape hatch, and Python implementations that are honest about what "optimal" actually buys you in live trading.
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Risk Metrics for Engineers: VaR, Sharpe, Sortino, and Max Drawdown Sharpe, Sortino, VaR, CVaR, and max drawdown — each metric captures one slice of portfolio risk while hiding another. This guide explains what each measures, how to compute them in pandas, and where every single one will mislead you.
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R for Data Analysis: A Practical Guide for Engineers A technically honest guide to R for experienced engineers and data practitioners — covering Tidyverse, ggplot2, R Markdown, Shiny, statistical modeling, and a frank R vs Python comparison.