Probability

Reasoning about uncertainty, from Bayes and the central limit theorem to the puzzles that break everyone’s intuition the first time.

7 articles, newest first.

• Evaluation · Jun 18, 2026 · 7 min Your model says 90%. Should anyone believe it? Probability calibration: why good classifiers output bad probabilities, how to see it with a reliability curve, and when Platt scaling or isotonic regression fixes it.
• Reasoning under uncertainty · Part 10 of 33 · 7 min Markov chains, from states to stationary distributions What a Markov chain is, why the memoryless assumption is less crazy than it sounds, how a chain settles into a long-run distribution, and where you meet one in real work.
• Reasoning under uncertainty · Part 9 of 33 · 7 min Entropy, or how to measure surprise Information as surprise, why bits fall out of a logarithm, and the straight line from there to the cross-entropy loss you train with and the splits a decision tree picks.
• Reasoning under uncertainty · Part 6 of 33 · 7 min The central limit theorem, from first principles Why sums of many small independent effects turn into a bell curve, what the theorem promises about sample means, where it fails, and why "n > 30" is folklore.
• Reasoning under uncertainty · Part 8 of 33 · 11 min Monte Carlo methods: answering hard questions by rolling dice When the maths is too hard, sample instead. What Monte Carlo is from first principles, why error falls as one over root n, and where it earns its keep in real work.
• Reasoning under uncertainty · Part 5 of 33 · 6 min Bayes theorem from first principles Bayes as areas and counts rather than a formula: the medical-test example worked properly, why base rates dominate, and where the idea earns its keep in practice.
• Reasoning under uncertainty · Part 4 of 33 · 7 min The Monty Hall problem, and why switching wins Three doors, one car, a host who knows where it is. Switching wins two thirds of the time — here is the intuition, the enumeration, and the lesson underneath it.