🟦🎬 Bayes theorem, the geometry of changing beliefs

Tuesday 21 October, home at 21:40 from 🎓 Lecture 14 - Updating beliefs with Bayes with a formula I could copy and not use. Rasmus sent the link on the tram. Fifteen minutes of animation by a mathematician who draws everything in blue and brown. It stayed. That was the win for the day and I wrote it down as two words.

The picture

He takes the old puzzle from 🔬 Judgment under Uncertainty - Heuristics and Biases: a shy, tidy man called Steve, and is he more likely a librarian or a farmer? Everybody says librarian. Then he draws the people.

• Say there are about twenty farmers for every librarian. Draw 10 librarians and 200 farmers.
• Suppose the description fits 40 percent of librarians and 10 percent of farmers. That is 4 librarians and 20 farmers.
• So of the 24 people who fit, 4 are librarians. About one in six. The description made librarian more likely than it was and still left it unlikely.

Then he turns the people into a square: the width is split by the prior, each strip is filled to the height of its likelihood, and the answer is one shaded area as a share of all the shaded area. The formula in 📐 Bayes' rule is that picture written sideways.

What changed in my head

• Evidence does not decide what I believe. It moves what I believed already. If I never wrote down where I started, I cannot say how far I moved.
• The mistake is nearly always forgetting the wide strip: 🔤 Base rate, 🧩 Base-rate neglect.
• He says outright that the point is not to be good at plugging in numbers. It is to remember there was a ratio at all.

Filed with 00. Statistics for Product Decisions II Hub.

Rewatched

• 8 December. The night before 📌 Statistics II - Final exam. Drew the square four times from memory with different numbers. It came up in question 3 and I drew it in the margin first.
• 18 November. The evening Hana Kobayashi caught the confounded variable in my port delay project. We ended up drawing the square on the back of the printout to settle a different argument: whether a carrier's one bad month should move its score. It should, a little.
• 27 October. Before the Bayes quiz. 7 of 10. The three I lost were arithmetic, not the picture.
• 21 October. First time, at the kitchen table with the lecture handout face down.

Times watched: 4

Concepts & Permanent Notes: 🔤 Prior · 🔭 Bayesian thinking for product bets · 📌 Statistics II - Bayes quiz · 💎 A number without its base rate is a story