# Three Things I’ve Learned About Bayes’ Rule

source: https://ift.tt/dK5Hq3u tags: #literature uid: 202212101128 —

In the context of Bayes theorem 202212092211

Update Multiple Hypotheses

I tend to tell stories about evidence that cause me to under-update. For example, suppose I think I’m good at essay writing, but I am struggling to write a particular essay. The story I tell myself is, “I guess this essay was harder than I thought.” This story might be accurate, but it ignores that struggling is also evidence that I’m worse at writing than I thought.

Conditioning is Critical

I once read a story about someone (let’s call them Jane) trying to determine whether two people were courting. Jane observed the pair both going to a museum and having dinner. Jane estimated the prior odds that these people were courting at 1:20 and the odds ratios of “going to a museum” and “having dinner” to both be 10:1, arriving at a posterior of 100:20, or 5:1. The pair turned out to be siblings.

In theory, it is not a mistake to assign a high probability to a given false statement; it does suggest, however, that a mistake was made. Jane made a mistake in reasoning — subtle but damning. The first odds ratio Jane estimated was for “the pair went to a museum.” The second ratio Jane estimated should not have been for “the pair went to dinner”; it should have been for “the pair went to dinner, given that they had already gone to the museum.” The mistake Jane made was forgetting to condition when considering dependent pieces of evidence properly.

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