Comments on: Understanding Bayes Theorem With Ratios https://betterexplained.com/articles/understanding-bayes-theorem-with-ratios/ Math lessons that click Sat, 13 Aug 2022 16:50:12 +0000 hourly 1 By: Thoughts on the 2020 Democratic presidential primary – Unexpected Values https://betterexplained.com/articles/understanding-bayes-theorem-with-ratios/#comment-393096 Mon, 19 Apr 2021 19:53:04 +0000 http://betterexplained.com/?p=2939#comment-393096 […] Now, how do we actually estimate ? We need to model the fact that if a candidate is really unlikely to win — or almost guaranteed to win — a vote for that candidate isn’t all that likely to change the probability that they win, as compared to if the outcome is very uncertain. The best way I know of doing this is to think of a vote as changing the odds — rather than the probability — of a candidate winning by a constant factor. That is, if the odds of a candidate winning are , then an additional vote for the candidate changes those odds to for some small independent of the candidate. This model is well-motivated by Bayes’ theorem. […]

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]]> By: Steven Scott https://betterexplained.com/articles/understanding-bayes-theorem-with-ratios/#comment-336114 Wed, 08 Nov 2017 02:10:47 +0000 http://betterexplained.com/?p=2939#comment-336114 In the spam filter example, how is it that the old odds were just multiplied by the new odds, instead of first calculating the evidence adjustment (as in the deer/bear example) of each word and then multiplying that by the old odds?

To me, it appears the ‘hello’ evidence adjustment is 1:9 ((3:3) / (9:1) = 1 / 9 = 1:9), so, when the spam filter sees an email message with ‘hello’ the initial 9:1 old odds of it being spam adjust to 9:1 * 1:9 = 1:1 (old odds * evidence adjustment = new odds).

Therefore, the following evidence adjustments…
Hello = 1:9
Darling = 1:45
Buy = 1:6
Viagra = 1:3 (when occurring in 1 normal email)

…so, ‘hello darling’ would result in a final adjustment of 9:1 * 1:9 * 1:45 .

Doesn’t seem right, can someone explain?

]]> By: Laura Houghton https://betterexplained.com/articles/understanding-bayes-theorem-with-ratios/#comment-335198 Tue, 06 Jun 2017 10:14:49 +0000 http://betterexplained.com/?p=2939#comment-335198 I’m a bit confused…Shouldn’t it be:

P(event and evidence) = P(event) * P(evidence implies event) = P(event) * P(evidence|event).

?

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