Open thread, Mar. 16 - Mar. 22, 2015

MrMind

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If it's worth saying, but not worth its own post (even in Discussion), then it goes here.

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2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)

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I've just read Initation Ceremony. Is this really where Bayesian probability begins? Because I don't claim to understand it, but I worked it out easy enough, just not mentally but with calc.exe, using my usual method of assuming a sample of 100. So there are 100 people, 75 W and 25 M, 75x0.75=56.26 VW and 25x0.5 = 12.5 VM so our ratio is 12.5 to 56.26 so a 22.2% chance (Because only the Sith deal in incomprehensible verbal-math like " two to nine, or a probability of two-elevenths". Percentages are IMHO way more intuitive. I use a sample size of 100 precisely because then I can say of 100 people 56.26 are VW and thus 56.26% of a sample of any size.)

At what point "okay, let's calculate on a sample of 100" breaks down and I really need to learn the Bayes Theorem and its applications? Note: the sample-100 method works well with the other example of diagnostic methods giving false positives for rare illnesses.

It is also possible percentages are not as intuitive to others as to me. To me 22% is visualized as drawing a 10 by 10 square on a grid paper and paint 22 of the constituent squares black, then throwing darts on the square. Assuming darts cannot land outside the cube.

For calculations of conditional probabilities I've found an initial sample size of 10,000 is more manageable. But that's just me.

0Kindly11y

For numerical calculations, your method doesn't ever really break down and, moreover, Brennan is essentially doing the same thing you are, but with a sample of 16 people instead of 100 to make the math simple enough to do mentally. A more Bayes-theorem styled calculation tells us that we have 1:3 odds initially (as there are 1/4 men and 3/4 women) and the Virtuist evidence updates it by a factor of 2:3 (as Virtuists are 2/4 of men and 3/4 of women), so we end with 2:9 odds. I think this is easier than what either you or Brennan are doing, but it's a matter of taste and of what's more intuitive. (Which certainly varies from person to person; I find two-elevenths easier to grasp than 22.2%) Doing Bayesian calculations formally is more important where you are doing symbolic calculations, especially with continuous probability distributions. Edit: Also, 22.2% is wrong, which I didn't realize at first; it's 2/9, not 2/11. You want to compute 12.5/(12.5+56.25) instead.