Fun with Bayes!

[kent_allard_jr]

I'm always happy when xkcd does stat jokes:



I may talk about Bayes' Theorem in class this semester (the first time I'll be doing so). For those who enjoy these little games... Assume only 1 in 2 million Americans knows 'that statistic.' If you walk down the road and find an American killed by lightening, what's the chance that he knew it?

Comments

[kent-allard-jr.livejournal.com]

My result was close: I said P(A) was the chance of dying by lighting strike (1/7,000,000), P(A|B) was the chance of dying if you knew the stat (1/6) and P(B) was the chance of knowing the stat (1/2,000,000). Plug 'em into Bayes and you get (1/6)*(1/2,000,000)/(1/7,000,000)=7/12 or 58%. Since I never studied Bayesian Statistics, though, I may be doing something wrong here.

[kokoinai.livejournal.com]

The discrepancy is from agrumer's population assumption. 45 * 7mil is 315mil: using agrumer's method with 315mil yields exactly 58.33333333333... which is 7/12ths. Math works!

[avram]

But 315 million is high; most sources I'm seeing report somewhere in the 307-310 million range.

I figure our estimates are close enough, given the imprecision of the data sources.

[feiran.livejournal.com]

Bayes FTW. I miss stats class. :)

[bigscary.livejournal.com]

Go into epidemiology, use stat always and forever.