kent_allard_jr: (Default)
kent_allard_jr ([personal profile] kent_allard_jr) wrote2010-09-20 01:32 pm
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Fun with Bayes!

I'm always happy when xkcd does stat jokes:

'Dude, wait -- I'm not American! So my risk is basically zero!'

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?
avram: (Default)

[personal profile] avram 2010-09-20 07:58 pm (UTC)(link)
Taking the US population as 300 million (to make the math easy), that'd mean that 150 Americans know that statistic, and if one in six of them dies (I'm assuming that Munroe means rate of death by lightning strike even though he just says death rate) of lightning strike in a year, that's 25/year who know the statistic and die.

Taking the cartoon's stated figure of 45 Americans killed by lightning each year, which should include the 25 described above, that means that 55% of lightning deaths are people who know the statistic.

[identity profile] kent-allard-jr.livejournal.com 2010-09-20 08:31 pm (UTC)(link)
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.

[identity profile] kokoinai.livejournal.com 2010-09-21 01:00 am (UTC)(link)
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: (Default)

[personal profile] avram 2010-09-21 01:42 am (UTC)(link)
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.

[identity profile] feiran.livejournal.com 2010-09-21 01:12 am (UTC)(link)
Bayes FTW. I miss stats class. :)

[identity profile] bigscary.livejournal.com 2010-09-21 01:23 pm (UTC)(link)
Go into epidemiology, use stat always and forever.