The conditional probability of A given B is my shepherd, I shall not want. It makes me multiply through marginal probabilities, it leadeth me beside flat priors...
And the people sang "P of A given B is equal to the prior probability of A times P of B given A over the marginal probability of B"
The trouble with applying Bayesianism in science is that your conclusion becomes dependent on what priors you think are reasonable. If different people disagree about that, then it becomes a debate about beliefs, not science. (Unless the priors can actually be determined, of course.)
This seems to largely be the case in climate issues, where it's clear that some people have such strong priors against anthropogenic climate change that the evidence needed to convince them outstrip what science reasonably can provide.
Would the climate issue thing be any different even if nobody applied any Bayesian methods and only went by frequentist statistics?
It's not that this is a problem with applying Bayesianism in science, it's that our thought is Bayesian on a fundamental level. And it couldn't be otherwise, at least not for beings as intelligent as humans.
I listened last year to a great set of lectures about the Philosophy of Science. Too much to go into here, save for the fact that, at the end of the day, it very well may end up that probabilities are all we have to go on for a wide swath of things.
I'm not yet ready to make the leap to total Bayesianism -- those priors can really bite you when you least expect it -- but there is some really good stuff here. Thanks Kaj.
Perhaps we'll see some kind of structured cross between Peirce and Bayes in the next few decades.
It's been a while since I've worked with conditional probabilities, but isn't he missing the case in which the headache is caused by both a cold and a tumor?
Yeah, but since that probability of that happening is the product of the two probabilities, it's probably not a big deal. If the two probabilities were each 75%, then you'd be in trouble.
And the people sang "P of A given B is equal to the prior probability of A times P of B given A over the marginal probability of B"