>By what rational means do we apply the precise
>mathematical model of
>Bayes to items in the real world,
>especially when those items are as
>obscenely complex and chaotic as human ideas?
I agree that in the real world applying Bayesian methods is hideously
complex, with so many variable to consider (observational weighting,
observers bias, publication bias, experimental error, non-quantifiable
information, etc.) But look at it this way: We have to use some kind of
inference system. What's the alternative?
Also, the case against non-Bayesian methods is a bit stronger than you put
it. If somebody is using non-Bayesian methods it is always possible to cook
up a set of bets such that the agent will accept each one but when you add
all the bets together the risks cancel each other out and the non-Bayesian
agent is guaranteed a loss. This is called "Dutch book". It can be applied
to any system where the bets are quantifiable, which includes basically
anything where money is involved (insurance, futures, stocks) and not just
simple probablistic situations. It's not that a Bayesian outcompetes a
non-Bayesian in simple probability problems; it's that a Bayesian can take a
non-Bayesian to the cleaners whenever money must be staked on an unclear
outcome.
The real-world defense against Dutch book is that in order to lure somebody
into Dutch book you must be able to predict their inference process.