On 4 May 2001 04:11:23 -0700, [EMAIL PROTECTED] (Will Hopkins)
wrote:
>For example, I might believe that the individual's true score is 70 units,
>and that the likely range is +/- 10 units. So what describes
>"likely"? 90%, 95%, 99%...? Do Bayesians have any validated way to work
>that out? If they don't, then the whole Bayesian edifice might just come
>crashing down. I put this to a Bayesian who has been helping me, but I
>have received no reply from him since I sent the message, so I suspect the
>worst.
It's hard to get the value very accurately, but the appropriate way is
to look at betting behaviour. If you're claiming a 50% belief that
the value is between 60 and 80, then you should be indifferent to
accepting a bet at even odds of the value being inside or outside that
interval. For other levels, it would be a bet with different odds:
e.g. you'd be willing to offer or accept 9 to 1 odds that it is in
your 90% interval.
Of course, there are other psychological things affecting the decision
to accept or reject such a bet (can I afford to lose? Is winning
worth the trouble of thinking about it? Do I think gambling is
immoral? etc.), but the idea of indifference to each alternative is
the key idea.
Duncan Murdoch
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