# Re: Optimal Prediction

From: Hal Finney <hal.domain.name.hidden>
Date: Fri, 29 Mar 2002 09:36:10 -0800

Sorry, I mis-edited that message. Here it is cleaned up for clarity:

Bill Jefferys writes, quoting Hal Finney:
> >But not always. You give the example of a strongly biased coin being
> >a simpler hypothesis than a fair coin. I don't think that is what
> >most people mean by "simpler". If anything, the fair coin seems like
> >a simpler hypothesis (by the common meaning) since a biased coin has a
> >parameter to tweak, the degree of bias.

> Depends on whether you know the degree of bias. If you are choosing
> between a two-headed coin and a fair coin, the two-headed coin is
> simpler since it can explain only one outcome, whereas a fair coin
> would be consistent with any outcome. On the other hand, if you don't
> know the bias, then between a fair coin and a coin with unknown bias,
> the fair coin is simpler. This automatically pops out when you do the
> analysis.

That's true, but even so, a coin with a .95 chance of coming up heads
and a .05 chance of coming up tails is "simpler" by your definition
than a fair coin, right? Even though the parameter is not adjustable,
the presence of an ad hoc value like .95 makes it seem intuitively less
simple than a fair coin, at least to me.

Hal Finney
Received on Fri Mar 29 2002 - 09:48:25 PST

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