In a message dated 99-05-18 17:15:37 EDT, Jacques Mallah writes:
<< You don't seem to understand: that's NOT how to take an
expectation value. It bears little resemblance to the formula for an
expectation value, regardless of what "the distribution of m" is. >>
The concept of scales and distributions are kind of related: having a uniform
distribution over a logarithmic scale is equivalent to having an exponential
distribution over a linear scale.
The result if a calculation of an expectation value is predicated on the
scale used. For example if the expectation value of the sound intensity is
desired it could be calculated either using watts or using decibels with
vastly different results since the sound intensity in decibels has a
logarithmic relationship with its intensity in energy units. There are
numerous other examples in physics in which logarithmic scales run parallel
to linear scales. Who is to say that one particular scale is more "natural"
than the other? In monetary terms are dollars more natural than francs? Is
present day capital more natural than future compounded capital? Or is future
capital more natural than interest? (they bear an exponential relationship).
I still maintain that the scale issue in the Bayesian problem comes in the
back door and must be dealt with. In the Bayesian case, the problem itself
defines the scale to be used. And selecting a logarithmic scale (for example)
guarantees that the expectation value of the box not chosen is exactly equal
to m, which agrees with common sense.
<< I'm not your enemy, any more than NATO is the enemy of the Serbian
people. But I am your opponent in this debate.
Neither have you earned my friendship.>>
In so far as friendship is concerned, I believe that if we continue to have a
vigorous and honest conversation, it will come naturally.