- Contemporary messages sorted: [ by date ] [ by thread ] [ by subject ] [ by author ] [ by messages with attachments ]

From: <GSLevy.domain.name.hidden>

Date: Wed, 19 May 1999 01:04:49 EDT

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.

George :-)

Received on Tue May 18 1999 - 22:06:24 PDT

Date: Wed, 19 May 1999 01:04:49 EDT

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.

George :-)

Received on Tue May 18 1999 - 22:06:24 PDT

*
This archive was generated by hypermail 2.3.0
: Fri Feb 16 2018 - 13:20:06 PST
*