"John Uebersax" <[EMAIL PROTECTED]> wrote:
> The principle of indifference states "given no reason to think
> otherwise, consider all alternatives equally likely." The rub is
> that the set of alternatives can be structured in different ways.
The crucial issue is how to estimate the probability when the frequencies are
low. Laplace suggested that instead of computing the probability as n/N, one
should do something like n_a+1/(N+A), where A is the number of outcomes, n_a is
the count for outcome a, and N is the total outcome count.
Effectively, Laplace suggested a uniform prior in the Bayesian context. This
isn't "logical", but we use these things very often in machine learning, and we
obtain improved predictive accuracy. This is what we normally cite:
@inproceedings{,
author={Cestnik, B.},
title={Estimating probabilities: A crucial task in machine learning},
booktitle={Proc. 9th European Conference on Artificial Intelligence},
year={1990},
pages={147--149}
}
Aleks
.
.
=================================================================
Instructions for joining and leaving this list, remarks about the
problem of INAPPROPRIATE MESSAGES, and archives are available at:
. http://jse.stat.ncsu.edu/ .
=================================================================
