sigmoid as a posterior

[Dr James W Kay]

Note the connection with the work of the late J.A.Anderson within the statistical community.

In his paper on logistic discrimination(Biometrika 1972, 59,19-35),
he modelled the posterior probabilities directly using logistic functions.
While this includes the Gaussian, equal covariance, situation as a special case,
it is more general.. and of course his formulation could today be directly implemented as an ANN.

In his paper he cites earlier related work by Cox, Day and Kerridge.

He uses maximum likelihood to "learn the weights", but later he advocated the
use of penalised maximum likelihood(or Bayesian or Regularisation, by other names).

It is easy to see how additional hidden units could be incorporated within this
framework and this would ess
be essentially a version of projection pursuit logistic discrimination.

JIm Kay