Neural Networks and statistics (was Re: ANN - Tiberius V2.8 now released)

beliavsky_at_aol.com
Date: 01/26/05 

Date: 26 Jan 2005 06:12:39 -0800

Yaroslav Bulatov wrote:
>Perhaps off-topic, but what's the use of neural networks in
statistics?
>Since neural networks don't have probabilistic semantics, it's hard to
>do things like confidence intervals of predictions of neural networks,
>or to figure out exactly what sort of prior "Use Network X"
>represents....so when would a statistician need to bother with ANN's?

ANN's have been used to test for nonlinearity -- one can Google "test
nonlinearity neural network" for references.

For predicting continous, unbounded outputs, I prefer to use a "smooth
transition regression" (STR) instead of a neural network, because it
can more easily model a function that is locally linear, both in the
interior of the predictor space and in the tails. Besides papers than
can be found using Google, some good books covering STR's are

Non-Linear Time Series Models in Empirical Finance
by Philip Hans Franses, *** Van Dijk
Cambridge UP (2000)

Modelling Nonlinear Economic Relationships
by Clive W.J. Granger, Timo Terasvirta
Oxford UP (1993)

In 1-D, an STR with one transition point at x = d is just

f(x) = a + b*x + (a1 + b1*x)*g(c*(x-d)),

where g(x) is a transition function such as the logistic, with range
(0,1), or Gaussian, exp(-x^2).

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