  This paper shows that the common method used for making predictions under
uncertainty in A1 and science is in error. This method is to use currently
available data to select the best model from a given class of models-this
process is called abduction-and then to use this model to make predictions
about future data. The correct method requires averaging over all the models to
make a prediction-we call this method transduction. Using transduction, an AI
system will not give misleading results when basing predictions on small
amounts of data, when no model is clearly best. For common classes of models we
show that the optimal solution can be given in closed form.
