FIELD-THEORIES FOR LEARNING PROBABILITY-DISTRIBUTIONS

Imagine being shown N samples of random variables drawn independently from the same distribution. What can you say about the distribution? I n general, of course, the answer is nothing, unless you have some prio r notions about what to expect. From a Bayesian point of view one need s an a priori distribution on the space of possible probability distri butions, which defines st scalar field theory. In one dimension, free field theory with a normalization constraint provides a tractable form ulation of the problem, and we discuss generalizations to higher dimen sions.