Inferring Probabilistic Theories from Data

Edwin P. D. Pednault

When formulating a theory based on observations influenced by noise or other sources of uncertainty, it becomes necessary to decide whether the proposed theory agrees with the data "well enough." This paper presents a criterion for making this judgement. The criterion is based on a gambling scenario involving an infinite sequence of observations. In addition, a rule derived from the idea of minimal-length representations is presented for selecting an appropriate theory based on a finite set of observations. A proof is briefly outlined demonstrating that the theories selected by the rule obey the success criterion given a sufficient number of observations.

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