# Bayes / Bayesian / Bayes’ Theorem

## Definition(s)

A general term used to describe Algorithms and other methods that estimate the overall Probability of some eventuality (e.g., that a Document is Relevant), based on the combination of evidence gleaned from separate observations. In Electronic Discovery, the most common evidence that is combined is the occurrence of particular words in a Document. For example, a Bayesian Algorithm might combine the evidence gleaned from the fact that a Document contains the words “credit,” “default,” and “swap” to indicate that there is a 99% Probability that the Document concerns financial derivatives, but only a 40% Probability if the words “credit” and “default,” but not “swap,” are present. The most elementary Bayesian Algorithm is Naïve Bayes; however most Algorithms dubbed “Bayesian” are more complex. Bayesian Algorithms are named after Bayes’ Theorem, coined by the 18th century mathematician, Thomas Bayes. Bayes’ Theorem derives the Probability of an outcome, given the evidence, from: (i) the probability of the outcome, independent of the evidence; (ii) the probability of the evidence, given the outcome; and (iii) the probability of the evidence, independent of the outcome. 1

## Notes

1. Maura R. Grossman and Gordon V. Cormack, EDRM page & The Grossman-Cormack Glossary of Technology-Assisted Review, with Foreword by John M. Facciola, U.S. Magistrate Judge2013 Fed. Cts. L. Rev. 7 (January 2013).