Decision Algorithms, Bayes’ Theorem and Flow Graphs

Abstract

The paper concerns some relationships between decision algorithms, Bayes’ theorem and flow graphs. It is shown it this paper that every decision algorithm reveals probabilistic properties, particularly it satisfies the total probability theorem and Bayes’ theorem. This leads to a new look on Bayesian inference methodology, showing that Bayes’ theorem can be used to reason directly from data without referring to prior and posterior probabilities, inherently associated with Bayesian inference. Besides, a new form of Bayes’ theorem is introduced, based on the strength of decision rules, which simplifies essentially computations. Moreover it is shown that decision algorithms can be depicted in a form of a flow graph in which flow is ruled by the total probability theorem and Bayes’ theorem. This leads to a new class of flow networks, unlike to those introduced by Ford and Fulkerson. Interpretation of flow graphs as a kind of neural network is briefly discussed.