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theory

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• noun (pl. theories) 1 a supposition or a system of ideas intended to explain something, especially one based on general principles independent of the thing to be explained. 2 an idea accounting for or justifying something. 3 a set of principles on which an activity is based. (Compact Oxford English Dictionary)

Decision theory is a formal theory of decision making under uncertainty. (Kathryn Blackmond Laskey, Department of Systems Engineering and Operations Research, George Mason University)

The approach to statistics which formally seeks to utilize prior information is called Bayesian analysis. Bayesian analysis and decision theory go rather naturally together, partly because of their common goal of utilizing nonexperimental sources of information, and partly because of some deep theoretical ties; thus, we will emphasize Bayesian decision theory in the book. Statistical Decision Theory and Bayesian Analysis by James O. Berger