Formal Decisioning System

Context:
- It can be proposed by a Decision Theory Researcher.
- It can include a Decision Utility Function.
- It can be a Task Input to a Decisioning Task.
- …
Example(s):
- a Causal Decision Theory.
- an Economic Decision Theory, such as Rational Choice Theory.
- a Moral Decision Theory.
- …
Counter-Example(s):
- a Statistical Decision Theory.
- a Probability Theory.
- an Epistemic Utility Theory.
See: Inference Step, Decision Step, Course of Action.

References

(Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Decision_theory
- Decision theory in economics, psychology, philosophy, mathematics, and statistics is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision. It is closely related to the field of game theory as to interactions of agents with at least partially conflicting interests whose decisions affect each other.

http://plato.stanford.edu/entries/epistemic-utility/
- Traditional utility theory (also known as decision theory) explores a particular strategy for establishing the norms that govern which actions it is rational for us to perform in a given situation. The framework for the theory includes states of the world, actions, and, for each agent, a utility function, which takes a state of the world and an action and returns a measure of the extent to which the agent values the outcome of performing that action at that world. We call this measure the utility of the outcome at the world. …

(Bishop, 2006) ⇒ Christopher M. Bishop. (2006). “Pattern Recognition and Machine Learning." Springer, Information Science and Statistics. ISBN:0387310738
- QUOTE: We have seen in Section 1.2 how probability theory provides us with a consistent mathematical framework for quantifying and manipulating uncertainty. Here we turn to the discussion of decision theory that, when combined with probability theory, allows us to make optimal decisions in situations involving uncertainty such as those encountered in pattern recognition.
  Suppose we have an input vector [math]\displaystyle{ \bf{x} }[/math] together with a corresponding vector [math]\displaystyle{ \bf{t} }[/math] of target variables, and our goal is to predict [math]\displaystyle{ \bf{t} }[/math] given a new value for [math]\displaystyle{ \bf{x} }[/math]. For regression problems, [math]\displaystyle{ \bf{t} }[/math] will comprise continuous variables, whereas for classification problems [math]\displaystyle{ \bf{t} }[/math] will represent class labels. The joint probability distribution [math]\displaystyle{ p(\bf{x},\bf{t}) }[/math] provide a complete summary of the uncertainty associated with these variables. . …

(Raiffa, 1974) ⇒ Howard Raiffa. (1974). “Applied Statistical Decision Theory." Harvard University. ISBN:0875840175