A computation method in robust Bayesian decision theory

A Unied Bayesian Decision Theory

This paper provides new foundations for Bayesian Decision Theory based on a representation theorem for preferences de…ned on a set of prospects containing both factual and conditional possibilities. This use of a rich set of prospects not only provides a framework within which the main theoretical claims of Savage, Ramsey, Je¤rey and others can be stated and compared, but also allows for the po...

Bayesian Decision Making Theory

A Minimal Extension of Bayesian Decision Theory

Savage denied that Bayesian decision theory applies in large worlds. This paper proposes a minimal extension of Bayesian decision theory to a large-world context that evaluates an event E by assigning it a number π(E) that reduces to an orthodox probability for a class of measurable events. The Hurwicz criterion evaluates π(E) as a weighted arithmetic mean of its upper and lower probabilities, ...

Bayesian decision theory: A simple toy problem

We give here a comparison of the expected outcome theory, the expected utility theory, and the Bayesian decision theory, by way of a simple numerical toy problem in which we look at the investment willingness to avert a high impact low probability event. It will be found that for this toy problem the modeled investment willingness under the Bayesian decision theory is minimally three times high...

Game Theory, Maximum Entropy, Minimum Discrepancy and Robust Bayesian Decision Theory

We describe and develop a close relationship between two problems that have customarily been regarded as distinct: that of maximizing entropy, and that of minimizing worst-case expected loss. Using a formulation grounded in the equilibrium theory of zero-sum games between Decision Maker and Nature, these two problems are shown to be dual to each other, the solution to each providing that to the...