Decision making
Nathan Huntley, Robert Hable, Matthias C. M. Troffaes · Wiley series in probability and statistics · 2014
This chapter begins by discussing a single choice under uncertainty: the subject must choose one of a number of possible actions, each of which leads to an uncertain reward. It discusses sequential decision problems where the subject has to make more than one decision, at different times. An introductory overview of some simple approaches that can be applied using coherent lower previsions is provided in the chapter. Ellsberg's paradox is a simple example that shows that the presence of complex uncertainty, that is uncertainty about the true probabilities, and leads to situations where reasonable behaviour can violate the classical axioms of subjective expected utility, namely the so-called sure-thing principle. It is common to formalize Bayesian statistical problems by use of decision theory. In order to increase the reliability of statistical conclusions, a theory of robust Bayesian statistics has been developed.