No abstract

The use of the conjugacy property for members of the exponential family of distributions is commonplace within Bayesian statistical analysis, allowing for tractable and simple solutions to problems of inference. However, despite a shared motivation, there has been little previous development of a similar property for using utility functions within a Bayesian decision analysis. As such, this article explores a class of utility functions that appear to be reasonable for modeling the preferences of a decisionmaker in many real‐life situations, but that also permit a tractable and simple analysis within sequential decision problems.

Accurate information sources are vital prerequisites for good decision making. In this thesis we consider a multiple participant setting, where all decision makers (DMs) have a collection of neighbours with whom they share their beliefs about some common relevant uncertain quantity. When determining which course of action to follow a DM takes into account all the information received from her neighbours. Over time, in light of the returns observed from choices made, DMs update their own beliefs over the uncertain event, and also adjust the degree of consideration that they afford to the opinions of each neighbour based on the level of reliability that the information they provide is ascertained to have. Much of this thesis is concerned with constructing a method that incorporates both of these learning facets in a dynamic fashion. This technique, termed the Plug-in approach, is motivated and derived, and attempts are made to justify its use by consideration of some attractive properties it obeys, in addition to studies conducted using both simulated and real data which compared its performance to some rational alternatives. Generalisations of this method are also provided to a setting where DMs specify their opinions nonparametrically rather than using probability distributions, as well as in a group setting where utilities as well as opinions must be amalgamated. Two subjective approaches are also briefly discussed, before we conclude with numerous suggestions for further research in this field.