Bayesian Methods in Health Economics

80 Bayesian Methods in Health Economics

the set of outcomes O =Ω×T,theexpected utility U : T→R asso-

ciates a unique numerical value with each option t. This is consistent with

the marginalisation process operated on the uncertainty about the random

quantities on Ω.

As remarked by Spiegelhalter et al. (2004), the frequentist version of de-

cision theory does not produce an average with respect to prior or posterior

distributions. Thus, the decision-making strategy generally maximises the util-

ity, whatever the “true” value of the parameter might be. This can be thought

of as assuming the most pessimistic prior distribution.

The Bayesian procedure can ...