[I]t now appears that from a fundamental standpoint loss functions are less firmly grounded than are prior probabilities. This is just the opposite of the view that propelled the Wald-inspired development of decision theory in the 1950s, when priors [prior probabilities] were regarded as vague and ill-defined, but nobody seemed to notice that loss functions are far more so. For reasons we cannot explain, loss functions appeared to workers at that time to be "real" and definite, although no principles for determining them were ever given, beyond the truism that any function with a continuous derivative appears linear if we examine a sufficiently small piece of it.
In the meantime, there have been several advances in the technique for assigning priors by logical analysis of prior information. But, to the best of our knowledge, we have as yet no formal principles at all for assigning numerical values to loss functions; not even when the criterion is purely economic, because the utility function of money remains ill-defined.
Friday, October 29, 2004
Inference Is Better-Grounded than Choice; and Analysis of Evidence Is More Secure than Economic Analysis -- Is It So?
E.T. Haynes, PROBABILITY OF THEORY: THE LOGIC OF SCIENCE Section 13.12.4 at 424 (2003):