Bayes Rule specifies how probabilities over parameters should be updated given any kind of information. But in some cases, the kind of information provided by both simulation and physical experiments is information on how certain output parameters may change when other input parameters are changed. There are three different approaches to this problem, one of which leads to the Garbage-In/garbage-out Paradox, the second of which violates the Borel Paradox, and the third of which is a supra-Bayesian heuristic. This paper shows (...) how to derive a fully Bayesian formula which avoids the Garbage-In/garbage-out and Borel Paradoxes. We also compare a Laplacian approximation of this formula with Bayesian synthesis and Bayesian melding and find that the Bayesian formula sometimes coincides with the Bayesian melding solution. (shrink)

Sometimes conducting an experiment to ascertain the state of a system changes the state of the system being measured. Kahneman & Tversky modelled this effect with ‘support theory’. Quantum physics models this effect with probability amplitude mechanics. As this paper shows, probability amplitude mechanics is similar to support theory. Additionally, Viscusi's proposed generalized expected utility model has an analogy in quantum mechanics.