Avoiding both the Garbage-In/Garbage-Out and the Borel Paradox in updating probabilities given experimental information

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 (Bayesian...