While the axiomatic introduction of a probability distribution over a space
is common, its use for making predictions, using physical theories and prior
knowledge, suffers from a lack of formalization. We propose to introduce, in
the space of all probability distributions, two operations, the OR and the AND
operation, that bring to the space the necessary structure for making
inferences on possible values of physical parameters. While physical theories
are often asumed to be analytical, we argue that consistent inference needs to
replace analytical theories by probability distributions over the parameter
space, and we propose a systematic way of obtaining such "theoretical
correlations", using the OR operation on the results of physical experiments.
Predicting the outcome of an experiment or solving "inverse problems" are then
examples of the use of the AND operation. This leads to a simple and complete
mathematical basis for general physical inference.Comment: 24 pages, 4 figure
