I changed the subject line to make it more specific.
I think that Evidence is a tricky, slippery subject. It seems to be both
traces (i.e. records of something) and in many cases, inferences. Those
inferences probably shouldn't be called evidence, but they are the
reason that some data are considered evidence, and others not, and hence
often get included.
To take the radiology example below
So evidence is a function of the facts, the
analysis method, the method of inference, and perhaps even the
observer (e.g., if the evidence is a radiology image or physical
exam, there is inter-observer variation).
And it's definitely necessary to relate the hypotheses to the
evidence with probabilities
I would suggest that the interpretation of the evidence is a function of
the facts (plus other things). However, the facts are not stable (e.g.
with a physical examination) and may conflict with each other; therefore
inconsistency is not a just a matter of which inference procedure you
choose, it is also a matter of which facts (your premises) you start from.
It is also not "definitely necessary to relate hypotheses to evidence
with probability" (although it may be useful). There are a load of other
techniques that don't use probability: e.g. Wigmore Charts (from 1930's
onwards) and more recently, non-monotonic logical techniques.
For a good intro. I would recommend David's Schum's book "The Evidential
Foundations of Probabilistic Reasoning". Also,a look at the evidence
science website might be good: http://www.evidencescience.org/
HTH,
Matt
