Science in its ultimate form, is not about evidence
I don't really understand what you're trying to say?
This is what I take science to be:
o Refers to data being collected through direct observation or experiment.
o Empirical evidence does not rely on argument or belief.
o Instead experiments and observations are carried out carefully and reported in detail so that other investigators can repeat and attempt to verify the work.
o Researchers should remain totally value free when studying; they should try to remain totally unbiased in their investigations. I.e. Researchers are not influenced by personal feelings and experiences.
o Objectivity means that all sources of bias are minimized and that personal or subjective ideas are eliminated. The pursuit of science implies that the facts will speak for themselves even if they turn out to be different from what the investigator hoped.
o All extraneous variables need to be controlled in order to be able to establish cause (Indepedent Variables) and effect (Dependent Variables).
o We should be aiming to be able to predict future behaviour from the findings of our research.
o E.g. a statement made at the beginning of an investigation that serves as a prediction and is derived from a theory. There are different types of hypotheses (null and alternative), which need to be stated in a form that can be tested (i.e. operationalized and unambiguous).
o This refers to whether a particular method and finding can be repeated with different/same people and/or on different occasions, to see if the results are similar.
o If a dramatic discovery is reported but it cannot be replicated by other scientists it will not be accepted.
o If we get the same results over and over again under the same conditions, we can be sure of their accuracy beyond reasonable doubt.
o This gives us confidence that the results are reliable and can be used to build up a body of knowledge or a theory: vital in establishing a scientific theory.
So basically, once all the empirical evidence has been confirmed we have a theory. Notice that it is not just simply and "idea". It is a theory backed up with evidence. E.g. the theory of evolution is backed up with actual hard evidence etc.
I also think that the science phrase "correlation doesn't imply cause" is relevent here. The correlation of all these childrens stories doesn't imply that the cause was that they have been reborn. There may be another cause yet to be discovered.
Reading about all the stories of children talking about past lives reminds of the belief in miracles. This belief also relies upon people recounting what the saw/heard/felt etc. It relies upon the testimony of others and it is well known that the human mind can concoct all sorts of illusions if the conditions are right. No so called miracle has ever been scientifically proven.
So with all this in mind I would still like to read about what the scientific evidence is for the Buddhist belief in rebirth?