On May 19, 2006, at 6:51, Travis H. wrote:

As I understand it, when looking at output, one can take a
hypothetical source model (e.g. "P(0) = 0.3, P(1) = 0.7, all bits
independent") and come up with a probability that the source may have
generated that output.

One can come up with the probability that the defined source will generate that output in a single run.

  One cannot, however, say what probability such
a source had generated the output, because there is an infinite number
of sources (e.g. "P(0) = 0.29999.., P(1) = 7.000...").  Can one say
that, if the source must be A or B, what probability it actually was A
(and if so, how)?

If you can put your question into the form, "Source A or B is chosen with probability pA or 1-pA. Output X is generated. What is the probability that it was source A that was chosen?" then Bayesian inference can answer the question. However, you don't generally have a known a priori probability of each source being chosen, and you don't even know the characteristics of the "other" source. You can generalize to an arbitrary number of alternative sources, but that doesn't provide the prior data that's lacking.

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