statistical inferences and PRNG characterization
Matt Crawford
crawdad at fnal.gov
Fri May 19 18:02:12 EDT 2006
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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