statistical inferences and PRNG characterization

[Matt Crawford]

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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