(In progress, saving this spot)

So the simple solution is that he lists a set of possible starting theories, doing his limited best to carve up all available regions of idea-space visible to him, then describes which sequences he would consider evidence for each theory, then describe how to compare the relative ratios; again, this is all simple things Keltham taught them. He'll also want to come up with a way to mathematically describe 'all theories have unexpectedly low predictive power'; that ought to be very simple given that Keltham already told them what it looks like...

... The obvious way to note an error is just them getting very different results. In particular, getting results that form very different curves; if it looks like slightly different concentrations along a curve when you combine them, or one of them being thrown by one odd result, those are checkable things, but if, in general, it looks like the thing they are measuring has a different shape, probably the thing they are measuring has a very different shape; if they can’t predict each other, a very plausible outcome is that they aren’t the each other they’re trying to predict, he can put that into math...

And Alexandre will quietly enjoy himself, producing not really a general solution for the problem, because given that individual people will start with their own individual beliefs, many of which they are not explicitly writing down anywhere, he does not think he can do that, but something that, given a little work to turn his neat little descriptions into pseudocode, would work quite well as a computer program for interpreting results and adjusting your priors into posteriors based on them, if any computers happened to exist in Golarion that could run it.