[llasram]

Neat! I work on a system with some very similar math, but a slightly different model. I really like how in bayesect making the error rates asymmetric via independent Beta priors on bidirectional errors allows the computations to be nice and symmetric.

I haven't worked these all the way through, but I'm slightly skeptical or at least confused by a few details:

1. Another way to frame P(D|B=b) would be to have the old vs new side draws be beta-binomial distributed, in which case we should then have binomial coefficients for each of the draw side probabilities for the number of possible orderings of the observations. Do they end up cancelling out somewhere? [ed: Oh yes, of course -- D includes that in each case we observe exactly one of the C(n,k) orderings.]

2. I think your expected conditional entropy code is treating the imputed new observations as independent from the past observations, though even if that's the case it may not affect it much in this model. If it does though, it might be worth explicitly unit-testing the naive vs efficient calculations to ensure they match.

Anyway, thanks for sharing!