Open drphilmarshall opened 9 years ago
Alright! Looks like @abmantz did this little exercise, but in R instead. In this simplest possible case, the population variance is a sufficient statistic, so ABC can work exactly - and indeed, Adam gets a nice posterior (from the histogram of accepted prior samples). Could be interesting to see if other summary statistics (something KS-related?) give similar results. Otherwise: suggestions for the next example problem?
I was thinking the next simple problem would be joint constraints on the mean and width of a Gaussian. That way, we would have a slightly meatier case (still with an exact solution) to test methods other than rejection on.
But already it's pretty clear that the hurdle to using ABC in practice will be finding the best summary statistic, and figuring out whether the results can be trusted if it is not sufficient.
Things to do: