Ok so that makes sense. Is your DGP1 bimodal as well? It should be I think.
Backing up 3 posts, where you said
There is a peak at approximately 0.25. But the model can’t place a peak there, because the model is a mixture of 0.0001 and 0.5. The data is a mixture of zeros (when
simulated_data["sample_type"] == 0) and a mixture of 0.0001 and 0.5 (whensimulated_data["sample_type"] == 1).
Its not 0s when sample type is 0, its observed_count = background_rate when sample_type is 0. So those samples should fully identify/resolve p0
When sample type is 1 and fixed fractions of 0.5, its observed_count = 0.5 * Bin(n,p1) + background count. Background count is fully resolved from the above samples. So, p1 is fully identifiable/resolvable.
While the peak is at 0.025, since this is coming from 0.5 * Bin, the p1 should be 0.05.
Is this clear/do you disagree?