More flexible interpretation of mutation rate when getting emission probability when using `_tskit.lshmm` about tskit HOT 4 OPEN

Shouldn't the probability of match and probability of mismatch sum to 1? If that is the case, then I suspect there is a bug.

In this code snippet:

p_e = mu;
if (is_match) {
    p_e = 1 - (num_alleles - 1) * mu;
}

Probability of mismatch = mu
Probability of match = 1 - (num_alleles - 1) * mu

Their sum is not 1 when num_alleles > 2.

Probability of match should be (1 - mu), unless probability of mismatch is (num_alleles - 1) * mu.

EDIT: Please disregard the above. I didn't realise it's the Rosen & Paten (2019) formulation, which rescales the mutation rate based on the number of alleles at the site. So, not a bug.

from tskit.

I agree it is a weird parameterisation, and doesn't belong in the core HMM. We should make this type of rescaling optional at the Python level.

from tskit.

I'm just looking at how computation of emission probability is done in test_haplotype_matching.py. It seems like it is going with a slightly different interpretation of mu (when there is no scaling based on the number of alleles)?

if is_match:
    p_e = 1 - mu
else:
    p_e = mu / (n_alleles - 1)

from tskit.

Maybe mu has been rescaled somewhere else? There may well be inconsistencies here, though

from tskit.