How should one deal with mixture models where there is influence (like ordering constraints, sums) between the different RVs - e.g. it’s known that the normal distributions should be spaced with ideally little to no overlap - however we do not have the same amounts of observed data for each normal distribution input into the model.

So like what if we had 100 samples on normal distribution #1 (broken into u and sigma RV components) and 12 observations on distribution#2 - what’s a general way to update the model, but keep feeding the remaining of the 100 samples after we’ve ran out of distribution#2 observations.

my initial thought is sample from the posterior distribution for distributions I’m out of observations on and keep feeding that in - however I’m not sure that’s best and I want to take care to not lead the u and sigma rv params astray.

There’s more than 2 normal distributions in general as food for thought for generic approaches.