Mixture models and different observed data counts

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.

Hi! I don’t quite get the model you’re thinking about. Is it a Mixture with unbalanced weights, or is it just two separate Normal likeilhoods? Or something else?

two (or more) separate normal likelihoods that should be mostly non-overlapping - it’s expected there will be a shift between the two, as there is an inherent increasing mean value in the system for each normal distribution. I know which distribution each observation belongs to.

My thought was since the true value is guaranteed non-overlapping but in neighborhood enough to have some of the tails overlapping until sample counts get high that I shouldn’t treat it as separate distributions.

Then it’s not a mixture?

oh my bad, sorry I’m rusty on a few things - I guess then it’s just a network of normal distributions?