Forcing separation in location parameters for Gaussian mixture models

Ultimately exchangeable mixture models are not well suited for Bayesian inference

I had hoped this wasn’t the case, and I wait with abated breath for your updatea on the mixture model write-up.

In my case I have a large data-set and an unknown K of Gaussian sub-populations. I can see a way through if I knew K. So if I just had some way of determining K, I could incrementally solve the rest.

Where a mixture model is the right choice, is there typically an alternative that would also be appropriate?