Mixture Model Latent Variable (augmented-data) example

Questions v5
4

I see, I didn’t know what you meant with augmented. For me that’s the normal Mixture model without marginalizing the indicator variable.

You can do that by sampling the latent variables and use those to index the parameters, a bit like the coal mining example: Introductory Overview of PyMC — PyMC 5.6.1 documentation

Otherwise if you want a mixture among different distributions and can’t just use a parameters switch, you can use CustomDist, something like

import pymc as pm

def dist(idx, mu1, mu2, sigma1, sigma2, size):
  comp1 = pm.Normal.dist(mu1, sigma1, size=size)
  comp2 = pm.Laplace(mu2, sigma2, size=size)
  return pm.math.switch(idx, comp1, comp2)

with pm.Model() as m:
  # Prior for idicator variables
  idx = pm.Bernoulli("idx", p=0.5, size=(3,))  # can use categorical for more components
  # Prior for mixture components parameters
  mu1 = ...
  mu2 = ...
  sigma1= ...
  sigma2 = ...
  # Mixture likelihood with custom distribution 
  llike = pm.CustomDist("llike", idx, mu1, mu2, sigma1, sigma2, dist=dist, observed=[2, 2, 3])