How to model a mixture of 3 Normals in PyMC?

Question

There is a question on CrossValidated on how to use PyMC to fit two Normal distributions to data. The answer of Cam.Davidson.Pilon was to use a Bernoulli distribution to ass

Answer 1

there is a mc.Categorical object that does just this.

p =  [0.2, 0.3, .5]
t = mc.Categorical('test', p )
t.random()
#array(2, dtype=int32)

It returns an int between 0 and len(p)-1. To model the 3 Normals, you make p a mc.Dirichlet object (it accepts a k length array as the hyperparameters; setting the values in the array to be the same is setting the prior probabilities to be equal). The rest of the model is nearly identical.

This is a generalization of the model I suggested above.

---

Update:

Okay, so instead of having different means, we can collapse them all into 1:

means = Normal( "means", 0, 0.001, size=3 )

...

@mc.deterministic
def mean(categorical=categorical, means = means):
   return means[categorical]