variable_mixture_weights

import pymc3 as pm
import numpy as np

def sigmoid(x):
    return np.exp(x) / (1. + np.exp(x))

# Create toy dataset
n = 100
n_components = 2
p = 2
beta_true = np.random.randn(p,n_components)
x         = np.random.randn(n,p)
prob      = sigmoid(x @ beta_true)
prob      = prob / prob.sum(axis=1,keepdims=True)
labels    = (prob > 0.5).astype(int)

mu = [-2, 2]
sd = np.ones([1,1])
y_raw = labels * mu + np.random.randn(n,n_components)*labels*sd
y     = y_raw.sum(axis=1)

with pm.Model() as model:
    mu   = pm.Normal('mu', sd=10, shape=n_components)
    sd   = pm.Exponential('sd', lam=1, shape=n_components)

    beta = pm.Normal('beta', sd=10, shape=(p,n_components))
    p    = pm.Deterministic('p',pm.math.sigmoid(x@beta))
    
    components = [pm.Normal.dist(mu=mu[i], sd=sd[i]) for i in range(n_components)]

    like = pm.Mixture('like', w=p, comp_dists=components, observed=y)
    
    trace = pm.sample(init='adapt_diag')