Mixture of gaussians not converging in pyMC3

Question

I have a mixture of 3 gaussians but no matter how much I tweak the priors I can't get the posterior means to move from their prior values..

k = 3

n1 = 1000
n2 = 1000
n3 = 1000

n = n1+n2+n3

mean1 = 17.3
mean2 = 42.0
mean3 = 31.0

precision = 0.1

sigma = np.sqrt(1 / precision)

print "Standard deviation: %s" % sigma

data1 = np.random.normal(mean1,sigma,n1)
data2 = np.random.normal(mean2,sigma,n2)
data3 = np.random.normal(mean3,sigma,n3)

data = np.concatenate([data1 , data2, data3])

hist(data, bins=200,  color="k", histtype="stepfilled", alpha=0.8)
plt.title("Histogram of the dataset")
plt.ylim([0, None])

with pm.Model() as model:
    dd = pm.Dirichlet('dd', a=np.array([float(n/k) for i in range(k)]), shape=k)
    sd = pm.Uniform('precs', lower=1, upper=5, shape=k)
    means = pm.Normal('means', [25, 30, 35], 0.01, shape=k)
    category = pm.Categorical('category', p=dd, shape=n)

    points = pm.Normal('obs',
                     means[category],
                     sd=sd[category],
                     observed=data)
    tr = pm.sample(100000, step=pm.Metropolis())
    pm.traceplot(tr, vars=['means', 'precs', 'dd'])

output:

Standard deviation: 3.16227766017
 [-----------------100%-----------------] 100000 of 100000 complete in 157.2 sec

As you can see there is no convergence and the means do not move from their initial values

Answer 1

Unfortunately, this is a known issue: https://github.com/pymc-devs/pymc/issues/452 and https://github.com/pymc-devs/pymc/issues/443 which we are working on.

Note that there are other step-methods you can use for the categorical as in the example models in the issues. But even that doesn't lead to convergence.