Correctly specifying a model with a multimodal distribution

Questions version agnostic
7

So I tried the following:

data = np.array([1.73, 1.59, 1.64, 1.58])

with pm.Model(coords={"cluster": range(k)}) as model_mix:
    μ = pm.Normal(
        "μ",
        mu=0,
        sigma=.01,
        transform=pm.distributions.transforms.ordered,
        initval=[1.72, 1.78, 1.88],
        dims="cluster",
    )
    σ = pm.HalfNormal("σ", sigma=np.array([.025, .025, 0.01]), dims="cluster")
    weights = pm.Dirichlet("w", np.ones(k), dims="cluster")
    pred = pm.NormalMixture("x", w=weights, mu=μ, sigma=σ, observed=data)

    trace_mix = pm.sample()

with model_mix:
    trace_mix.extend(pm.sample_prior_predictive())
    trace_mix.extend(pm.sample_posterior_predictive(trace_mix))

plt.hist(trace_mix['prior_predictive']['x'].to_numpy().reshape(-1))

However, sampling from the prior predictive as above just gives a normal-like distribution with a mean of 0. So something isn’t right.

Curious what the difference is between the formulation above using NormalMixture versus the example from here.

I would probably have to specify 2 priors for each of the distributions under this formulation (so 6 priors in total):

# 2-Mixture Poisson using iterable of distributions.
with pm.Model() as model:
    lam1 = pm.Exponential('lam1', lam=1)
    lam2 = pm.Exponential('lam2', lam=1)

    pois1 = pm.Poisson.dist(mu=lam1)
    pois2 = pm.Poisson.dist(mu=lam2)

    w = pm.Dirichlet('w', a=np.array([1, 1]))

    like = pm.Mixture('like', w=w, comp_dists = [pois1, pois2], observed=data)