I’m new to pyro. I’m trying to set up an MCMC of a toy problem - Gaussian Mixture Model with same mean but different variance (e.g., sig1 = 1, sig2=0.1). Prior over mean is uniform, and so posterior is also a GMM.

Not sure how to do it. I tried the following code:

```
def model(obs=None):
mu = pyro.sample("mu", dist.Uniform(-10*torch.ones(dim), high=10*torch.ones(dim)))
sigma = pyro.param("sigma", lambda: torch.ones(()) if torch.randn(()) < 0.5 else 0.1*torch.ones(()), constraint=constraints.positive)
return pyro.sample("obs", dist.Normal(mu, sigma), obs=obs)
nuts_kernel = NUTS(model)
mcmc = MCMC(
nuts_kernel,
num_samples=1000,
warmup_steps=1000,
num_chains=1,
)
mcmc.run(torch.zeros(1))
mcmc.summary(prob=0.5)
samples = mcmc.get_samples()
```

But got bad results (KDE plot of posterior looks bad).