Hi,

I have written the following code, extending HMM example to a Gaussian Likelihood. One Gaussian per HMM state.

```
def model_0(sequences, lengths, args, batch_size=None, include_prior=True):
assert not torch._C._get_tracing_state()
num_sequences, max_length, data_dim = sequences.shape
# Our prior on transition probabilities will be:
# stay in the same state with 50% probability; uniformly jump to another
# state with 50% probability.
probs_x = pyro.sample("probs_x",
dist.Dirichlet(0.5 * torch.eye(args.hidden_dim) + 0.5)
.to_event(1))
# K-Gaussians, one for each state
v0 = 1. # scales variance of normal
with pyro.plate("components", args.hidden_dim):
sig_inv = pyro.sample("scales_y", dist.Gamma(2.0, 2.0).expand([data_dim]).to_event(1))
mu = pyro.sample("locs_y", dist.Normal(0., torch.sqrt((1/sig_inv)*v0)).to_event(1))
# In this first model we'll sequentially iterate over sequences in a
# minibatch; this will make it easy to reason about tensor shapes.
tones_plate = pyro.plate("tones", data_dim, dim=-1)
with pyro.plate("sequences", num_sequences, batch_size, dim=-2) as batch:
lengths = lengths[batch]
x = 0
for t in pyro.markov(range(max_length if args.jit else lengths.max())):
# On the next line, we'll overwrite the value of x with an updated
# value. If we wanted to record all x values, we could instead
# write x[t] = pyro.sample(...x[t-1]...).
with poutine.mask(mask=(t < lengths).unsqueeze(-1)):
x = pyro.sample("x_{}".format(t), dist.Categorical(probs_x[x]),
infer={"enumerate": "parallel"})
with tones_plate:
pyro.sample("y_{}".format(t), dist.Normal(
mu[x.squeeze(-1)], sig[x.squeeze(-1)]),
obs=sequences[batch, t])
```

It is not throwing any error. Do you think it is a reasonable implementation? or do you see any bugs/issues with the implementation.

I wanted to have a global normal-inverse gamma prior on the parameters of the Gaussians. Do you think it is reasonable to do it as mentioned above in the code or should I implement a separate stochastic function named NormalInverseGamma?

Thanks for the feedback