I am writing a fairly simple dynamical model that has a Markov dependency structure where the state at time t depends only on the state at time t-1. This is my model and guide:

```
def model(prior, var, data, F):
prior1 = prior
for t in range(len(data)):
state = pyro.sample("state_{}".format(t), dist.MultivariateNormal(prior1,var))
pyro.sample("measurement_{}".format(t), dist.MultivariateNormal(state, 0.05*torch.eye(4)), obs = data[t])
prior1 = F@state.T
def guide(prior, var, data, F):
for t in range(len(data)):
x_value = pyro.param("x_value_{}".format(t), Variable(prior, requires_grad=True))
var_value = pyro.param("var_value_{}".format(t), Variable(var, requires_grad=True), constraint=dist.constraints.lower_cholesky)
state = pyro.sample("state_{}".format(t), dist.MultivariateNormal(x_value, scale_tril=var_value))
prior = F@state.T
```

I am running the stochastic variational inference procedure on my model and guide that looks like this:

```
svi = pyro.infer.SVI(model=model,
guide=guide,
optim = optim,
loss=pyro.infer.Trace_ELBO(num_particles=2, vectorize_particles=False, retain_graph=True, strict_enumeration_warning=True))
```

I want to improve my results by increasing the number of particles, however this makes the program slow. I could increase the speed of the program by parallelization that is conducted if you set vectorize_particles=True. However my model and guide cannot handle this, probably because I have a for-loop in my model and guide instead of a pyro.plate structure.

Is a pyro.plate structure possible for a model that uses the results from a previous time step (t-1)? And if so how?

How should I change my model to allow for vectorize_particles=True?

Another question I have is, is pyro.plate possible if you have this dependency structure?

Thanks in advance for your answer.