code: def model_4(data, history, vectorized):
      w_dim, x_dim, y_dim = 2, 3, 2
      w_init = pyro.param(
          "w_init",
          lambda: torch.rand(w_dim),
          constraint=constraints.simplex,
      )
      w_trans = pyro.param(
          "w_trans",
          lambda: torch.rand((w_dim, w_dim)),
          constraint=constraints.simplex,
      )
      x_init = pyro.param(
          "x_init",
          lambda: torch.rand(w_dim, x_dim),
          constraint=constraints.simplex,
      )
      x_trans = pyro.param(
          "x_trans",
          lambda: torch.rand((w_dim, x_dim, x_dim)),
          constraint=constraints.simplex,
      )
      y_probs = pyro.param(
          "y_probs",
          lambda: torch.rand(w_dim, x_dim, y_dim),
          constraint=constraints.simplex,
      )
  
      w_prev = x_prev = None
      markov_loop = (
          pyro.vectorized_markov(
              name="time", size=len(data), dim=-2, history=history
          )
          if vectorized
          else pyro.markov(range(len(data)), history=history)
      )
      for i in markov_loop:
          w_curr = pyro.sample(
              "w_{}".format(i),
              dist.Categorical(
                  w_init
                  if isinstance(i, int) and i < 1
                  else w_trans[w_prev]
              ),
          )
          x_curr = pyro.sample(
              "x_{}".format(i),
              dist.Categorical(
                  x_init[w_curr]
                  if isinstance(i, int) and i < 1
                  else x_trans[w_curr, x_prev]
              ),
          )
          with pyro.plate("tones", data.shape[-1], dim=-1):
              pyro.sample(
                  "y_{}".format(i),
                  dist.Categorical(Vindex(y_probs)[w_curr, x_curr]),
                  obs=data[i],
              )
          x_prev, w_prev = x_curr, w_curr
  
imports: import pytest
  import torch
  from pyroapi import pyro_backend
  from torch.distributions import constraints
  from pyro.ops.indexing import Vindex
label_desc: Use image node_id 5 for calling a global function with example usage: model_4(data, history, vectorized) without return types