code: def model_2(data, history, vectorized):
      x_dim, y_dim = 3, 2
      x_init = pyro.param(
          "x_init",
          lambda: torch.rand(x_dim),
          constraint=constraints.simplex,
      )
      x_trans = pyro.param(
          "x_trans",
          lambda: torch.rand((x_dim, x_dim)),
          constraint=constraints.simplex,
      )
      y_init = pyro.param(
          "y_init",
          lambda: torch.rand(x_dim, y_dim),
          constraint=constraints.simplex,
      )
      y_trans = pyro.param(
          "y_trans",
          lambda: torch.rand((x_dim, y_dim, y_dim)),
          constraint=constraints.simplex,
      )
  
      x_prev = y_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:
          x_curr = pyro.sample(
              "x_{}".format(i),
              dist.Categorical(
                  x_init
                  if isinstance(i, int) and i < 1
                  else x_trans[x_prev]
              ),
          )
          with pyro.plate("tones", data.shape[-1], dim=-1):
              y_curr = pyro.sample(
                  "y_{}".format(i),
                  dist.Categorical(
                      y_init[x_curr]
                      if isinstance(i, int) and i < 1
                      else Vindex(y_trans)[x_curr, y_prev]
                  ),
                  obs=data[i],
              )
          x_prev, y_prev = x_curr, y_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 3 for calling a global function with example usage: model_2(data, history, vectorized) without return types