code: def forward(self, observations, add_bias=True):
      obs_dim = 2 * self.num_sensors
      bias_scale = self.log_bias_scale.exp()
      obs_noise = self.log_obs_noise.exp()
      trans_noise = self.log_trans_noise.exp()
  
      # bias distribution
      bias = Variable("bias", Reals[obs_dim])
      assert not torch.isnan(bias_scale), "bias scales was nan"
      bias_dist = dist_to_funsor(
          dist.MultivariateNormal(
              torch.zeros(obs_dim),
              scale_tril=bias_scale * torch.eye(2 * self.num_sensors),
          )
      )(value=bias)
  
      init_dist = dist.MultivariateNormal(
          torch.zeros(4), scale_tril=100.0 * torch.eye(4)
      )
      self.init = dist_to_funsor(init_dist)(value="state")
  
      # hidden states
      prev = Variable("prev", Reals[4])
      curr = Variable("curr", Reals[4])
      self.trans_dist = f_dist.MultivariateNormal(
          loc=prev @ NCV_TRANSITION_MATRIX,
          scale_tril=trans_noise
          * torch.linalg.cholesky(NCV_PROCESS_NOISE),
          value=curr,
      )
  
      state = Variable("state", Reals[4])
      obs = Variable("obs", Reals[obs_dim])
      observation_matrix = Tensor(
          torch.eye(4, 2)
          .unsqueeze(-1)
          .expand(-1, -1, self.num_sensors)
          .reshape(4, -1)
      )
      assert observation_matrix.output.shape == (
          4,
          obs_dim,
      ), observation_matrix.output.shape
      obs_loc = state @ observation_matrix
      if add_bias:
          obs_loc += bias
      self.observation_dist = f_dist.MultivariateNormal(
          loc=obs_loc,
          scale_tril=obs_noise * torch.eye(obs_dim),
          value=obs,
      )
  
      logp = bias_dist
      curr = "state_init"
      logp += self.init(state=curr)
      for t, x in enumerate(observations):
          prev, curr = curr, "state_{}".format(t)
          logp += self.trans_dist(prev=prev, curr=curr)
          logp += self.observation_dist(state=curr, obs=x)
          # marginalize out previous state
          logp = logp.reduce(ops.logaddexp, prev)
      # marginalize out bias variable
      logp = logp.reduce(ops.logaddexp, "bias")
  
      # save posterior over the final state
      assert set(logp.inputs) == {
          "state_{}".format(len(observations) - 1)
      }
      posterior = funsor_to_mvn(logp, ndims=0)
  
      # marginalize out remaining variables
      logp = logp.reduce(ops.logaddexp)
      assert (
          isinstance(logp, Tensor) and logp.shape == ()
      ), logp.pretty()
      return logp.data, posterior
  
imports: import argparse
  import itertools
  import math
  import os
  import pyro.distributions
  import torch
  import torch.nn
  from torch.optim import Adam
  import funsor
  import funsor.ops
  import funsor.torch.distributions
  from funsor.domains import Reals
  from funsor.pyro.convert import dist_to_funsor, funsor_to_mvn
  from funsor.tensor import Tensor, Variable
label_desc: Use image node_id 2 for calling the Model obj's underlying member method code with example usage: obj.forward(observations, add_bias) and returns: logp,  posterior