text: import jax
  import jax.numpy as jnp
  import numpy as np
  import numpyro.distributions as dists
  from numpyro.primitives import sample, plate
  import pandas as pd
  from typing import Tuple, Iterable
  
  def preprocess(x: pd.DataFrame) -> Tuple[Iterable[pd.DataFrame], int]:
      y = x.copy()
      y.columns = ['new_first', 'new_second']
      y['foo'] += 2
      return (y,), len(y)
  
  def model(z = None, num_obs_total = None) -> None:
      batch_size = 1
      if z is not None:
          batch_size = z.shape[0]
      if num_obs_total is None:
          num_obs_total = batch_size
  
      mu = sample('mu', dists.Normal().expand_by((2,)).to_event(1))
      sigma = sample('sigma', dists.InverseGamma(1.).expand_by((2,)).to_event(1))
      with plate('batch', num_obs_total, batch_size):
          sample('x', dists.Normal(mu, sigma).to_event(1), obs=z)
  