code: def test_mle_jacobian(bounded):
      """Test MAP / MLE estimation for distributions with flat priors."""
      truth = 10.0  # Simple normal model should give mu=10.0
      rtol = 1e-4  # this rtol should work on both floatX precisions
  
      start, model, _ = models.simple_normal(bounded_prior=bounded)
      with model:
          map_estimate = find_MAP(method="BFGS", model=model)
      assert_allclose(map_estimate["mu_i"], truth, rtol=rtol)
  
imports: import re
  import numpy
  import pytest
  from numpy.testing import assert_allclose
  import pymc
  from pymc.exceptions import ImputationWarning
  from pymc.step_methods.metropolis import tune
  from pymc.testing import select_by_precision
  from pymc.tuning import find_MAP
  from tests import models
  from tests.models import non_normal, simple_arbitrary_det, simple_model
label_desc: Use image node_id 1 for calling a global function with example usage: test_mle_jacobian(bounded) without return types