code: def _emcee_lnprior(theta):
      """Proper function to allow pickling."""
      mu, tau, eta = theta[0], theta[1], theta[2:]
      # Half-cauchy prior, hwhm=25
      if tau < 0:
          return -np.inf
      prior_tau = -np.log(tau**2 + 25**2)
      prior_mu = -((mu / 10) ** 2)  # normal prior, loc=0, scale=10
      prior_eta = -np.sum(eta**2)  # normal prior, loc=0, scale=1
      return prior_mu + prior_tau + prior_eta
  
imports: import gzip
  import importlib
  import logging
  import os
  import sys
  from typing import Any, Dict, List, Optional, Tuple, Union
  import cloudpickle
  import numpy
  import pytest
  from _pytest.outcomes import Skipped
  from packaging.version import Version
  from ..data import InferenceData, from_dict
label_desc: Use image node_id 13 for calling a global function with example usage: _emcee_lnprior(theta) and returns: unknown, unknown