code: def compare(
      compare_dict: Mapping[str, InferenceData],
      ic: Optional[ICKeyword] = None,
      method: Literal[
          "stacking", "BB-pseudo-BMA", "pseudo-BMA"
      ] = "stacking",
      b_samples: int = 1000,
      alpha: float = 1,
      seed=None,
      scale: Optional[ScaleKeyword] = None,
      var_name: Optional[str] = None,
  ):
      r"""Compare models based on  their expected log pointwise predictive density (ELPD).
  
      The ELPD is estimated either by Pareto smoothed importance sampling leave-one-out
      cross-validation (LOO) or using the widely applicable information criterion (WAIC).
      We recommend loo. Read more theory here - in a paper by some of the
      leading authorities on model comparison dx.doi.org/10.1111/1467-9868.00353
  
      Parameters
      ----------
      compare_dict: dict of {str: InferenceData or ELPDData}
          A dictionary of model names and :class:`arviz.InferenceData` or ``ELPDData``.
      ic: str, optional
          Method to estimate the ELPD, available options are "loo" or "waic". Defaults to
          ``rcParams["stats.information_criterion"]``.
      method: str, optional
          Method used to estimate the weights for each model. Available options are:
  
          - 'stacking' : stacking of predictive distributions.
          - 'BB-pseudo-BMA' : pseudo-Bayesian Model averaging using Akaike-type
            weighting. The weights are stabilized using the Bayesian bootstrap.
          - 'pseudo-BMA': pseudo-Bayesian Model averaging using Akaike-type
            weighting, without Bootstrap stabilization (not recommended).
  
          For more information read https://arxiv.org/abs/1704.02030
      b_samples: int, optional default = 1000
          Number of samples taken by the Bayesian bootstrap estimation.
          Only useful when method = 'BB-pseudo-BMA'.
          Defaults to ``rcParams["stats.ic_compare_method"]``.
      alpha: float, optional
          The shape parameter in the Dirichlet distribution used for the Bayesian bootstrap. Only
          useful when method = 'BB-pseudo-BMA'. When alpha=1 (default), the distribution is uniform
          on the simplex. A smaller alpha will keeps the final weights more away from 0 and 1.
      seed: int or np.random.RandomState instance, optional
          If int or RandomState, use it for seeding Bayesian bootstrap. Only
          useful when method = 'BB-pseudo-BMA'. Default None the global
          :mod:`numpy.random` state is used.
      scale: str, optional
          Output scale for IC. Available options are:
  
          - `log` : (default) log-score (after Vehtari et al. (2017))
          - `negative_log` : -1 * (log-score)
          - `deviance` : -2 * (log-score)
  
          A higher log-score (or a lower deviance) indicates a model with better predictive
          accuracy.
      var_name: str, optional
          If there is more than a single observed variable in the ``InferenceData``, which
          should be used as the basis for comparison.
  
      Returns
      -------
      A DataFrame, ordered from best to worst model (measured by the ELPD).
      The index reflects the key with which the models are passed to this function. The columns are:
      rank: The rank-order of the models. 0 is the best.
      elpd: ELPD estimated either using (PSIS-LOO-CV `elpd_loo` or WAIC `elpd_waic`).
          Higher ELPD indicates higher out-of-sample predictive fit ("better" model).
          If `scale` is `deviance` or `negative_log` smaller values indicates
          higher out-of-sample predictive fit ("better" model).
      pIC: Estimated effective number of parameters.
      elpd_diff: The difference in ELPD between two models.
          If more than two models are compared, the difference is computed relative to the
          top-ranked model, that always has a elpd_diff of 0.
      weight: Relative weight for each model.
          This can be loosely interpreted as the probability of each model (among the compared model)
          given the data. By default the uncertainty in the weights estimation is considered using
          Bayesian bootstrap.
      SE: Standard error of the ELPD estimate.
          If method = BB-pseudo-BMA these values are estimated using Bayesian bootstrap.
      dSE: Standard error of the difference in ELPD between each model and the top-ranked model.
          It's always 0 for the top-ranked model.
      warning: A value of 1 indicates that the computation of the ELPD may not be reliable.
          This could be indication of WAIC/LOO starting to fail see
          http://arxiv.org/abs/1507.04544 for details.
      scale: Scale used for the ELPD.
  
      Examples
      --------
      Compare the centered and non centered models of the eight school problem:
  
      .. ipython::
  
          In [1]: import arviz as az
             ...: data1 = az.load_arviz_data("non_centered_eight")
             ...: data2 = az.load_arviz_data("centered_eight")
             ...: compare_dict = {"non centered": data1, "centered": data2}
             ...: az.compare(compare_dict)
  
      Compare the models using PSIS-LOO-CV, returning the ELPD in log scale and calculating the
      weights using the stacking method.
  
      .. ipython::
  
          In [1]: az.compare(compare_dict, ic="loo", method="stacking", scale="log")
  
      See Also
      --------
      loo :
          Compute the ELPD using the Pareto smoothed importance sampling Leave-one-out
          cross-validation method.
      waic : Compute the ELPD using the widely applicable information criterion.
      plot_compare : Summary plot for model comparison.
  
      References
      ----------
      .. [1] Vehtari, A., Gelman, A. & Gabry, J. Practical Bayesian model evaluation using
          leave-one-out cross-validation and WAIC. Stat Comput 27, 1413–1432 (2017)
          see https://doi.org/10.1007/s11222-016-9696-4
  
      """
      try:
          (ics_dict, scale, ic) = _calculate_ics(
              compare_dict, scale=scale, ic=ic, var_name=var_name
          )
      except Exception as e:
          raise e.__class__(
              "Encountered error in ELPD computation of compare."
          ) from e
      names = list(ics_dict.keys())
      if ic == "loo":
          df_comp = pd.DataFrame(
              index=names,
              columns=[
                  "rank",
                  "elpd_loo",
                  "p_loo",
                  "elpd_diff",
                  "weight",
                  "se",
                  "dse",
                  "warning",
                  "scale",
              ],
              dtype=np.float_,
          )
      elif ic == "waic":
          df_comp = pd.DataFrame(
              index=names,
              columns=[
                  "rank",
                  "elpd_waic",
                  "p_waic",
                  "elpd_diff",
                  "weight",
                  "se",
                  "dse",
                  "warning",
                  "scale",
              ],
              dtype=np.float_,
          )
      else:
          raise NotImplementedError(
              f"The information criterion {ic} is not supported."
          )
  
      if scale == "log":
          scale_value = 1
          ascending = False
      else:
          if scale == "negative_log":
              scale_value = -1
          else:
              scale_value = -2
          ascending = True
  
      method = (
          rcParams["stats.ic_compare_method"]
          if method is None
          else method
      )
      if method.lower() not in [
          "stacking",
          "bb-pseudo-bma",
          "pseudo-bma",
      ]:
          raise ValueError(
              f"The method {method}, to compute weights, is not supported."
          )
  
      p_ic = f"p_{ic}"
      ic_i = f"{ic}_i"
  
      ics = pd.DataFrame.from_dict(ics_dict, orient="index")
      ics.sort_values(
          by=f"elpd_{ic}", inplace=True, ascending=ascending
      )
      ics[ic_i] = ics[ic_i].apply(lambda x: x.values.flatten())
  
      if method.lower() == "stacking":
          rows, cols, ic_i_val = _ic_matrix(ics, ic_i)
          exp_ic_i = np.exp(ic_i_val / scale_value)
          km1 = cols - 1
  
          def w_fuller(weights):
              return np.concatenate(
                  (weights, [max(1.0 - np.sum(weights), 0.0)])
              )
  
          def log_score(weights):
              w_full = w_fuller(weights)
              score = 0.0
              for i in range(rows):
                  score += np.log(np.dot(exp_ic_i[i], w_full))
              return -score
  
          def gradient(weights):
              w_full = w_fuller(weights)
              grad = np.zeros(km1)
              for k, i in itertools.product(range(km1), range(rows)):
                  grad[k] += (
                      exp_ic_i[i, k] - exp_ic_i[i, km1]
                  ) / np.dot(exp_ic_i[i], w_full)
              return -grad
  
          theta = np.full(km1, 1.0 / cols)
          bounds = [(0.0, 1.0) for _ in range(km1)]
          constraints = [
              {"type": "ineq", "fun": lambda x: -np.sum(x) + 1.0},
              {"type": "ineq", "fun": np.sum},
          ]
  
          weights = minimize(
              fun=log_score,
              x0=theta,
              jac=gradient,
              bounds=bounds,
              constraints=constraints,
          )
  
          weights = w_fuller(weights["x"])
          ses = ics["se"]
  
      elif method.lower() == "bb-pseudo-bma":
          rows, cols, ic_i_val = _ic_matrix(ics, ic_i)
          ic_i_val = ic_i_val * rows
  
          b_weighting = st.dirichlet.rvs(
              alpha=[alpha] * rows, size=b_samples, random_state=seed
          )
          weights = np.zeros((b_samples, cols))
          z_bs = np.zeros_like(weights)
          for i in range(b_samples):
              z_b = np.dot(b_weighting[i], ic_i_val)
              u_weights = np.exp((z_b - np.max(z_b)) / scale_value)
              z_bs[
                  i
              ] = z_b  # pylint: disable=unsupported-assignment-operation
              weights[i] = u_weights / np.sum(u_weights)
  
          weights = weights.mean(axis=0)
          ses = pd.Series(
              z_bs.std(axis=0), index=names
          )  # pylint: disable=no-member
  
      elif method.lower() == "pseudo-bma":
          min_ic = ics.iloc[0][f"elpd_{ic}"]
          z_rv = np.exp((ics[f"elpd_{ic}"] - min_ic) / scale_value)
          weights = z_rv / np.sum(z_rv)
          ses = ics["se"]
  
      if np.any(weights):
          min_ic_i_val = ics[ic_i].iloc[0]
          for idx, val in enumerate(ics.index):
              res = ics.loc[val]
              if scale_value < 0:
                  diff = res[ic_i] - min_ic_i_val
              else:
                  diff = min_ic_i_val - res[ic_i]
              d_ic = np.sum(diff)
              d_std_err = np.sqrt(len(diff) * np.var(diff))
              std_err = ses.loc[val]
              weight = weights[idx]
              df_comp.loc[val] = (
                  idx,
                  res[f"elpd_{ic}"],
                  res[p_ic],
                  d_ic,
                  weight,
                  std_err,
                  d_std_err,
                  res["warning"],
                  res["scale"],
              )
  
      df_comp["rank"] = df_comp["rank"].astype(int)
      df_comp["warning"] = df_comp["warning"].astype(bool)
      return df_comp.sort_values(by=f"elpd_{ic}", ascending=ascending)
  
imports: import itertools
  import warnings
  from copy import deepcopy
  from typing import List, Optional, Tuple, Union, Mapping, cast, Callable
  import numpy
  import pandas
  import scipy.stats
  from xarray_einstats import stats
  import xarray
  from scipy.optimize import minimize
  from typing_extensions import Literal
  from ..None import _log
  from ..data import InferenceData, convert_to_dataset, convert_to_inference_data, extract
  from ..rcparams import rcParams, ScaleKeyword, ICKeyword
  from ..utils import Numba, _numba_var, _var_names, get_coords
  from .density_utils import get_bins
  from .density_utils import histogram
  from .density_utils import kde
  from .diagnostics import _mc_error, _multichain_statistics, ess
  from .stats_utils import ELPDData, _circular_standard_deviation, smooth_data
  from .stats_utils import get_log_likelihood
  from .stats_utils import get_log_prior
  from .stats_utils import logsumexp
  from .stats_utils import make_ufunc
  from .stats_utils import stats_variance_2d
  from .stats_utils import wrap_xarray_ufunc
  from ..sel_utils import xarray_var_iter
  from ..labels import BaseLabeller
label_desc: Use image node_id 1 for calling a global function with example usage: compare(compare_dict, ic, method, b_samples, alpha, seed, scale, var_name) and returns: df_comp, np, unknown, unknown