code: def _accumulate_sufficient_statistics(
      self, stats, X, lattice, posteriors, fwdlattice, bwdlattice
  ):
      super()._accumulate_sufficient_statistics(
          stats=stats,
          X=X,
          lattice=lattice,
          posteriors=posteriors,
          fwdlattice=fwdlattice,
          bwdlattice=bwdlattice,
      )
  
      if self._needs_sufficient_statistics_for_mean():
          stats["post"] += posteriors.sum(axis=0)
          stats["obs"] += posteriors.T @ X
  
      if self._needs_sufficient_statistics_for_covars():
          if self.covariance_type in ("spherical", "diag"):
              stats["obs**2"] += posteriors.T @ X**2
          elif self.covariance_type in ("tied", "full"):
              # posteriors: (nt, nc); obs: (nt, nf); obs: (nt, nf)
              # -> (nc, nf, nf)
              stats["obs*obs.T"] += np.einsum(
                  "ij,ik,il->jkl", posteriors, X, X
              )
  
imports: import functools
  import inspect
  import warnings
  import numpy
  from scipy import special
  from scipy.stats import multinomial, poisson
  from sklearn.utils import check_random_state
  from .base import BaseHMM, _AbstractHMM
  from .stats import log_multivariate_normal_density
  from .utils import fill_covars, log_normalize
label_desc: Use image node_id 4 for calling the BaseGaussianHMM obj's underlying member method code with example usage: obj._accumulate_sufficient_statistics(stats, X, lattice, posteriors, fwdlattice, bwdlattice) without return types