docs: def expectation(p, obj1, obj2=None, nghp=None):
      """
      Compute the expectation <obj1(x) obj2(x)>_p(x)
      Uses multiple-dispatch to select an analytical implementation,
      if one is available. If not, it falls back to quadrature.
  
      :type p: (mu, cov) tuple or a `ProbabilityDistribution` object
      :type obj1: kernel, mean function, (kernel, features), or None
      :type obj2: kernel, mean function, (kernel, features), or None
      :param int nghp: passed to `_quadrature_expectation` to set the number
                       of Gauss-Hermite points used: `num_gauss_hermite_points`
      :return: a 1-D, 2-D, or 3-D tensor containing the expectation
  
      Allowed combinations
  
      - Psi statistics:
          >>> eKdiag = expectation(p, kern)  (N)  # Psi0
          >>> eKxz = expectation(p, (kern, feat))  (NxM)  # Psi1
          >>> exKxz = expectation(p, identity_mean, (kern, feat))  (NxDxM)
          >>> eKzxKxz = expectation(p, (kern, feat), (kern, feat))  (NxMxM)  # Psi2
  
      - kernels and mean functions:
          >>> eKzxMx = expectation(p, (kern, feat), mean)  (NxMxQ)
          >>> eMxKxz = expectation(p, mean, (kern, feat))  (NxQxM)
  
      - only mean functions:
          >>> eMx = expectation(p, mean)  (NxQ)
          >>> eM1x_M2x = expectation(p, mean1, mean2)  (NxQ1xQ2)
          .. note:: mean(x) is 1xQ (row vector)
  
      - different kernels. This occurs, for instance, when we are calculating Psi2 for Sum kernels:
          >>> eK1zxK2xz = expectation(p, (kern1, feat), (kern2, feat))  (NxMxM)
      """
      if isinstance(p, tuple):
          assert len(p) == 2
  
          if   p[1].shape.ndims == 2:
              p = DiagonalGaussian(*p)
          elif p[1].shape.ndims == 3:
              p = Gaussian(*p)
          elif p[1].shape.ndims == 4:
              p = MarkovGaussian(*p)
  
      if isinstance(obj1, tuple):
          obj1, feat1 = obj1
      else:
          feat1 = None
  
      if isinstance(obj2, tuple):
          obj2, feat2 = obj2
      else:
          feat2 = None
  
      try:
          return _expectation(p, obj1, feat1, obj2, feat2, nghp=nghp)
      except NotImplementedError as e:  # pragma: no cover
  
          warn_msg = "Quadrature is used to calculate the expectation. " + str(e)
          logger.warning(warn_msg)
  
          return _quadrature_expectation(p, obj1, feat1, obj2, feat2, nghp)