class_docstr: Particular IMM with an additional null class.
  The data is supplied together
  with a sample-related probability of being under the null.
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docstr: One step in the sampling procedure (one data sweep)
  
  Parameters
  ----------
  x: array of shape(n_samples, dim),
     the input data
  z: array of shape(n_samples),
     the associated membership variables
  plike: array of shape(n_samples),
         the likelihood under the prior
  null_class_proba: array of shape(n_samples),
                    prior probability to be under the null
  
  Returns
  -------
  like: array od shape(n_samples),
        the likelihood of the data under the H1 hypothesis
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code: def simple_update(self, x, z, plike, null_class_proba):
      """One step in the sampling procedure (one data sweep)
  
      Parameters
      ----------
      x: array of shape(n_samples, dim),
         the input data
      z: array of shape(n_samples),
         the associated membership variables
      plike: array of shape(n_samples),
             the likelihood under the prior
      null_class_proba: array of shape(n_samples),
                        prior probability to be under the null
  
      Returns
      -------
      like: array od shape(n_samples),
            the likelihood of the data under the H1 hypothesis
      """
      like = self.likelihood(x, plike)
      # standard + likelihood under the prior
      # like has shape (x.shape[0], self.k+1)
  
      z = self.sample_indicator(like, null_class_proba)
      # almost standard, but many new components can be created
  
      self.reduce(z)
      self.update(x, z)
      return like.sum(1)
  
imports: import math
  import numpy
  from scipy.special import gammaln
  from .bgmm import BGMM, detsh
label_desc: Use image node_id 4 for calling the MixedIMM obj's underlying member method code with example usage: obj.simple_update(x, z, plike, null_class_proba) and returns: like