The EM algorithm and the Laplace Approximation
  The Laplace approximation calls for the computation of second derivatives at the likelihood maximum. When the maximum is found by the EM-algorithm, there is a convenient way to compute these derivatives. The likelihood gradient can be obtained from the EM-auxiliary, while the Hessian can be obtained from this gradient with the Pearlmutter trick. 
Niko Br\"ummer
stat.ML