Statistics and Computing

, Volume 18, Issue 4, pp 447-459

First online:

Adaptive importance sampling in general mixture classes

  • Olivier CappéAffiliated withLTCI, TELECOM ParisTech, CNRS
  • , Randal DoucAffiliated withTELECOM SudParis
  • , Arnaud GuillinAffiliated withLATP, Ecole Centrale Marseille, CNRS
  • , Jean-Michel MarinAffiliated withProject select, INRIA SaclayCREST, INSEE Email author 
  • , Christian P. RobertAffiliated withCEREMADE, Université Paris Dauphine, CNRSCREST, INSEE

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In this paper, we propose an adaptive algorithm that iteratively updates both the weights and component parameters of a mixture importance sampling density so as to optimise the performance of importance sampling, as measured by an entropy criterion. The method, called M-PMC, is shown to be applicable to a wide class of importance sampling densities, which includes in particular mixtures of multivariate Student t distributions. The performance of the proposed scheme is studied on both artificial and real examples, highlighting in particular the benefit of a novel Rao-Blackwellisation device which can be easily incorporated in the updating scheme.


Importance sampling Adaptive Monte Carlo Mixture model Entropy Kullback-Leibler divergence EM algorithm Population Monte Carlo