Adaptive Monte Carlo Maximum Likelihood

  • Błażej Miasojedow
  • Wojciech Niemiro
  • Jan Palczewski
  • Wojciech Rejchel
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 605)

Abstract

We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We examine asymptotics of adaptive importance sampling and a new algorithm, which uses resampling and MCMC. This algorithm is designed to reduce problems with degeneracy of importance weights. Our analysis is based on martingale limit theorems. We also describe how adaptive maximization algorithms of Newton-Raphson type can be combined with the resampling techniques. The paper includes results of a small scale simulation study in which we compare the performance of adaptive and non-adaptive Monte Carlo maximum likelihood algorithms.

Keywords

Maximum likelihood Importance sampling Adaptation MCMC Resampling 

Notes

Acknowledgments

This work was partially supported by Polish National Science Center No. N N201 608 740.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Błażej Miasojedow
    • 1
  • Wojciech Niemiro
    • 1
    • 3
  • Jan Palczewski
    • 2
  • Wojciech Rejchel
    • 3
  1. 1.Faculty of Mathematics, Informatics and MechanicsUniversity of WarsawWarsawPoland
  2. 2.School of MathematicsUniversity of LeedsLeedsUK
  3. 3.Faculty of Mathematics and Computer ScienceNicolaus Copernicus UniversityToruńPoland

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