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Adaptive polar sampling, a class of flexibel and robust Monte Carlo integration methods

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Author Info

  • Bauwens, L.
  • Bos, C.S.
  • van Dijk, H.K.
  • van Oest, R.D.

Abstract

Adaptive Polar Sampling (APS) algorithms are proposed for Bayesian analysis of models with nonelliptical, possibly, multimodal posterior distributions. A location-scale transformation and a transformation to polar coordinates are used. After the transformation to polar coordinates, a Metropolis-Hastings method or, alternatively, an importance sampling method is applied to sample directions and, conditionally on these, distances are generated by inverting the cumulative distribution function. A sequential procedure is applied to update the initial location and scaling matrix in order to sample directions in an efficient way. Tested on a set of canonical mixture models that feature multimodality, strong correlation, and skewness, the APS algorithms compare favourably with the standard Metropolis-Hastings and importance samplers in terms of flexibility and robustness. APS is applied to several econometric and statistical examples. The empirical results for a regression model with scale contamination, an ARMA-GARCH-Student t model with near cancellation of roots and heavy tails, a mixture model for economic growth, and a nonlinear threshold model for industrial production growth confirm the practical flexibility and robustness of APS.

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File URL: http://repub.eur.nl/pub/555/feweco20020917131720.pdf
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Bibliographic Info

Paper provided by Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute in its series Econometric Institute Research Papers with number EI 2002-27.

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Date of creation: 17 Sep 2002
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Handle: RePEc:ems:eureir:555

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Related research

Keywords: Importance sampling; Markov chain Monte Carlo; Polar coordinates;

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Cited by:
  1. BAUWENS, Luc & BOS, Charles S. & VAN DIJK, Herman K. & VAN OEST, Rutger D., . "Adaptive radial-based direction sampling: some flexible and robust Monte Carlo integration methods," CORE Discussion Papers RP -1731, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Lennart F. Hoogerheide & Johan F. Kaashoek, 2004. "Functional Approximations to Likelihoods/Posterior Densities: A Neural Network Approach to Efficient Sampling," Computing in Economics and Finance 2004 74, Society for Computational Economics.
  3. Andrzej Kociêcki, 2003. "On Priors for Impulse Responses in Bayesian Structural VAR Models," Econometrics 0307006, EconWPA.

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