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


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


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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  • Bauwens, L. & Bos, C.S. & van Dijk, H.K. & van Oest, R.D., 2002. "Adaptive polar sampling, a class of flexibel and robust Monte Carlo integration methods," Econometric Institute Research Papers EI 2002-27, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  • Handle: RePEc:ems:eureir:555

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    References listed on IDEAS

    1. de Brito, M.P. & Flapper, S.D.P. & Dekker, R., 2002. "Reverse logistics," Econometric Institute Research Papers EI 2002-21, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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    Cited by:

    1. Bauwens, Luc & Bos, Charles S. & van Dijk, Herman K. & van Oest, Rutger D., 2004. "Adaptive radial-based direction sampling: some flexible and robust Monte Carlo integration methods," Journal of Econometrics, Elsevier, vol. 123(2), pages 201-225, December.
    2. Andrzej Kociêcki, 2003. "On Priors for Impulse Responses in Bayesian Structural VAR Models," Econometrics 0307006, EconWPA.
    3. 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.


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