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

Listed author(s):
  • 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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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
Handle: RePEc:ems:eureir:555
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