Adaptive polar sampling, a class of flexibel and robust Monte Carlo integration methods
AbstractAdaptive 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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Bibliographic InfoPaper provided by Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute in its series Econometric Institute Research Papers with number EI 2002-27.
Date of creation: 17 Sep 2002
Date of revision:
Importance sampling; Markov chain Monte Carlo; Polar coordinates;
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- Bauwens, L. & Bos, C.S. & van Dijk, H.K. & van Oest, R.D., 2003.
"Adaptive radial-based direction sampling; Some flexible and robust Monte Carlo integration methods,"
Econometric Institute Research Papers, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute
EI 2003-22, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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