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

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

Author Info

L. Bauwens ()
C.S. Bos ()
H.K. Van Dijk ()
R.D. Van Oest () (FEW-Econometrie en besliskunde)

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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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Paper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number 278.

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Date of creation: 2002
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Handle: RePEc:dgr:eureir:2002278

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Find related papers by JEL classification:
C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Bayesian Analysis
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques

This paper has been announced in the following NEP Reports:

NEP-ALL-2002-09-28 (All new papers)
NEP-ECM-2002-09-28 (Econometrics)
NEP-ETS-2002-09-28 (Econometric Time Series)

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Hop, J Peter & Van Dijk, Herman K, 1992. "SISAM and MIXIN: Two Algorithms for the Computation of Posterior Moments and Densities Using Monte Carlo Integration," Computer Science in Economics & Management, Springer, vol. 5(3), pages 183-220, August.
C.S. Bos & R.J. Mahieu & H.K. Van Dijk, 2000. "Daily exchange rate behaviour and hedging of currency risk," Econometric Institute Report 201, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
Other versions:
- Bos, C.S. & Mahieu, R.J. & van Dijk, H.K., 1999. "Daily Exchange Rate Behaviour and Hedging of Currency Risk," Papers 9936/a, Erasmus University of Rotterdam - Econometric Institute.
- Charles S. Bos & Ronald J. Mahieu & Herman K. van Dijk, 1999. "Daily Exchange Rate Behaviour and Hedging of Currency Risk," Tinbergen Institute Discussion Papers 99-078/4, Tinbergen Institute. [Downloadable!]
- Charles S. Bos & Ronald J. Mahieu & Herman K. van Dijk, 2001. "Daily Exchange Rate Behaviour and Hedging of Currency Risk," Tinbergen Institute Discussion Papers 01-017/4, Tinbergen Institute. [Downloadable!]
- C.S. Bos & R.J. Mahieu & H.K. van Dijk, 1999. "Daily exchange rate behaviour and hedging of currency risk," Econometric Institute Report 164, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
- Charles S. Bos & Ronald J. Mahieu & Herman K. van Dijk, 2000. "Daily Exchange Rate Behaviour and Hedging of Currency Risk," Econometric Society World Congress 2000 Contributed Papers 0504, Econometric Society. [Downloadable!]
- Charles S. Bos & Ronald J. Mahieu & Herman K. Van Dijk, 2000. "Daily exchange rate behaviour and hedging of currency risk," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(6), pages 671-696. [Downloadable!]
van Dijk, H. K. & Kloek, T., 1980. "Further experience in Bayesian analysis using Monte Carlo integration," Journal of Econometrics, Elsevier, vol. 14(3), pages 307-328, December. [Downloadable!] (restricted)
L. Bauwens & C.S. Bos & H.K. van Dijk, 1999. "Adaptive Polar Sampling with an application to a Bayes measure of Value-at-Risk," Econometric Institute Report 167, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
Other versions:
- Luc Bauwens & Charles S. Bos & Herman K. van Dijk, 1999. "Adaptive Polar Sampling with an Application to a Bayes Measure of Value-at-Risk," Tinbergen Institute Discussion Papers 99-082/4, Tinbergen Institute. [Downloadable!]
- K. Van Dijk & Luc Bauwens & Charles Bos, 2000. "Adaptive Polar Sampling With An Application To A Bayes Measure Of Value-At-Risk," Computing in Economics and Finance 2000 145, Society for Computational Economics.
- Bauwens, L. & Bos, C.S. & Van Dijk, H.K., 1999. "Adaptive Polar Sampling with an Application to a Bayes Measure of Value-at-Risk," Papers 9957, Catholique de Louvain - Center for Operations Research and Economics.
Luc Bauwens & Charles S. Bos & Herman K. van Dijk & Rutger D. van Oest, 2002. "Adaptive Polar Sampling," Computing in Economics and Finance 2002 307, Society for Computational Economics.
Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November. [Downloadable!] (restricted)
Charles S. Bos, 2002. "A Comparison of Marginal Likelihood Computation Methods," Tinbergen Institute Discussion Papers 02-084/4, Tinbergen Institute. [Downloadable!]
Luc Bauwens & Michel Lubrano, 1998. "Bayesian inference on GARCH models using the Gibbs sampler," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages C23-C46.
Other versions:
- Bauwens, L. & Lubrano, M., 1996. "Bayesian Inference on Garch Models Using the Gibbs Sampler," Papers 9627, Catholique de Louvain - Center for Operations Research and Economics.
- Bauwens, L. & Lubrano, M., 1996. "Bayesian Inference on GARCH Models Using the Gibbs Sampler," G.R.E.Q.A.M. 96a21, Universite Aix-Marseille III.
Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January. [Downloadable!] (restricted)
Enders, Walter & Granger, Clive W J, 1998. "Unit-Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 304-11, July.
Other versions:
- Walter Enders & C. W.J. Granger, 1996. "Unit-Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," University of California at San Diego, Economics Working Paper Series 96-27, Department of Economics, UC San Diego. [Downloadable!]
repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS

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