Adaptive Radial-Based Direction Sampling: Some Flexible and Robust Monte Carlo Integration Methods

Posted: 14 Apr 2005

See all articles by Luc Bauwens

Luc Bauwens

Université catholique de Louvain

Charles S. Bos

VU University Amsterdam

H. K. van Dijk

Tinbergen Institute; Econometric Institute

R.D. van Oest

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE); Tinbergen Institute

Abstract

Adaptive radial-based direction sampling (ARDS) algorithms are specified for Bayesian analysis of models with nonelliptical, possibly, multimodal target distributions. A key step is a radial-based transformation to directions and distances. After the transformations a Metropolis-Hastings method or, alternatively, an importance sampling method is applied to evaluate generated directions. Next, distances are generated from the exact target distribution by means of the numerical inverse transformation method. An adaptive procedure is applied to update the initial location and covariance matrix in order to sample directions in an efficient way. Tested on a set of models that feature multimodality, strong correlation, and skewness, the ARDS algorithms compare favourably with the standard Metropolis-Hastings and importance samplers in terms of flexibility and robustness. The examples include a regression model with scale contamination and a mixture model for economic growth of the USA.

Keywords: Markov chain Monte Carlo, importance sampling, radial coordinates

JEL Classification: C11, C15, C63

Suggested Citation

Bauwens, Luc and Bos, Charles S. and van Dijk, Herman K. and van Oest, Rutger, Adaptive Radial-Based Direction Sampling: Some Flexible and Robust Monte Carlo Integration Methods. Journal of Econometrics, Vol. 123, No. 3, pp. 201-225. Available at SSRN: https://ssrn.com/abstract=691888

Luc Bauwens (Contact Author)

Université catholique de Louvain ( email )

CORE
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B-1348 Louvain-la-Neuve, b-1348
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Charles S. Bos

VU University Amsterdam ( email )

De Boelelaan 1105
1081 HV Amsterdam
Netherlands

HOME PAGE: http://personal.vu.nl/c.s.bos

Herman K. Van Dijk

Tinbergen Institute ( email )

Gustav Mahlerplein 117
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Amsterdam/Rotterdam, 1082 MS
Netherlands
+31104088955 (Phone)
+31104089031 (Fax)

HOME PAGE: http://people.few.eur.nl/hkvandijk/

Econometric Institute ( email )

P.O. Box 1738
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Netherlands
+31 10 4088955 (Phone)
+31 10 4527746 (Fax)

Rutger Van Oest

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE) ( email )

P.O. Box 1738
3000 DR Rotterdam, NL 3062 PA
Netherlands
+31 10 408 8946 (Phone)
+31 10 408 9162 (Fax)

Tinbergen Institute

P.O. Box 1738
H16-32
3000 DR Rotterdam
Netherlands

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