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Adaptive radial-based direction sampling; Some flexible and robust Monte Carlo integration methods

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Author Info
Bauwens, L.
Bos, C.S.
Dijk, H.K. van
Oest, R.D. van (Erasmus Econometric Institute)

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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 canonical mixture 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 empirical examples include a regression model with scale contamination and a mixture model for economic growth of the USA.

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File URL: http://hdl.handle.net/1765/1722
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Publisher Info
Paper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number EI 2003-22 Revision_Date: 2009-10-14.

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Date of creation: 06 Aug 2003
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Handle: RePEc:dgr:eureir:1765001722

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Related research
Keywords: Markov chain Monte Carlo; importance sampling; radial coordinates;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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.
  2. 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)
  3. 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.
  4. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November. [Downloadable!] (restricted)
  5. Kleibergen, F.R. & Van Dijk, H.K., 1993. "On the Shape of the Likelyhood/Posterior in Cointegration Models," Papers 9315-a, Erasmus University of Rotterdam - Econometric Institute.
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  6. G. Koop & H.K. van Dijk, 1999. "Testing for integration using evolving trend and seasonal models A Bayesian approach," Econometric Institute Report 163, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. HOOGERHEIDE, Lennart F. & KAASHOEK, Johan F. & VAN DIJK, Herman K., 2005. "On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: An application of flexible sampling methods using neural networks," CORE Discussion Papers 2005029, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
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  2. David Ardia & Lennart Hoogerheide & Herman K. van Dijk, 2009. "To Bridge, to Warp or to Wrap? A Comparative Study of Monte Carlo Methods for Efficient Evaluation of Marginal Likelihoods," Tinbergen Institute Discussion Papers 09-017/4, Tinbergen Institute. [Downloadable!]
  3. Luc Bauwens & Jeroen V.K. Rombouts, 2006. "Bayesian inference for the mixed conditional heteroskedasticity model," Cahiers de recherche 06-07, HEC Montréal, Institut d'économie appliquée. [Downloadable!]
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