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Adaptive radial-based direction sampling: some flexible and robust Monte Carlo integration methods

Author

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  • BAUWENS, Luc
  • BOS, Charles S.
  • VAN DIJK, Herman K.
  • VAN OEST, Rutger D.
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.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • BAUWENS, Luc & BOS, Charles S. & VAN DIJK, Herman K. & VAN OEST, Rutger D., 2004. "Adaptive radial-based direction sampling: some flexible and robust Monte Carlo integration methods," LIDAM Reprints CORE 1731, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:1731
    DOI: 10.1016/j.jeconom.2003.12.002
    Note: In : Journal of Econometrics, 123, 201-225, 2004
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    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Koop, Gary & Dijk, Herman K. Van, 2000. "Testing for integration using evolving trend and seasonals models: A Bayesian approach," Journal of Econometrics, Elsevier, vol. 97(2), pages 261-291, August.
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    5. Kleibergen, Frank & van Dijk, Herman K., 1998. "Bayesian Simultaneous Equations Analysis Using Reduced Rank Structures," Econometric Theory, Cambridge University Press, vol. 14(6), pages 701-743, December.
    6. 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.
    7. Kleibergen, Frank & van Dijk, Herman K., 1994. "On the Shape of the Likelihood/Posterior in Cointegration Models," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 514-551, August.
    8. John Geweke, 1999. "Using Simulation Methods for Bayesian Econometric Models," Computing in Economics and Finance 1999 832, Society for Computational Economics.
    9. 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, Kluwer;Society for Computational Economics, vol. 5(3), pages 183-220, August.
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    11. Bauwens, L. & Bos, C.S. & van Dijk, H.K. & van Oest, R.D., 2002. "Adaptive polar sampling, a class of flexibel and robust Monte Carlo integration methods," Econometric Institute Research Papers EI 2002-27, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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    Cited by:

    1. Dellaportas, Petros & Tsionas, Mike G., 2019. "Importance sampling from posterior distributions using copula-like approximations," Journal of Econometrics, Elsevier, vol. 210(1), pages 45-57.
    2. Hoogerheide, L.F. & van Dijk, H.K., 2007. "Note on neural network sampling for Bayesian inference of mixture processes," Econometric Institute Research Papers EI 2007-15, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. L. Bauwens & J.V.K. Rombouts, 2007. "Bayesian inference for the mixed conditional heteroskedasticity model," Econometrics Journal, Royal Economic Society, vol. 10(2), pages 408-425, July.
    4. Burda Martin & Maheu John M., 2013. "Bayesian adaptively updated Hamiltonian Monte Carlo with an application to high-dimensional BEKK GARCH models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(4), pages 345-372, September.
    5. Hoogerheide, Lennart F. & Kaashoek, Johan F. & van Dijk, Herman K., 2007. "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," Journal of Econometrics, Elsevier, vol. 139(1), pages 154-180, July.
    6. Waggoner, Daniel F. & Wu, Hongwei & Zha, Tao, 2016. "Striated Metropolis–Hastings sampler for high-dimensional models," Journal of Econometrics, Elsevier, vol. 192(2), pages 406-420.
    7. McCausland, William J., 2008. "On Bayesian analysis and computation for functions with monotonicity and curvature restrictions," Journal of Econometrics, Elsevier, vol. 142(1), pages 484-507, January.
    8. Ardia, David & Baştürk, Nalan & Hoogerheide, Lennart & van Dijk, Herman K., 2012. "A comparative study of Monte Carlo methods for efficient evaluation of marginal likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3398-3414.
    9. Hoogerheide, L.F. & Kaashoek, J.F. & van Dijk, H.K., 2004. "Neural network based approximations to posterior densities: a class of flexible sampling methods with applications to reduced rank models," Econometric Institute Research Papers EI 2004-19, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    10. Bauwens, L. & Bos, C.S. & van Dijk, H.K. & van Oest, R.D., 2003. "Explaining Adaptive Radial-Based Direction Sampling," Econometric Institute Research Papers EI 2003-37, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    11. Hoogerheide, L.F. & van Dijk, H.K. & van Oest, R.D., 2007. "Simulation based bayesian econometric inference: principles and some recent computational advances," Econometric Institute Research Papers EI 2007-03, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    12. Rodney Strachan & Herman K. van Dijk, "undated". "Bayesian Model Averaging in Vector Autoregressive Processes with an Investigation of Stability of the US Great Ratios and Risk of a Liquidity Trap in the USA, UK and Japan," MRG Discussion Paper Series 1407, School of Economics, University of Queensland, Australia.
    13. 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.
    14. Tsionas, Mike G., 2019. "Multi-objective optimization using statistical models," European Journal of Operational Research, Elsevier, vol. 276(1), pages 364-378.
    15. Martin Burda & John Maheu, 2011. "Bayesian Adaptive Hamiltonian Monte Carlo with an Application to High-Dimensional BEKK GARCH Models," Working Papers tecipa-438, University of Toronto, Department of Economics.

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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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