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Experiments With Some Alternatives For Simple Importance Sampling In Monte Carlo Integration

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  • van Dijk, H. K.
  • Kloek, T.

Abstract

Some alternatives for simple importance sampling [compare Kloek and van Dijk (1978) and van Dijk and Kloek (1980)] are investigated for the compu— tation of posterior moments and densities. An importance sampling method that is based on a mixture of a finite number of multivariate normal densities is compared with simple importance sampling and with a method that is based on a combination of Monte Carlo and classical numerical integration. These methods are intended to handle econometric applications where a simple importance function that is a reasonable approximation to the posterior density is difficult to find. For illustrative purposes use is made of a small econometric model. The results include bivariate marginal densities of the importance functions and the posterior plotted in three dimensional figures.

Suggested Citation

  • van Dijk, H. K. & Kloek, T., 1983. "Experiments With Some Alternatives For Simple Importance Sampling In Monte Carlo Integration," Econometric Institute Archives 272281, Erasmus University Rotterdam.
    • Handle: RePEc:ags:eureia:272281
    DOI: 10.22004/ag.econ.272281
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    References listed on IDEAS

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    1. 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.
    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.
    3. van Dijk, H. K. & Kloek, T., 1982. "Posterior Moments Of The Klein-Goldberger Model," Econometric Institute Archives 272269, Erasmus University Rotterdam.
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    1. Nalan Basturk & Cem Cakmakli & S. Pinar Ceyhan & Herman K. van Dijk, 2013. "Historical Developments in Bayesian Econometrics after Cowles Foundation Monographs 10, 14," Tinbergen Institute Discussion Papers 13-191/III, Tinbergen Institute.
    2. Nalan Basturk & Cem Cakmakli & S. Pinar Ceyhan & Herman K. van Dijk, 2014. "On the Rise of Bayesian Econometrics after Cowles Foundation Monographs 10, 14," Tinbergen Institute Discussion Papers 14-085/III, Tinbergen Institute, revised 04 Sep 2014.
    3. VAN DIJK, Herman K., 1987. "Some advances in Bayesian estimations methods using Monte Carlo Integration," LIDAM Reprints CORE 783, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. 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.
    5. Lennart F. Hoogerheide & Johan F. Kaashoek, 2004. "Functional Approximations to Likelihoods/Posterior Densities: A Neural Network Approach to Efficient Sampling," Computing in Economics and Finance 2004 74, Society for Computational Economics.

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