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Some advances in Bayesian estimations methods using Monte Carlo Integration

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  • VAN DIJK, Herman K.

Abstract

In this paper some Monte Carlo integration methods are discussed that can be used for the efficient computation of posterior moments and densities of parameters of econometric and, more generally, statistical models. The methods are based on the principle of importance sampling and are intended for the evaluation of multi-dimensional integrals where the integrand is unimodal and multivariate skew. That is, the integrand has different tail behavior in different directions. Illustrative results are presented on the dynamic behavior and the probability of explosion of a small scale macro-economic model. This application involves nine-dimensional numerical integration.
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  • 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).
    • Handle: RePEc:cor:louvrp:783
    Note: In : Advances in Econometrics, 6, 215-261, 1987
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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. Kiefer, Nicholas M, 1981. "Limited Information Analysis of a Small Underidentified Macroeconomic Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(2), pages 429-442, June.
    3. Van Dijk, Herman K. & Kloek, Teun & Boender, C. Guus E., 1985. "Posterior moments computed by mixed integration," Journal of Econometrics, Elsevier, vol. 29(1-2), pages 3-18.
    4. van Dijk, H. K. & Hop, J. P. & Louter, A. S., 1986. "An Algorithm For The Computation Of Posterior Moments And Densities Using Simple Importance Sampling," Econometric Institute Archives 272354, Erasmus University Rotterdam.
    5. van Dijk, H. K. & Kloek, T., 1982. "Posterior Moments Of The Klein-Goldberger Model," Econometric Institute Archives 272269, Erasmus University Rotterdam.
    6. 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.
    7. van Dijk, H. K. & Kloek, T., 1982. "Monte Carlo Analysis Of Skew Posterior Distributions: An Illustrative Econometric Example," Econometric Institute Archives 272268, Erasmus University Rotterdam.
    8. Geweke, John, 1986. "Exact Inference in the Inequality Constrained Normal Linear Regression Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 1(2), pages 127-141, April.
    9. Quandt, Richard E., 1983. "Computational problems and methods," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 12, pages 699-764, Elsevier.
    10. Kooiman, Peter & Van Dijk, Herman K. & Thurik, A. Roy, 1985. "Likelihood diagnostics and Bayesian analysis of a micro-economic disequilibrium model for retail services," Journal of Econometrics, Elsevier, vol. 29(1-2), pages 121-148.
    11. Hendry, David F., 1984. "Monte carlo experimentation in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 16, pages 937-976, Elsevier.
    12. 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.
    13. van Dijk, H. K. & Kloek, T., 1976. "PREDICTIVE MOMENTS OF SIMULTANEOUS ECONOMETRIC MODELS A Bayesian Approach," Econometric Institute Archives 272131, Erasmus University Rotterdam.
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    Cited by:

    1. Bauwens, L. & Dijk, H. K., 1989. "Bayesian Limited Information Analysis Revisited," Econometric Institute Archives 272386, Erasmus University Rotterdam.
    2. van Dijk, H.K., 2002. "On Bayesian structural inference in a simultaneous equation model," Econometric Institute Research Papers EI 2002-10, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Hop, J. P. & van Duk, H. K., 1990. "Two Algorithms For The Computation Of Posterior Moments And Densities Using Monte Carlo Integration," Econometric Institute Archives 272483, Erasmus University Rotterdam.

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