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Simulation based Bayesian econometric inference: principles and some recent computational advances

  • HOOGERHEIDE, Lennart F.
  • VAN DIJK, Herman K.
  • VAN OEST, Rutger D.

In this paper we discuss several aspects of simulation based Bayesian econometric inference. We start at an elementary level on basic concepts of Bayesian analysis; evaluating integrals by simulation methods is a crucial ingredient in Bayesian inference. Next, the most popular and well-known simulation techniques are discussed, the MetropolisHastings algorithm and Gibbs sampling (being the most popular Markov chain Monte Carlo methods) and importance sampling. After that, we discuss two recently developed sampling methods: adaptive radial based direction sampling [ARDS], which makes use of a transformation to radial coordinates, and neural network sampling, which makes use of a neural network approximation to the posterior distribution of interest. Both methods are especially useful in cases where the posterior distribution is not well-behaved, in the sense of having highly non-elliptical shapes. The simulation techniques are illustrated in several example models, such as a model for the real US GNP and models for binary data of a US recession indicator.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2007015.

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Date of creation: 00 Mar 2007
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Handle: RePEc:cor:louvco:2007015
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  1. Roberts, G. O. & Gilks, W. R., 1994. "Convergence of Adaptive Direction Sampling," Journal of Multivariate Analysis, Elsevier, vol. 49(2), pages 287-298, May.
  2. BAUWENS, Luc & BOS, Charles S. & VAN DIJK, Herman K. & VAN OEST, Rutger D., . "Adaptive radial-based direction sampling: some flexible and robust Monte Carlo integration methods," CORE Discussion Papers RP -1731, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. J. A. Hausman & D. A. Wise, 1976. "A Conditional Profit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Working papers 173, Massachusetts Institute of Technology (MIT), Department of Economics.
  4. McCulloch, Robert & Rossi, Peter E., 1994. "An exact likelihood analysis of the multinomial probit model," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 207-240.
  5. John Geweke, 1998. "Using simulation methods for Bayesian econometric models: inference, development, and communication," Staff Report 249, Federal Reserve Bank of Minneapolis.
  6. H. K. Van Dijk, 1999. "Some remarks on the simulation revolution in bayesian econometric inference," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 105-112.
  7. Chib, Siddhartha, 1992. "Bayes inference in the Tobit censored regression model," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 79-99.
  8. P. Damlen & J. Wakefield & S. Walker, 1999. "Gibbs sampling for Bayesian non-conjugate and hierarchical models by using auxiliary variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 331-344.
  9. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  10. L. Randall Wray & Stephanie Bell, 2004. "Introduction," Chapters, in: Credit and State Theories of Money, chapter 1 Edward Elgar.
  11. 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.
  12. 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.
  13. 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.
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