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The R Package MitISEM: Mixture of Student-t Distributions using Importance Sampling Weighted Expectation Maximization for Efficient and Robust Simulation

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Author Info

  • Nalan Basturk

    (Erasmus University Rotterdam)

  • Lennart Hoogerheide

    (VU University Amsterdam)

  • Anne Opschoor

    (Erasmus University Rotterdam)

  • Herman K. van Dijk

    (EUR & VU)

Abstract

This paper presents the R package MitISEM, which provides an automatic and flexible method to approximate a non-elliptical target density using adaptive mixtures of Student-t densities, where only a kernel of the target density is required. The approximation can be used as a candidate density in Importance Sampling or Metropolis Hastings methods for Bayesian inference on model parameters and probabilities. The package provides also an extended MitISEM algorithm, ‘sequential MitISEM’, which substantially decreases the computational time when the target density has to be approximated for increasing data samples. This occurs when the posterior distribution is updated with new observations and/or when one computes model probabilities using predictive likelihoods. We illustrate the MitISEM algorithm using three canonical statistical and econometric models that are characterized by several types of non-elliptical posterior shapes and that describe well-known data patterns in econometrics and finance. We show that the candidate distribution obtained by MitISEM outperforms those obtained by ‘naive’ approximations in terms of numerical efficiency. Further, the MitISEM approach can be used for Bayesian model comparison, using the predictive likelihoods.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 12-096/III.

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Date of creation: 20 Sep 2012
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Handle: RePEc:dgr:uvatin:20120096

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Web page: http://www.tinbergen.nl

Related research

Keywords: finite mixtures; Student-t distributions; Importance Sampling; MCMC; Metropolis-Hastings algorithm; Expectation Maximization; Bayesian inference; R software;

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References

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  1. David Ardia & Lennart F. Hoogerheide & Herman K. van Dijk, . "Adaptive Mixture of Student-t Distributions as a Flexible Candidate Distribution for Efficient Simulation: The R Package AdMit," Journal of Statistical Software, American Statistical Association, vol. 29(i03).
  2. 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, Society for Computational Economics, vol. 5(3), pages 183-220, August.
  3. Hoogerheide, Lennart & Kleibergen, Frank & van Dijk, Herman K., 2007. "Natural conjugate priors for the instrumental variables regression model applied to the Angrist-Krueger data," Journal of Econometrics, Elsevier, vol. 138(1), pages 63-103, May.
  4. Lennart Hoogerheide & Anne Opschoor & Herman K. van Dijk, 2012. "A Class of Adaptive Importance Sampling Weighted EM Algorithms for Efficient and Robust Posterior and Predictive Simulation," Tinbergen Institute Discussion Papers 12-026/4, Tinbergen Institute.
  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. Charles S. Bos & Ronald J. Mahieu & Herman K. van Dijk, 2001. "Daily Exchange Rate Behaviour and Hedging of Currency Risk," Tinbergen Institute Discussion Papers 01-017/4, Tinbergen Institute.
  7. Eklund, Jana & Karlsson, Sune, 2005. "Forecast Combination and Model Averaging using Predictive Measures," Working Paper Series 191, Sveriges Riksbank (Central Bank of Sweden).
  8. Frank Kleibergen & Herman K. van Dijk, 1998. "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures," Tinbergen Institute Discussion Papers 98-025/4, Tinbergen Institute.
  9. Ardia, David & Hoogerheide, Lennart F. & van Dijk, Herman K., 2008. "AdMit: Adaptive Mixtures of Student-t Distributions," DQE Working Papers 10, Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland, revised 07 Jan 2009.
  10. 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.
  11. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  12. Bowden,Roger J. & Turkington,Darrell A., 1990. "Instrumental Variables," Cambridge Books, Cambridge University Press, number 9780521385824.
  13. Dreze, Jacques H., 1977. "Bayesian regression analysis using poly-t densities," Journal of Econometrics, Elsevier, vol. 6(3), pages 329-354, November.
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