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Improving MCMC Using Efficient Importance Sampling

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  • Liesenfeld, Roman
  • Richard, Jean-François

Abstract

This paper develops a systematic Markov Chain Monte Carlo (MCMC) framework based upon Efficient Importance Sampling (EIS) which can be used for the analysis of a wide range of econometric models involving integrals without an analytical solution. EIS is a simple, generic and yet accurate Monte-Carlo integration procedure based on sampling densities which are chosen to be global approximations to the integrand. By embedding EIS within MCMC procedures based on Metropolis-Hastings (MH) one can significantly improve their numerical properties, essentially by providing a fully automated selection of critical MCMC components such as auxiliary sampling densities, normalizing constants and starting values. The potential of this integrated MCMC- EIS approach is illustrated with simple univariate integration problems and with the Bayesian posterior analysis of stochastic volatility models and stationary autoregressive processes. --

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Bibliographic Info

Paper provided by Christian-Albrechts-University of Kiel, Department of Economics in its series Economics Working Papers with number 2006,05.

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Date of creation: 2006
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Handle: RePEc:zbw:cauewp:4349

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Keywords: Autoregressive models; Bayesian posterior analysis; Dynamic latent variables; Gibbs sampling; Metropolis Hastings; Stochastic volatility;

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References

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  1. John Geweke, 1998. "Using simulation methods for Bayesian econometric models: inference, development, and communication," Staff Report 249, Federal Reserve Bank of Minneapolis.
  2. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 371-89, October.
  3. BAUWENS, Luc & HAUTSCH, Nikolaus, 2003. "Dynamic latent factor models for intensity processes," CORE Discussion Papers 2003103, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996. "Stochastic Volatility: Likelihood Inference And Comparison With Arch Models," Econometrics 9610002, EconWPA.
  5. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
  6. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  7. Roman Liesenfeld & Jean-Francois Richard, 2006. "Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 335-360.
  8. Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
  9. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  10. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  11. Luc Bauwens & Nikolaus Hautsch, 2006. "Stochastic Conditional Intensity Processes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(3), pages 450-493.
  12. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Estimation of Dynamic Bivariate Mixture Models: Comments on Watanabe (2000)," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 570-76, October.
  13. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
  14. Sandmann, Gleb & Koopman, Siem Jan, 1998. "Estimation of stochastic volatility models via Monte Carlo maximum likelihood," Journal of Econometrics, Elsevier, vol. 87(2), pages 271-301, September.
  15. Richard, Jean-Francois & Zhang, Wei, 2007. "Efficient high-dimensional importance sampling," Journal of Econometrics, Elsevier, vol. 141(2), pages 1385-1411, December.
  16. Neil Shephard & Siem Jan Koopman, 2002. "Testing the assumptions behind the use of importance sampling," Economics Series Working Papers 2002-W17, University of Oxford, Department of Economics.
  17. 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.
  18. Neil Shephard & Michael K Pitt, 1995. "Likelihood analysis of non-Gaussian parameter driven models," Economics Papers 15 & 108., Economics Group, Nuffield College, University of Oxford.
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Citations

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Cited by:
  1. BAUWENS, Luc & GALLI, Fausto, 2007. "Efficient importance sampling for ML estimation of SCD models," CORE Discussion Papers 2007053, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Naylor, J.C. & Tremayne, A.R. & Marriott, J.M., 2010. "Exploratory data analysis and model criticism with posterior plots," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2707-2720, November.
  3. Pastorello, S. & Rossi, E., 2010. "Efficient importance sampling maximum likelihood estimation of stochastic differential equations," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2753-2762, November.

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