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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.

Suggested Citation

  • Liesenfeld, Roman & Richard, Jean-François, 2006. "Improving MCMC Using Efficient Importance Sampling," Economics Working Papers 2006-05, Christian-Albrechts-University of Kiel, Department of Economics.
  • Handle: RePEc:zbw:cauewp:4349
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    References listed on IDEAS

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    Cited by:

    1. Bauwens, L. & Galli, F., 2009. "Efficient importance sampling for ML estimation of SCD models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1974-1992, April.
    2. Bastian Gribisch, 2016. "Multivariate Wishart stochastic volatility and changes in regime," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 443-473, October.
    3. Raices Cruz, Ivette & Lindström, Johan & Troffaes, Matthias C.M. & Sahlin, Ullrika, 2022. "Iterative importance sampling with Markov chain Monte Carlo sampling in robust Bayesian analysis," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    4. 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.
    5. Charles S. Bos, 2011. "Relating Stochastic Volatility Estimation Methods," Tinbergen Institute Discussion Papers 11-049/4, Tinbergen Institute.
    6. 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.

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