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The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference

Author

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  • Baştürk, Nalan
  • Grassi, Stefano
  • Hoogerheide, Lennart
  • Opschoor, Anne
  • van Dijk, Herman K.
Abstract
This paper presents the R package MitISEM (mixture of t by importance sampling weighted expectation maximization) which provides an automatic and flexible two-stage method to approximate a non-elliptical target density kernel - typically a posterior density kernel - using an adaptive mixture of Student t densities as approximating density. In the first stage a mixture of Student t densities is fitted to the target using an expectation maximization algorithm where each step of the optimization procedure is weighted using importance sampling. In the second stage this mixture density is a candidate density for efficient and robust application of importance sampling or the Metropolis-Hastings (MH) method to estimate properties of the target distribution. The package enables Bayesian inference and prediction on model parameters and probabilities, in particular, for models where densities have multi-modal or other non-elliptical shapes like curved ridges. These shapes occur in research topics in several scientific fields. For instance, analysis of DNA data in bio-informatics, obtaining loans in the banking sector by heterogeneous groups in financial economics and analysis of education's effect on earned income in labor economics. The package MitISEM provides also an extended algorithm, 'sequential MitISEM', which substantially decreases computation time when the target density has to be approximated for increasing data samples. This occurs when the posterior or predictive density 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 MH using the candidate density obtained by MitISEM outperforms, in terms of numerical efficiency, MH using a simpler candidate, as well as the Gibbs sampler. The MitISEM approach is also used for Bayesian model comparison using predictive likelihoods.

Suggested Citation

  • Baştürk, Nalan & Grassi, Stefano & Hoogerheide, Lennart & Opschoor, Anne & van Dijk, Herman K., 2017. "The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 79(i01).
    • Handle: RePEc:jss:jstsof:v:079:i01
    DOI: http://hdl.handle.net/10.18637/jss.v079.i01
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    References listed on IDEAS

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    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Ardia, David & Hoogerheide, Lennart F. & van Dijk, Herman K., 2009. "Adaptive Mixture of Student-t Distributions as a Flexible Candidate Distribution for Efficient Simulation: The R Package AdMit," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 29(i03).
    3. 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.
    4. 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.
    5. Ausin, Maria Concepcion & Galeano, Pedro, 2007. "Bayesian estimation of the Gaussian mixture GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2636-2652, February.
    6. Jana Eklund & Sune Karlsson, 2007. "Forecast Combination and Model Averaging Using Predictive Measures," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 329-363.
    7. Bowden,Roger J. & Turkington,Darrell A., 1990. "Instrumental Variables," Cambridge Books, Cambridge University Press, number 9780521385824, September.
    8. 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.
    9. Charles S. Bos & Ronald J. Mahieu & Herman K. Van Dijk, 2000. "Daily exchange rate behaviour and hedging of currency risk," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(6), pages 671-696.
    10. Koop,Gary & Poirier,Dale J. & Tobias,Justin L., 2007. "Bayesian Econometric Methods," Cambridge Books, Cambridge University Press, number 9780521671736, June.
    11. Kleibergen, Frank & van Dijk, Herman K., 1998. "Bayesian Simultaneous Equations Analysis Using Reduced Rank Structures," Econometric Theory, Cambridge University Press, vol. 14(6), pages 701-743, December.
    12. Chan,Joshua & Koop,Gary & Poirier,Dale J. & Tobias,Justin L., 2019. "Bayesian Econometric Methods," Cambridge Books, Cambridge University Press, number 9781108423380, September.
    13. Hoogerheide, Lennart & Opschoor, Anne & van Dijk, Herman K., 2012. "A class of adaptive importance sampling weighted EM algorithms for efficient and robust posterior and predictive simulation," Journal of Econometrics, Elsevier, vol. 171(2), pages 101-120.
    14. Ardia, David & Hoogerheide, Lennart F. & van Dijk, Herman K., 2009. "Adaptive Mixture of Student-t Distributions as a Flexible Candidate Distribution for Efficient Simulation: The R Package AdMit," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 29(i03).
    15. Chan,Joshua & Koop,Gary & Poirier,Dale J. & Tobias,Justin L., 2019. "Bayesian Econometric Methods," Cambridge Books, Cambridge University Press, number 9781108437493, September.
    16. Martin, Andrew D. & Quinn, Kevin M. & Park, Jong Hee, 2011. "MCMCpack: Markov Chain Monte Carlo in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 42(i09).
    17. Arnold Zellner & Tomohiro Ando & Nalan Baştük & Lennart Hoogerheide & Herman K. van Dijk, 2014. "Bayesian Analysis of Instrumental Variable Models: Acceptance-Rejection within Direct Monte Carlo," Econometric Reviews, Taylor & Francis Journals, vol. 33(1-4), pages 3-35, June.
    18. 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.
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    Cited by:

    1. Baştürk, N. & Borowska, A. & Grassi, S. & Hoogerheide, L. & van Dijk, H.K., 2019. "Forecast density combinations of dynamic models and data driven portfolio strategies," Journal of Econometrics, Elsevier, vol. 210(1), pages 170-186.
    2. Ivan Mendieta-Munoz & Mengheng Li, 2019. "The Multivariate Simultaneous Unobserved Compenents Model and Identification via Heteroskedasticity," Working Paper Series, Department of Economics, University of Utah 2019_06, University of Utah, Department of Economics.
    3. Dellaportas, Petros & Tsionas, Mike G., 2019. "Importance sampling from posterior distributions using copula-like approximations," Journal of Econometrics, Elsevier, vol. 210(1), pages 45-57.
    4. Geweke, John & Durham, Garland, 2019. "Sequentially adaptive Bayesian learning algorithms for inference and optimization," Journal of Econometrics, Elsevier, vol. 210(1), pages 4-25.
    5. Nalan Basturk & Stefano Grassi & Lennart Hoogerheide & Herman K. van Dijk, 2016. "Time-varying Combinations of Bayesian Dynamic Models and Equity Momentum Strategies," Tinbergen Institute Discussion Papers 16-099/III, Tinbergen Institute.

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    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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