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Marginal likelihoods for non-Gaussian models using auxiliary mixture sampling

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  • Frühwirth-Schnatter, Sylvia
  • Wagner, Helga

Abstract

Several new estimators of the marginal likelihood for complex non-Gaussian models are developed. These estimators make use of the output of auxiliary mixture sampling for count data and for binary and multinomial data. One of these estimators is based on combining Chib's estimator with data augmentation as in auxiliary mixture sampling, while the other estimators are importance sampling and bridge sampling based on constructing an unsupervised importance density from the output of auxiliary mixture sampling. These estimators are applied to a logit regression model, to a Poisson regression model, to a binomial model with random intercept, as well as to state space modeling of count data.

Suggested Citation

  • Frühwirth-Schnatter, Sylvia & Wagner, Helga, 2008. "Marginal likelihoods for non-Gaussian models using auxiliary mixture sampling," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4608-4624, June.
  • Handle: RePEc:eee:csdana:v:52:y:2008:i:10:p:4608-4624
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    Citations

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    Cited by:

    1. Bauwens, Luc & Rombouts, Jeroen V.K., 2012. "On marginal likelihood computation in change-point models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3415-3429.
    2. Chan, Joshua C.C. & Koop, Gary, 2014. "Modelling breaks and clusters in the steady states of macroeconomic variables," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 186-193.
    3. Joshua C. C. Chan & Eric Eisenstat, 2015. "Marginal Likelihood Estimation with the Cross-Entropy Method," Econometric Reviews, Taylor & Francis Journals, vol. 34(3), pages 256-285, March.
    4. Ardia, David & Baştürk, Nalan & Hoogerheide, Lennart & van Dijk, Herman K., 2012. "A comparative study of Monte Carlo methods for efficient evaluation of marginal likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3398-3414.
    5. Koop, Gary & Korobilis, Dimitris, 2010. "Bayesian Multivariate Time Series Methods for Empirical Macroeconomics," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(4), pages 267-358, July.
    6. Frühwirth-Schnatter, Sylvia & Wagner, Helga, 2010. "Stochastic model specification search for Gaussian and partial non-Gaussian state space models," Journal of Econometrics, Elsevier, vol. 154(1), pages 85-100, January.
    7. Joshua C.C. Chan & Eric Eisenstat, 2015. "Bayesian model comparison for time-varying parameter VARs with stochastic volatility," CAMA Working Papers 2015-32, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    8. Joshua C.C. Chan, 2015. "Specification tests for time-varying parameter models with stochastic volatility," CAMA Working Papers 2015-42, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    9. 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.
    10. Chan, Joshua C.C. & Grant, Angelia L., 2015. "Pitfalls of estimating the marginal likelihood using the modified harmonic mean," Economics Letters, Elsevier, vol. 131(C), pages 29-33.
    11. Bijwaard, Govert E. & Franses, Philip Hans, 2009. "The effect of rounding on payment efficiency," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1449-1461, February.
    12. Arnold Zellner & Tomohiro Ando & Nalan Basturk & Lennart Hoogerheide & Herman K. van Dijk, 2011. "Instrumental Variables, Errors in Variables, and Simultaneous Equations Models: Applicability and Limitations of Direct Monte Carlo," Tinbergen Institute Discussion Papers 11-137/4, Tinbergen Institute.
    13. Joshua C.C. Chan, 2015. "Large Bayesian VARs: A flexible Kronecker error covariance structure," CAMA Working Papers 2015-41, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.

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