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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.

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  • 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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    8. Joshua Chan & Eric Eisenstat & Xuewen Yu, 2022. "Large Bayesian VARs with Factor Stochastic Volatility: Identification, Order Invariance and Structural Analysis," Papers 2207.03988, arXiv.org.
    9. Antonio Pacifico, 2021. "Structural Panel Bayesian VAR with Multivariate Time-Varying Volatility to Jointly Deal with Structural Changes, Policy Regime Shifts, and Endogeneity Issues," Econometrics, MDPI, vol. 9(2), pages 1-35, May.
    10. 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.
    11. 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.
    12. 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.
    13. Pacifico, Antonio, 2020. "Structural Panel Bayesian VAR with Multivariate Time-varying Volatility to jointly deal with Structural Changes, Policy Regime Shifts, and Endogeneity Issues," MPRA Paper 104292, University Library of Munich, Germany.
    14. Reichl Johannes, 2020. "Estimating marginal likelihoods from the posterior draws through a geometric identity," Monte Carlo Methods and Applications, De Gruyter, vol. 26(3), pages 205-221, September.
    15. Jamie L. Cross & Aubrey Poon, 2020. "On the contribution of international shocks in Australian business cycle fluctuations," Empirical Economics, Springer, vol. 59(6), pages 2613-2637, December.
    16. Joshua C. C. Chan, 2020. "Large Bayesian VARs: A Flexible Kronecker Error Covariance Structure," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(1), pages 68-79, January.
    17. 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.
    18. 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.
    19. Joshua C. C. Chan, 2018. "Specification tests for time-varying parameter models with stochastic volatility," Econometric Reviews, Taylor & Francis Journals, vol. 37(8), pages 807-823, September.
    20. Joshua C. C. Chan & Liana Jacobi & Dan Zhu, 2022. "An automated prior robustness analysis in Bayesian model comparison," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 583-602, April.
    21. 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.
    22. Joshua C. C. Chan & Eric Eisenstat, 2018. "Bayesian model comparison for time‐varying parameter VARs with stochastic volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(4), pages 509-532, June.
    23. Junior A. Ojeda Cunya & Gabriel Rodríguez, 2022. "Time-Varying Effects of External Shocks on Macroeconomic Fluctuations in Peru: An Empirical Application using TVP-VAR- SV Models," Documentos de Trabajo / Working Papers 2022-507, Departamento de Economía - Pontificia Universidad Católica del Perú.
    24. Afees A. Salisu & Ahamuefula Ephraim Ogbonna, 2018. "Does time-variation matter in the stochastic volatility components for G7 stock returns," Working Papers 062, Centre for Econometric and Allied Research, University of Ibadan.
    25. 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.

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