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In mixed company: Bayesian inference for bivariate conditional copula models with discrete and continuous outcomes

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  • Craiu, V. Radu
  • Sabeti, Avideh

Abstract

Conditional copula models are flexible tools for modelling complex dependence structures in regression settings. We construct Bayesian inference for the conditional copula model adapted to regression settings in which the bivariate outcome is continuous or mixed. The dependence between the copula parameter and the covariate is modelled using cubic splines. The proposed joint Bayesian inference is carried out using adaptive Markov chain Monte Carlo sampling. The deviance information criterion (DIC) is used for selecting the copula family that best approximates the data and for choosing the calibration function. The performances of the estimation and model selection methods are investigated using simulations.

Suggested Citation

  • Craiu, V. Radu & Sabeti, Avideh, 2012. "In mixed company: Bayesian inference for bivariate conditional copula models with discrete and continuous outcomes," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 106-120.
    • Handle: RePEc:eee:jmvana:v:110:y:2012:i:c:p:106-120
    DOI: 10.1016/j.jmva.2012.03.010
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    References listed on IDEAS

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    3. Grazian, Clara & Dalla Valle, Luciana & Liseo, Brunero, 2022. "Approximate Bayesian conditional copulas," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    4. Kang, Xiaoning & Kang, Lulu & Chen, Wei & Deng, Xinwei, 2022. "A generative approach to modeling data with quantitative and qualitative responses," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    5. Nicolai Hans & Nadja Klein & Florian Faschingbauer & Michael Schneider & Andreas Mayr, 2023. "Boosting distributional copula regression," Biometrics, The International Biometric Society, vol. 79(3), pages 2298-2310, September.
    6. Luciana Dalla Valle & Fabrizio Leisen & Luca Rossini, 2018. "Bayesian non‐parametric conditional copula estimation of twin data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(3), pages 523-548, April.
    7. Levi, Evgeny & Craiu, Radu V., 2018. "Bayesian inference for conditional copulas using Gaussian Process single index models," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 115-134.
    8. Quanrui Song & Jianxu Liu & Songsak Sriboonchitta, 2019. "Risk Measurement of Stock Markets in BRICS, G7, and G20: Vine Copulas versus Factor Copulas," Mathematics, MDPI, vol. 7(3), pages 1-16, March.
    9. Vatter, Thibault & Chavez-Demoulin, Valérie, 2015. "Generalized additive models for conditional dependence structures," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 147-167.
    10. Derumigny Alexis & Fermanian Jean-David, 2017. "About tests of the “simplifying” assumption for conditional copulas," Dependence Modeling, De Gruyter, vol. 5(1), pages 154-197, August.
    11. Smith, Michael Stanley, 2023. "Implicit Copulas: An Overview," Econometrics and Statistics, Elsevier, vol. 28(C), pages 81-104.
    12. Acar, Elif F. & Czado, Claudia & Lysy, Martin, 2019. "Flexible dynamic vine copula models for multivariate time series data," Econometrics and Statistics, Elsevier, vol. 12(C), pages 181-197.

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