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Copula modelling with penalized complexity priors: the bivariate case

Author

Listed:
  • Diego Battagliese

    (University of Sassari)

  • Clara Grazian

    (University of Sidney
    University of Sydney)

  • Brunero Liseo

    (Sapienza University of Rome)

  • Cristiano Villa

    (Newcastle University)

Abstract

We explore the use of penalized complexity (PC) priors for assessing the dependence structure in a multivariate distribution F, with a particular emphasis on the bivariate case. We use the copula representation of F and derive the PC prior for the parameter governing the copula. We show that any $$\alpha $$ α -divergence between a multivariate distribution and its counterpart with independent components does not depend on the marginal distribution of the components. This implies that the PC prior for the parameters of the copula can be elicited independently of the specific form of the marginal distributions. This represents a useful simplification in the model building step and may offer a new perspective in the field of objective Bayesian methodology. We also consider strategies for minimizing the role of subjective inputs in the prior elicitation step. Finally, we explore the use of PC priors in Bayesian hypothesis testing. Our prior is compared with competing default priors both for estimation purposes and testing.

Suggested Citation

  • Diego Battagliese & Clara Grazian & Brunero Liseo & Cristiano Villa, 2023. "Copula modelling with penalized complexity priors: the bivariate case," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 542-565, June.
    • Handle: RePEc:spr:testjl:v:32:y:2023:i:2:d:10.1007_s11749-022-00843-w
    DOI: 10.1007/s11749-022-00843-w
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    References listed on IDEAS

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    1. Cristiano Villa & Stephen Walker, 2015. "An Objective Bayesian Criterion to Determine Model Prior Probabilities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 947-966, December.
    2. M. J. Bayarri & G. García‐Donato, 2008. "Generalization of Jeffreys divergence‐based priors for Bayesian hypothesis testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 981-1003, November.
    3. Sigrunn Holbek Sørbye & Håvard Rue, 2017. "Penalised Complexity Priors for Stationary Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 923-935, November.
    4. M.J. Bayarri & Gonzalo García-Donato, 2007. "Extending conventional priors for testing general hypotheses in linear models," Biometrika, Biometrika Trust, vol. 94(1), pages 135-152.
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