Copula modelling with penalized complexity priors: the bivariate case

• Diego Battagliese ^[1] ; Clara Grazian ^[3] ; Brunero Liseo ^[4] ; Cristiano Villa ^[2]
  1. [1] University of Sassari

     University of Sassari

     Sassari, Italia

     
  2. [2] Newcastle University

     Newcastle University

     Reino Unido

     
  3. [3] University of Sidney
  4. [4] University of Rome

  Mostrar afiliaciones +
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 32, Nº. 2, 2023, págs. 542-565
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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 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.