Copula modelling with penalized complexity priors: the bivariate case

Diego Battagliese (), Clara Grazian (), Brunero Liseo () and Cristiano Villa ()
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Diego Battagliese: University of Sassari
Clara Grazian: University of Sidney
Brunero Liseo: Sapienza University of Rome
Cristiano Villa: Newcastle University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2023, vol. 32, issue 2, No 8, 542-565

Abstract: 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.

Keywords: $$\alpha $$ α -divergence; Hierarchical PC prior; Intrinsic prior; Jeffreys’ prior; Objective PC prior; PC prior; 62F15; 62H99 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11749-022-00843-w

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