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Title: Copula modelling with penalised complexity priors Authors:  Cristiano Villa - Newcastle University (United Kingdom)
Liseo Brunero - La Sapienza University of Rome (Italy)
Diego Battagliese - University of Rome La Sapienza (Italy)
Clara Grazian - University of Sydney (Australia) [presenting]
Abstract: The use of penalised complexity priors is explored for assessing the dependence structure in a multivariate distribution. We use the copula representation and derive penalised complexity priors for the parameter governing the copula. We show that any alpha-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 penalised complexity prior to 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 minimising the role of subjective inputs in the prior elicitation step. Finally, we explore the use of penalised complexity priors in Bayesian hypothesis testing. Our prior is compared with competing default priors both for estimation purposes and testing.