Bayesian model selection for D-vine pair-copula constructions Aleksey MIN and Claudia CZADO Abstract In recent years analyses of dependence structures using copulas have become more popular than the standard correlation analysis. Starting from Aas, Czado, Frigessi, and Bakken (2009) regular vine pair-copula constructions (PCCs) are considered the most flexible class of multivariate copulas. PCCs are involved objects but (conditional) independence present in data can simplify and reduce them significantly. In this paper the authors detect (conditional) independence in a particular vine PCC model based on bivariate t−copulas by deriving and implementing a reversible jump Markov chain Monte Carlo algorithm. However the methodology is general and can be extended to any regular vine PCC and to all known bivariate copula families. The proposed approach considers model selection and estimation problems for PCCs simultaneously. The effectiveness of the developed algo- rithm is shown in simulations and its usefulness is illustrated in two real data applications. Keywords: copula, D-vine, Metropolis-Hastings algorithm, pair-copula construction, re- versible jump Markov chain Monte Carlo. 1 Introduction Over the past decade there has been a large interest in copulas as a tool for capturing the dependence structure between random variables. Since Frees and Valdez (1998), Li (2000) and Embrechts, McNeil, and Straumann (2002), copulas have been widely used in economics, finance and risk management and subsequently applied to other fields. For a comprehensive review on this topic we refer readers to Genest and Favre (2007), Genest, Gendron, and Bourdeau-Brien (2009) and Patton (2009). Most copula applications deal with bivariate data while examples involving multivari- ate copulas of dimension d ≥ 3 are often restricted to Archimedean copulas, elliptical (usually Gaussian or t) copulas or their extensions (see e.g. Song, 2000; Frahm, Junker, 1