Bayesian inference for d-vines: Estimation and model selection

In the last two decades the advent of fast computers has made Bayesian inference, based on Markov chain Monte Carlo (MCMC) methods, very popular in many fields of science. These Bayesian methods, are good alternatives to traditional maximum likelihood (ML) methods since they can often estimate complicated statistical models for which an ML approach fails. In this chapter we review available MCMC estimation and model selection algorithms as well as their possible extensions for D-vine pair-copula constructions (PCC) based on bivariate t-copulae. However the discussed methods can easily be extended for an arbitrary regular vine PCC based on any bivariate copulae. A Bayesian inference for Australian electricity loads demonstrates the addressed algorithms at work.