The key operation in Bayesian inference is to compute high-dimensional integrals. An old approximate technique is the Laplace method or approximation, which dates back to Pierre-Simon Laplace (1774). This simple idea approximates the integrand with a second-order Taylor expansion around the mode...

We present a general methodology based on skew t copulas and Bayesian inference for modelling extreme multivariate dependent losses and the regulatory capital for operational risk. Current approaches fail to model both asymmetric dependence and accurate extreme upper tail dependence (e.g. 99.9%...