Gareth Peters (UCL)
Sequential Monte Carlo Samplers for capital allocation under copula-dependent risk models
In this talk we assume a multivariate risk model has been developed for a portfolio and its capital derived as a homogeneous risk measure. The Euler (or gradient) principle, then, states that the capital to be allocated to each component of the portfolio has to be calculated as an expectation conditional to a rare event, which can be challenging to evaluate in practice. We exploit the copula-dependence within the portfolio risks to design a Sequential Monte Carlo Samplers based estimate to the marginal conditional expectations involved in the problem, showing its efficiency through a series of computational examples.

Leonard Held (University of Zurich)
Adaptive prior weighting in generalized linear models
The prior distribution is a key ingredient in Bayesian inference. Prior information in generalized linear models may come from different sources and may or may not be in conflict with the observed data. Various methods have been proposed to quantify a potential prior-data conflict, such as Box's $p$-value. However, the literature is sparse on methodology what to do if the prior is not compatible with the observed data. To this end, we review and extend methods to adaptively weight the prior distribution. We relate empirical Bayes estimates of prior weight to Box's p-value and propose alternative fully Bayesian approaches. Prior weighting can be done for the joint prior distribution of the regression coefficients or - under prior independence - separately for each regression coefficient or for pre-specified blocks of regression coefficients. We outline how the proposed methodology can be implemented using integrated nested Laplace approximations (INLA) and illustrate the applicability with a logistic and a log-linear Poisson multiple regression model. This is joint work with Rafael Sauter.