In a first contribution, we revisit two certificates of positivity on (possibly non-compact) basic semialgebraic sets due to Putinar and Vasilescu (C R Acad Sci Ser I Math 328(6):495–499, 1999). We use Jacobi’s technique from (Math Z 237(2):259–273, 2001) provide an alternative proof with effective degree bound the sums squares weights in such certificates. As consequence, it allows one define ...

This work presents a framework for updating an estimate of probability distribution, arising from uncertainty propagation using Non-intrusive Polynomial Chaos (NIPC), with scarce experimental measurements Quantity Interest (QoI). In recent years much has been directed towards developing methods combining models different accuracies in order to propagate uncertainty, but the problem improving pr...