We introduce and analyze generalised polynomial chaos (gPC), considering both intrusive and non-intrusive approaches, as an uncertainty quantification method in studies of probabilistic robustness. The considered gPC methods are complementary to Monte Carlo (MC) methods and are shown to be fast and scalable, allowing for comprehensive and efficient exploration of parameter spaces. These properties enable robustness analysis of a wider set of models, compared to computationally expensive MC methods, while retaining desired levels of accuracy. We discuss the application of gPC methods to systems in biology and neuroscience, notably subject to multiple parametric uncertainties, and we examine a well-known model of neural dynamics as a case study.
