  Model error estimation remains one of the key challenges in uncertainty
quantification and predictive science. For computational models of complex
physical systems, model error, also known as structural error or model
inadequacy, is often the largest contributor to the overall predictive
uncertainty. This work builds on a recently developed framework of embedded,
internal model correction, in order to represent and quantify structural
errors, together with model parameters, within a Bayesian inference context. We
focus specifically on a Polynomial Chaos representation with additive
modification of existing model parameters, enabling a non-intrusive procedure
for efficient approximate likelihood construction, model error estimation, and
disambiguation of model and data errors' contributions to predictive
uncertainty. The framework is demonstrated on several synthetic examples, as
well as on a chemical ignition problem.
