  The ultimate purpose of most computational models is to make predictions,
commonly in support of some decision-making process (e.g., for design or
operation of some system). The quantities that need to be predicted (the
quantities of interest or QoIs) are generally not experimentally observable
before the prediction, since otherwise no prediction would be needed. Assessing
the validity of such extrapolative predictions, which is critical to informed
decision-making, is challenging. In classical approaches to validation, model
outputs for observed quantities are compared to observations to determine if
they are consistent. By itself, this consistency only ensures that the model
can predict the observed quantities under the conditions of the observations.
This limitation dramatically reduces the utility of the validation effort for
decision making because it implies nothing about predictions of unobserved QoIs
or for scenarios outside of the range of observations. However, there is no
agreement in the scientific community today regarding best practices for
validation of extrapolative predictions made using computational models. The
purpose of this paper is to propose and explore a validation and predictive
assessment process that supports extrapolative predictions for models with
known sources of error. The process includes stochastic modeling, calibration,
validation, and predictive assessment phases where representations of known
sources of uncertainty and error are built, informed, and tested. The proposed
methodology is applied to an illustrative extrapolation problem involving a
misspecified nonlinear oscillator.
