One major difficulty that exists in reconciling model predictions of a system with experimental measurements is assessing and accounting for the uncertainties in the system. There are several enumerated sources of uncertainty in model prediction of physical phenomena, the primary ones being: 1) Model form error, 2) Aleatoric uncertainty of model parameters, 3) Epistemic uncertainty of model parameters, and 4) Model solution error. These forms of uncertainty can have insidious consequences for modeling if not properly identified and accounted for. In particular, confusion between aleatoric and epistemic uncertainty can lead to a fundamentally incorrect model being inappropriately fit to data such that the model seems to be correct. As a consequence, model predictions may be nonphysical or nonsensical outside of the regime for which the model was calibrated. This research looks at the effects of aleatoric and epistemic uncertainty in order to make recommendations for properly accounting for them in a modeling framework.