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Mathematical models are often used to study the structure and dynamics of network-driven cellular processes. In cell biology, models representing biochemical reaction networks have provided significant insights but are often plagued by a dearth of available quantitative data necessary for simulation and analysis. This has in turn led to questions about the usefulness of biochemical network models with unidentifiable parameters and high-degree of parameter sloppiness. In response, approaches to incorporate highly-available non-quantitative data and use this data to improve model certainty have been undertaken with various degrees of success. Here we employ a Bayesian inference and Machine Learning approach to first explore how quantitative and non-quantitative data can constrain a mechanistic model of apoptosis execution, in which all models can be identified. We find that two orders of magnitude more ordinal data measurements than those typically collected are necessary to achieve the same accuracy as that obtained from a quantitative dataset. We also find that ordinal and nominal non-quantitative data on their own can be combined to reduce model uncertainty and thus improve model accuracy. Further analysis demonstrates that the accuracy and certainty of model predictions strongly depends on accurate formulations of the measurement as well as the size and make-up of the nonquantitative datasets. Finally, we demonstrate the potential of a data-driven Machine Learning measurement model to identify informative mechanistic features that predict or define nonquantitative cellular phenotypes, from a systems perspective.