37.9 Sensitivity and Uncertainty Analysis

Sensitivity and Uncertainty Analysis refers to the systematic evaluation of how a model's predictions respond to variation in its parameters, initial conditions, and structural assumptions, and the corresponding characterization of confidence bounds around those predictions, encompassing local and global sensitivity analysis, parameter ranking, initial and boundary condition sensitivity, structural and parameter uncertainty characterization, propagation of measurement uncertainty, prediction interval estimation, robustness region and failure boundary estimation, and the identification of dominant uncertainty sources to guide model refinement priorities. Where simulation and prediction generate specific forecasts from a calibrated model, sensitivity and uncertainty analysis evaluates how much confidence to place in those forecasts and which factors most strongly influence them.

Purpose of Sensitivity and Uncertainty Analysis

Identifying Which Factors Most Strongly Influence Model Predictions

Not all parameters and assumptions contribute equally to a model's output; sensitivity analysis identifies which specific factors drive the most significant variation in predictions, distinguishing influential from negligible factors.

Quantifying Confidence in Model-Based Predictions

Because models are built on imperfectly known parameters and simplifying assumptions, uncertainty analysis provides the necessary quantitative characterization of how much confidence a given prediction actually warrants.

Guiding Efficient Allocation of Further Modeling and Experimental Effort

By revealing which uncertainties dominate prediction unreliability, this analysis directs limited modeling and experimental resources toward the factors most likely to improve overall predictive confidence.

Sensitivity Analysis Methods

Synthetic Cell Local Sensitivity Analysis

Local sensitivity analysis evaluates how model output changes in response to small perturbations around a specific reference parameter value, providing a computationally efficient but locally valid measure of sensitivity.

Synthetic Cell Global Sensitivity Analysis

Global sensitivity analysis evaluates how model output varies across the full plausible range of parameter values simultaneously, providing a more comprehensive but computationally intensive sensitivity characterization than local analysis alone.

Synthetic Cell Parameter Sensitivity Ranking

Parameter sensitivity ranking orders model parameters according to their relative influence on model output, providing a prioritized list identifying which parameters most warrant precise determination.

Condition Sensitivity

Synthetic Cell Initial Condition Sensitivity

Initial condition sensitivity evaluates how strongly model predictions depend on the specific starting values assigned to state variables, relevant to assessing whether a model's long-term behavior is robust to initial uncertainty.

Synthetic Cell Boundary Condition Sensitivity

Boundary condition sensitivity evaluates how strongly model predictions depend on assumptions imposed at the edges of the spatial or system domain, particularly relevant to spatial and transport models.

Sources of Uncertainty

Synthetic Cell Structural Model Uncertainty

Structural uncertainty arises from simplifications and assumptions built into the model's mathematical form itself, representing uncertainty about whether the model's structure correctly captures the true underlying biology, distinct from uncertainty about parameter values within an assumed structure.

Synthetic Cell Parameter Uncertainty

Parameter uncertainty arises from imperfect knowledge of the true parameter values, reflecting limitations in the estimation and fitting procedures used during calibration.

Synthetic Cell Measurement Uncertainty Propagation

Measurement uncertainty propagation traces how uncertainty in the empirical measurements used for calibration carries through into uncertainty in model predictions, connecting measurement calibration and uncertainty directly to model-level prediction confidence.

Quantifying Prediction Reliability

Synthetic Cell Prediction Interval

A prediction interval provides a quantitative range within which a model's true output is expected to fall with a specified level of confidence, translating underlying parameter and structural uncertainty into an interpretable bound on predictions.

Synthetic Cell Robustness Region

A robustness region identifies the range of parameter or condition values over which a model's qualitative conclusions remain stable, distinguishing genuinely robust predictions from those sensitive to precise parameter values.

Synthetic Cell Failure Boundary Estimation

Failure boundary estimation quantifies the uncertainty surrounding a predicted failure condition threshold, providing a probabilistic rather than sharply defined boundary between functional and non-functional predicted behavior.

Guiding Further Effort

Dominant Uncertainty Source Identification

Dominant uncertainty source identification determines which specific uncertainty contributor — structural, parameter, or measurement — accounts for the largest share of overall prediction uncertainty, focusing subsequent refinement effort appropriately.

Model Refinement Priority Selection

Refinement priority selection uses sensitivity and uncertainty analysis results to determine which specific model components, parameters, or additional experimental measurements would most effectively improve overall predictive reliability.

Design Considerations

Balancing Local and Global Sensitivity Analysis Based on Available Computational Resources

Local sensitivity analysis is computationally efficient but only locally valid, while global analysis is more comprehensive but computationally demanding, requiring researchers to select an approach appropriate to available computational resources and the breadth of parameter space relevant to the modeling objective.

Communicating Uncertainty Transparently Alongside Point Predictions

Because point predictions without accompanying uncertainty characterization can be misleading, sensitivity and uncertainty results should be reported transparently alongside primary predictions rather than presented separately or omitted.