Likelihood based observability analysis and confidence intervals for predictions of dynamic models.

Area of Science:

• Systems Biology
• Computational Biology
• Mathematical Modeling

Background:

• Predicting system behavior via mathematical models is crucial in Systems Biology.
• Parameter uncertainty from experimental data must be translated into prediction confidence intervals.
• Nonlinearity and numerous parameters in dynamic biochemical models hinder classical confidence interval calculations.

Purpose of the Study:

• To develop a reliable method for calculating confidence intervals for model predictions.
• To enable data-based observability analysis using prediction confidence intervals.
• To address challenges posed by non-identifiable parameters in model predictions.

Main Methods:

• Utilizing the prediction profile likelihood for reliable confidence interval calculation.
• Applying prediction confidence intervals for data-based observability analysis.
• Introducing a validation profile likelihood for interpreting noisy validation experiments.

Main Results:

• Reliable confidence intervals for dynamic model predictions are calculated.
• The method facilitates data-based observability analysis, identifying non-observability due to non-identifiable parameters.
• A validation profile likelihood is introduced for handling noisy experimental data.

Conclusions:

• The methodology effectively propagates uncertainty from experimental data to model predictions.
• The approach is general and applicable beyond ordinary differential equations to other model types.
• Provided Matlab code serves as a template for implementing the prediction profile likelihood method.