Assessing model mismatch and model selection in a Bayesian uncertainty quantification analysis of a fluid-dynamics model of pulmonary blood circulation
Mihaela Paun (University of Glasgow)
Friday 5th February 15:00-16:00 ZOOM: https://www.smartsurvey.co.uk/s/MNW32H/
There have recently been impressive advancements in the mathematical modelling of complex cardio-vascular systems. However, parameter estimation and uncertainty quantification are still challenging problems in this field. In my talk, I will describe a study that uses Bayesian inference to quantify the uncertainty of model parameters and haemodynamic predictions in a one-dimensional pulmonary circulation model based on an integration of mouse haemodynamic and micro-computed tomography imaging data. I will discuss an often neglected, though important source of uncertainty: in the mathematical model form due to the discrepancy between the model and the reality, and in the measurements due to the wrong noise model (jointly called ‘model mismatch’). I will demonstrate that minimising the mean squared error between the measured and the predicted data (the conventional method) in the presence of model mismatch leads to biased and overly confident parameter estimates and haemodynamic predictions. I will show that the proposed method allowing for model mismatch, which is represented with Gaussian Processes, corrects the bias. Additionally, I will compare a linear and a non-linear wall model, as well as models with different vessel stiffness relations. I'll use formal model selection analysis based on the Watanabe Akaike Information Criterion to select the model that best predicts the pulmonary haemodynamics. Results show that the non-linear pressure-area relationship with stiffness dependent on the unstressed radius predicts best the data measured in a control mouse.
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