Bayesian Uncertainty Quantification for Data-Driven Applications in Engineering and Life Sciences

The world is quickly moving towards using computer modeling and simulations in various branches of science and engineering. The computational methods found their way to biology, chemistry, physics, social sciences and many other fields. Simulations allow the researchers to study phenomena which can not be directly observed in the experiments. In order to be trustworthy, the simulations must go through a thorough process of data-driven validation. Often, an adjustment of the free parameters of the computational model is required for it to match the experimental observations. One of the possibilities to find the right model parameters is an optimization with respect to the quantities of interest which one wishes to reproduce in the simulation. The amount of information which can be extracted from this deterministic approach is, however, very limited. The parameters sensitivity or their mutual correlations, which are crucial for making robust predictions, are not available in this approach. The solution to this problem lies in the area of probability, specifically in the Bayesian methodology. The value of the Bayesian approach in the modern computational science can hardly be overestimated. It updates the prior beliefs about the model parameters, expressed in the form of a probability distribution, using the available experimental data. This approach takes into account all the uncertainties arising in the inference process: the experimental, the modeling and the simulation ones, thus providing a reliable result. Blending together the simulation and the experiment outcomes, it constructs a conditional distribution of the model parameters given the observational data. From this distribution, one can extract the uncertainty bounds, the correlations, the sensitivities etc. for each of the parameters, as well as for any quantity of interest which can be computed using the calibrated model. All these useful features, however, come with a price of an excessive computa-