Uncertainty and variability is intrinsic to a plethora of biological processes that we want to understand, model and predict. In cardiac modelling, sources of uncertainty stem from the experimental error in the measurements from our protocols, lack of knowledge about the underlying mechanisms leading to structural error in our models, variability due to differences in cell and ion channel states due to cells being in different settings and gene expression patterns, and variability due to the inherent stochasticity of some of these processes exhibited at multiple time and spatial scales. To accommodate mathematical/phenomenological models in safety-critical clinical practice and drug development, it is therefore of utmost importance to quantify and propagate these uncertainties to model predictions. Bayesian statistics plays a major role in carrying out uncertainty quantification effectively. However, cardiac models pose a unique set of challenges for Bayesian statistical methods. In this talk I would present Bayesian statistical and modern machine learning approaches towards “forward” (from inputs to model predictions) and “inverse” (from experimental data to model structure) uncertainty quantification in cellular cardiac electropysiological models. Specifically, I would present approaches to overcome the computational and statistical challenges associated with uncertainty quantification in mechanistic models, described by differential equations, and highlight some of the open challenges. Furthermore, I would discuss the potential of modern machine learning techniques such as black-box variational inference and probabilistic programming towards solving the uncertainty quantification problem efficiently.
Following are the references accompanying this talk:
1) Sanmitra Ghosh, David Gavaghan, Gary Mirams, “Gaussian process emulation for discontinuous response surfaces with applications for cardiac electrophysiology models”, https://arxiv.org/abs/1805.10020v1
2) Sanmitra Ghosh “Probabilistic Programming for Mechanistic Models (P2M2) tutorial repository”, https://github.com/sanmitraghosh/P2M2