Statistical assessment and calibration of numerical models with functional response

Nicholas Tarabelloni

Lab MOX - Dipartimento di Matematica, Politecnico di Milano

Thursday 30th June 2016

11:30:00

Aula Seminari "Saleri" VI Piano MOX -Dipartimento di Matematica, POLITECNICO DI MILANO

Thanks to the rise in computational resources that are increasingly becoming available, numerical models of all fields are experiencing a growth of complexity and realism. This is especially the case for mathematical models dealing with biomedical phenomena, whose goal is to describe the behaviour of physiological processes of human beings. To this aim, it is now possible to combine them with diverse and complex data coming from real experiments, hospital collections and surveys in order to enhance the modelling. This is of extreme importance for the development of a personalised medicine practice able to instruct clinicians and recommend treatments for targeted patients. Within this context, we will focus on the problem of assessing the quality and calibrating numerical models producing functional observations, i.e. quantity of interest that can naturally be thought as continuously depending on some variable (e.g. time). To this aim, we will present a general statistical framework based on depth measures and spatial quantiles for multi-dimensional data which is able to naturally and non-parametrically exploit a whole collection of real measurements, to drive the calibration towards multiple possible goals and finally to enhance the agreement between simulated data and real data. We will show an application to the calibration of ODE and PDE based numerical models for the simulation of physiological ECG traces to a dataset of hospital recordings. contact: christian.vergara@polimi.it