It is a story as old as time. Models rife with uncertainty are developed for intriguing applications while simultaneously uncertainty quantification (UQ) methods are rapidly advanced. Yet, when the developers of the models and methods meet, it is rarely love at first sight. Either the UQ questions the modeler asks are like the third cousin to those the methods are intended to answer or the methods require certain types or quantities of data for which the modeler is not prepared to deliver. This minisymposium brings together pairs of collaborative researchers giving coordinated presentations on how an application and UQ method were finally joined in harmony. The first presentation focuses on the application, modeling, and types of UQ questions the researchers seek to answer. The second presentation focuses on how a UQ method was tailored to answer these questions under the constraints of the model.
14:00
Computational framework for applying electrical impedance tomography to head imaging
Nuutti Hyvönen | Aalto University | Finland
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Nuutti Hyvönen | Aalto University | Finland
Electrical impedance tomography is a noninvasive imaging method that is based on current and voltage measurements on the boundary of the examined physical body. This talk introduces a computational framework for applying (absolute) electrical impedance tomography to head imaging without accurate information on the head shape or the electrode positions. The potential applications for such imaging modality include differentiating between hemorrhagic and ischemic strokes as well as bedside monitoring of stroke patients. A library of fifty heads is employed to build a principal component model for the typical variations in the shape of the human head, which leads to a relatively accurate parametrization for head shapes with only a few free parameters. The estimation of these shape parameters and the electrode positions can then be incorporated in a regularized Newton-type output least squares reconstruction algorithm. An alternative approach is to introduce a Bayesian reconstruction algorithm that accounts for the geometric uncertainties by modelling their effect on the measurements as an auxiliary additive noise process.
14:30
Applying approximation error modelling to head imaging by electrical impedance tomography
Juha-Pekka Puska | Aalto University | Finland
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Juha-Pekka Puska | Aalto University | Finland
Application of electrical impedance tomography to head imaging suffers from unavoidable uncertainties in the electrode positions and the shape of the patient’s head; absolute impedance tomography is known to be highly sensitive to these kinds geometric inaccuracies. This work tests a potential remedy for the effect of such mismodelling: the so-called approximation error approach. The governing idea of the approximation error method is to treat the discrepancy in the measurements due to inaccurate modelling of the measurement setup as an auxiliary additive noise process. The (second order) statistics of this (random) measurement error are approximated via simulations based on prior probability models for the conductivity, the electrode positions and the head shape. This enables the introduction of a Gaussian approximation for the geometry-related measurement modelling errors, and this auxiliary Gaussian noise process can then be accounted for in any standard Bayesian reconstruction algorithm for electrical impedance tomography. The functionality of the approximation error method in head imaging is tested by numerical experiments.
15:00
Stock Price Bubbles - A Data-Driven Indicator: Practitioner's view
Martin Simon | Deka GmbH | Germany
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Martin Simon | Deka GmbH | Germany
In this talk we are going to discuss a data-driven mathematical indicator for stock price bubbles which uses option market data. The first introductory part recaps the strict local martingale theory for modeling asset price bubbles and its implications for pricing contingent claims. In the second part we present a novel forward-looking indicator based on the information content of bid and ask market quotes for exchange-traded plain vanilla options. This talk is based on joint work with Petteri Piiroinen, Lassi Roininen and Tobias Schoden.
15:30
Stock Price Bubbles - A Data-Driven Indicator: UQ view
Lassi Roininen | Lappeenranta-Lahti University of Technology | Finland
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Lassi Roininen | Lappeenranta-Lahti University of Technology | Finland
We will discuss modelling of different parameters in the stock price bubble estimation, i.e. show how the parameters are estimated in a consistent probabilistic framework as a Bayesian statistical inverse problem. Then we will discuss MCMC sampling, including adaptive Metropolis-Hastings and Hamiltonian Monte Carlo.