### Probabilistic Models for Integration Error in the Assessment of Functional Cardiac Models

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 Title: Probabilistic Models for Integration Error in the Assessment of Functional Cardiac Models Authors: Oates, CJNiederer, SLee, ABriol, F-XGirolami, M Item Type: Journal Article Abstract: This paper studies the numerical computation of integrals, representing estimates or predictions, over the output $f(x)$ of a computational model with respect to a distribution $p(\mathrm{d}x)$ over uncertain inputs $x$ to the model. For the functional cardiac models that motivate this work, neither $f$ nor $p$ possess a closed-form expression and evaluation of either requires $\approx$ 100 CPU hours, precluding standard numerical integration methods. Our proposal is to treat integration as an estimation problem, with a joint model for both the a priori unknown function $f$ and the a priori unknown distribution $p$. The result is a posterior distribution over the integral that explicitly accounts for dual sources of numerical approximation error due to a severely limited computational budget. This construction is applied to account, in a statistically principled manner, for the impact of numerical errors that (at present) are confounding factors in functional cardiac model assessment. Issue Date: 1-Jan-2017 URI: http://hdl.handle.net/10044/1/53204 Copyright Statement: © The Authors Keywords: stat.ME Notes: Fixed broken references and added acknowledgement to SAMSI Appears in Collections: MathematicsFaculty of Natural Sciences