Oates, CJ; Niederer, S; Lee, A; Briol, FX; Girolami, M; (2017) Probabilistic models for integration error in the assessment of functional cardiac models. In: Advances in Neural Information Processing Systems 30 (NIPS 2017) Proceedings. (pp. pp. 110-118). Neural Information Processing Systems Foundation, Inc.: Long Beach, CA, USA.

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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(dx) 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 ≈ 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

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