Probabilistic models for integration error in the assessment of functional cardiac models

TY - JOUR

T1 - Probabilistic models for integration error in the assessment of functional cardiac models

AU - Oates, Chris J.

AU - Niederer, Steven

AU - Lee, Angela

AU - Briol, François Xavier

AU - Girolami, Mark

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85045637293&partnerID=8YFLogxK

M3 - Conference paper

AN - SCOPUS:85045637293

SN - 1049-5258

VL - 2017-December

SP - 110

EP - 118

JO - ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS

JF - ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS

T2 - 31st Annual Conference on Neural Information Processing Systems, NIPS 2017

Y2 - 4 December 2017 through 9 December 2017

ER -