# Publications

## Citation

### BibTex format

@inproceedings{Oates:2017,author = {Oates, CJ and Niederer, S and Lee, A and Briol, F-X and Girolami, M},pages = {109--117},title = {Probabilistic Models for Integration Error in the Assessment of Functional Cardiac Models},url = {https://papers.nips.cc/paper/6616-probabilistic-models-for-integration-error-in-the-assessment-of-functional-cardiac-models},year = {2017}}

### RIS format (EndNote, RefMan)

TY  - CPAPERAB  - This paper studies the numerical computation of integrals, representingestimates or predictions, over the output $f(x)$ of a computational model withrespect to a distribution $p(\mathrm{d}x)$ over uncertain inputs $x$ to themodel. 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. Ourproposal is to treat integration as an estimation problem, with a joint modelfor both the a priori unknown function $f$ and the a priori unknowndistribution $p$. The result is a posterior distribution over the integral thatexplicitly accounts for dual sources of numerical approximation error due to aseverely 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.AU  - Oates,CJAU  - Niederer,SAU  - Lee,AAU  - Briol,F-XAU  - Girolami,MEP  - 117PY  - 2017///SP  - 109TI  - Probabilistic Models for Integration Error in the Assessment of Functional Cardiac ModelsUR  - https://papers.nips.cc/paper/6616-probabilistic-models-for-integration-error-in-the-assessment-of-functional-cardiac-modelsUR  - http://hdl.handle.net/10044/1/53204ER  -