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

arXiv: https://arxiv.org/abs/1606.06841 · HTML: https://mlsanity.com/paper/1606.06841/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jun 2016.

## Built on by (most cited first, 5 of 5)

- [Efficient Numerical Integration in Reproducing Kernel Hilbert Spaces via Leverage Scores Sampling](https://mlsanity.com/paper/2311.13548/) (2023)
- [Conditional Bayesian Quadrature](https://mlsanity.com/paper/2406.16530/) (2024)
- [Bayesian Numerical Integration with Neural Networks](https://mlsanity.com/paper/2305.13248/) (2023)
- [Bayesian Quadrature](https://mlsanity.com/paper/2602.16218/) (2026)
- [BayesSum: Bayesian Quadrature in Discrete Spaces](https://mlsanity.com/paper/2512.16105/) (2025)

## Abstract (arXiv)

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.