# Quantifying uncertainty in the numerical integration of evolution equations based on Bayesian isotonic regression

arXiv: https://arxiv.org/abs/2411.08338 · HTML: https://mlsanity.com/paper/2411.08338/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2024.

## Built on by (most cited first, 1 of 1)

- [Score-Based Stabilization for Time-Dependent Problems](https://mlsanity.com/paper/2607.25119/) (2026)

## Abstract (arXiv)

This paper presents a new Bayesian framework for quantifying discretization errors in numerical solutions of ordinary differential equations. By modelling the errors as random variables, we impose a monotonicity constraint on the variances, referred to as discretization error variances. The key to our approach is the use of a shrinkage prior for the variances coupled with variable transformations. This methodology extends existing Bayesian isotonic regression techniques to tackle the challenge of estimating the variances of a normal distribution. An additional key feature is the use of a Gaussian mixture model for the log-chi21 distribution, enabling the development of an efficient Gibbs sampling algorithm for the corresponding posterior.