# Monotone Function Estimation for Computer Experiments

arXiv: https://arxiv.org/abs/1309.3802 · HTML: https://mlsanity.com/paper/1309.3802/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2013.

## Built on by (most cited first, 9 of 9)

- [Additive Multi-Index Gaussian process modeling, with application to multi-physics surrogate modeling of the quark-gluon plasma](https://mlsanity.com/paper/2306.07299/) (2023)
- [High-dimensional additive Gaussian processes under monotonicity constraints](https://mlsanity.com/paper/2205.08528/) (2022)
- [Hierarchical shrinkage Gaussian processes: applications to computer code emulation and dynamical system recovery](https://mlsanity.com/paper/2302.00755/) (2023)
- [Monotonic Gaussian process for physics-constrained machine learning with materials science applications](https://mlsanity.com/paper/2209.00628/) (2022)
- [Efficient optimization of expensive black-box simulators via marginal means, with application to neutrino detector design](https://mlsanity.com/paper/2508.01834/) (2025)
- [Information fusion and machine learning for sensitivity analysis using physics knowledge and experimental data](https://mlsanity.com/paper/2608.17248/) (2026)
- [Predictive Modeling through Hyper-Bayesian Optimization](https://mlsanity.com/paper/2308.00285/) (2023)
- [Monotone Optimisation with Learned Projections](https://mlsanity.com/paper/2601.20983/) (2026)
- [Constrained Probabilistic Numerics: Gaussian Process Solvers for Linear PDEs under Linear Inequality Constraints](https://mlsanity.com/paper/2610.13804/) (2026)

## Abstract (arXiv)

In statistical modeling of computer experiments sometimes prior information is available about the underlying function. For example, the physical system simulated by the computer code may be known to be monotone with respect to some or all inputs. We develop a Bayesian approach to Gaussian process modelling capable of incorporating monotonicity information for computer model emulation. Markov chain Monte Carlo methods are used to sample from the posterior distribution of the process given the simulator output and monotonicity information. The performance of the proposed approach in terms of predictive accuracy and uncertainty quantification is demonstrated in a number of simulated examples as well as a real queueing system application.