# Gearing Gaussian process modeling and sequential design towards stochastic simulators

arXiv: https://arxiv.org/abs/2412.07306 · HTML: https://mlsanity.com/paper/2412.07306/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 93 references that are in the map.
- First posted on arXiv 10 Dec 2024.

## Builds on (most cited first, 30 of 31)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Constrained Bayesian Optimization with Noisy Experiments](https://mlsanity.com/paper/1706.07094/) (2017)
- [Uniform Error Bounds for Gaussian Process Regression with Application to Safe Control](https://mlsanity.com/paper/1906.01376/) (2019)
- [Pathwise Conditioning of Gaussian Processes](https://mlsanity.com/paper/2011.04026/) (2020)
- [Bayesian Optimization of Composite Functions](https://mlsanity.com/paper/1906.01537/) (2019)
- [Student-t Processes as Alternatives to Gaussian Processes](https://mlsanity.com/paper/1402.4306/) (2014)
- [MCMC for Variationally Sparse Gaussian Processes](https://mlsanity.com/paper/1506.04000/) (2015)
- [Practical heteroskedastic Gaussian process modeling for large simulation experiments](https://mlsanity.com/paper/1611.05902/) (2016)
- [Active Learning for Deep Gaussian Process Surrogates](https://mlsanity.com/paper/2012.08015/) (2020)
- [Replication or exploration? Sequential design for stochastic simulation experiments](https://mlsanity.com/paper/1710.03206/) (2017)
- [A Latent Variable Approach to Gaussian Process Modeling with Qualitative and Quantitative Factors](https://mlsanity.com/paper/1806.07504/) (2018)
- [Group kernels for Gaussian process metamodels with categorical inputs](https://mlsanity.com/paper/1802.02368/) (2018)
- [Bayesian Optimization over Hybrid Spaces](https://mlsanity.com/paper/2106.04682/) (2021)
- [Bayesian Optimization using Deep Gaussian Processes](https://mlsanity.com/paper/1905.03350/) (2019)
- [Bayesian Quantile and Expectile Optimisation](https://mlsanity.com/paper/2001.04833/) (2020)
- [GPflux: A Library for Deep Gaussian Processes](https://mlsanity.com/paper/2104.05674/) (2021)
- [Evaluating Gaussian Process Metamodels and Sequential Designs for Noisy Level Set Estimation](https://mlsanity.com/paper/1807.06712/) (2018)
- [Emulation of stochastic simulators using generalized lambda models](https://mlsanity.com/paper/2007.00996/) (2020)
- [Bayesian Optimization Allowing for Common Random Numbers](https://mlsanity.com/paper/1910.09259/) (2019)
- [A portfolio approach to massively parallel Bayesian optimization](https://mlsanity.com/paper/2110.09334/) (2021)
- [An analytic comparison of regularization methods for Gaussian Processes](https://mlsanity.com/paper/1602.00853/) (2016)
- [Chained Gaussian Processes](https://mlsanity.com/paper/1604.05263/) (2016)
- [Laplace approximation and the natural gradient for Gaussian process regression with the heteroscedastic Student-t model](https://mlsanity.com/paper/1712.07437/) (2017)
- [Stochastic simulators based optimization by Gaussian process metamodels -- Application to maintenance investments planning issues](https://mlsanity.com/paper/1512.07060/) (2015)
- [The connection between Bayesian estimation of a Gaussian random field and RKHS](https://mlsanity.com/paper/1301.5288/) (2013)
- [Trajectory-oriented optimization of stochastic epidemiological models](https://mlsanity.com/paper/2305.03926/) (2023)
- [Hypervolume-based Multi-objective Bayesian Optimization with Student-t Processes](https://mlsanity.com/paper/1612.00393/) (2016)

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

- [STREGO: A Scalable Implementation of a Trust-Region Framework for Noisy Bayesian Optimization](https://mlsanity.com/paper/2610.14338/) (2026)

## Abstract (arXiv)

This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance, non-Gaussian noise, or quantile modeling. These approaches are compared in terms of goal, data availability and inference procedure. A distinction is made between methods depending on their handling of repeated observations at the same location, also called replication. The chapter concludes with the corresponding adaptations of the sequential design procedures. These are illustrated in an example from epidemiology.