# Replication-based emulation of the response distribution of stochastic simulators using generalized lambda distributions

arXiv: https://arxiv.org/abs/1911.09067 · HTML: https://mlsanity.com/paper/1911.09067/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2019.

## Built on by (most cited first, 10 of 10)

- [A deep learning based surrogate model for stochastic simulators](https://mlsanity.com/paper/2110.13809/) (2021)
- [Deep Physics Corrector: A physics enhanced deep learning architecture for solving stochastic differential equations](https://mlsanity.com/paper/2209.09750/) (2022)
- [Polynomial Chaos Surrogate Construction for Random Fields with Parametric Uncertainty](https://mlsanity.com/paper/2311.00553/) (2023)
- [MD-NOMAD: Mixture density nonlinear manifold decoder for emulating stochastic differential equations and uncertainty propagation](https://mlsanity.com/paper/2404.15731/) (2024)
- [Reliability analysis for non-deterministic limit-states using stochastic emulators](https://mlsanity.com/paper/2412.13731/) (2024)
- [Goal-oriented adaptive sampling under random field modelling of response probability distributions](https://mlsanity.com/paper/2102.07612/) (2021)
- [AL-SPCE - Reliability analysis for nondeterministic models using stochastic polynomial chaos expansions and active learning](https://mlsanity.com/paper/2507.04553/) (2025)
- [High-dimensional reliability-based design optimization using stochastic emulators](https://mlsanity.com/paper/2604.05759/) (2026)
- [MF-GLaM: A multifidelity stochastic emulator using generalized lambda models](https://mlsanity.com/paper/2507.10303/) (2025)
- [Stochastic Emulation using Generalized Stratified Sampling for Performance-Based Risk Optimization of Structures](https://mlsanity.com/paper/2608.05006/) (2026)

## Abstract (arXiv)

Due to limited computational power, performing uncertainty quantification analyses with complex computational models can be a challenging task. This is exacerbated in the context of stochastic simulators, the response of which to a given set of input parameters, rather than being a deterministic value, is a random variable with unknown probability density function (PDF). Of interest in this paper is the construction of a surrogate that can accurately predict this response PDF for any input parameters. We suggest using a flexible distribution family -- the generalized lambda distribution -- to approximate the response PDF. The associated distribution parameters are cast as functions of input parameters and represented by sparse polynomial chaos expansions. To build such a surrogate model, we propose an approach based on a local inference of the response PDF at each point of the experimental design based on replicated model evaluations. Two versions of this framework are proposed and compared on analytical examples and case studies.