arXiv subjects

Henri Mermoz Kouye

Publications and source records attributed to Henri Mermoz Kouye.

2 recordsLinked to original sources

arXiv2024

Performing global sensitivity analysis on simulations of a continuous-time Markov chain model motivated by epidemiology

In this paper we apply a methodology introduced in Navarro Jimenez et al (2016) in the framework of chemical reaction networks to perform a global sensitivity analysis on simulations of a continuous-time Markov chain model motivated by epidemiology. Our goal is to quantify not only the effects of uncertain parameters such as epidemic parameters (transmission rate, mean sojourn duration in compartments), but also those of intrinsic randomness and interactions between epidemic parameters and intrinsic randomness. For that purpose, following what was proposed in Navarro Jimenez et al, we leverage three exact simulation algorithms for continuous-time Markov chains from the state of the art which we combine with common tools from variance-based sensitivity analysis as introduced in Sobol (1993). Also, we discuss the impact of the choice of the simulation algorithm used for the simulations on the results of sensitivity analysis. Such a discussion is new, at least to our knowledge. In a numerical section, we implement and compare three sensitivity analyses based on simulations obtained from different exact simulation algorithms of a SARS-CoV-2 epidemic model.

stat.ME↗

arXiv2024

Regularizing nested Monte Carlo Sobol' index estimators to balance the trade-off between explorations and repetitions in global sensitivity analysis of stochastic models

Sobol' sensitivity index estimators for stochastic models are functions of nested Monte Carlo estimators, which are estimators built from two nested Monte Carlo loops. The outer loop explores the input space and, for each of the explorations, the inner loop repeats model runs to estimate conditional expectations. Although the optimal allocation between explorations and repetitions of one's computational budget is well-known for nested Monte Carlo estimators, it is less clear how to deal with functions of nested Monte Carlo estimators, especially when those functions have unbounded Hessian matrices, as it is the case for Sobol' index estimators. To address this problem, a regularization method is introduced to bound the mean squared error of functions of nested Monte Carlo estimators. Based on a heuristic, an allocation strategy that seeks to minimize a bias-variance trade-off is proposed. The method is applied to Sobol' index estimators for stochastic models. A practical algorithm that adapts to the level of intrinsic randomness in the models is given and illustrated on numerical experiments.

math.ST↗