Bias and Variance in the Bayesian Subset Simulation Algorithm

Julien Bect (1, 2) , Roman Sueur (3) , Emmanuel Vazquez (1, 2)

1 L2S - Laboratoire des signaux et systèmes
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
3 EDF R&D MRI - Management des Risques Industriels

The Bayesian Subset Simulation (BSS) algorithm is a recently proposed approach, based on Sequential Monte Carlo simulation and Gaussian process modeling, for the estimation of the probability that $f(X)$ exceeds some thresold $u$ when $f$ is expensive to evaluate and $P(f(X)>u)$ is small. We discuss in this talk the bias an variance of the BSS algorithm, and propose a variant where the bias-variance trade-off is automatically tuned.

Domaines: Calcul [stat.CO]

Julien Bect, Roman Sueur, Emmanuel Vazquez. Bias and Variance in the Bayesian Subset Simulation Algorithm. 2016 SIAM Conference on Uncertainty Quantification, Apr 2016, Lausanne, Switzerland. ⟨hal-01377732⟩