Recent Results on Nonparametric Quantile Estimation in a Simulation Model

Krzyżak, Adam

doi:10.1007/978-3-319-18781-5_13

Cited by 1 publication

(1 citation statement)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Surrogate-based quantile estimation. The use of a truncated polynomial chaos expansion as in (5.8) or (5.12) as an approximation to {Y (x), x ∈ D} or χ in the quantile estimation may lead to an approximation error, which obeys the following result from [10,18]:…”

Section: 33mentioning

confidence: 99%

A Multifidelity Quantile-Based Approach for Confidence Sets of Random Excursion Sets with Application to Ice-Sheet Dynamics

Bulthuis

Pattyn

Arnst

2020

SIAM/ASA J. Uncertainty Quantification

View full text Add to dashboard Cite

In this paper, we address uncertainty quantification of physics-based computational models when the quantity of interest concerns geometrical characteristics of their spatial response. Within the probabilistic context of the random set theory, we develop the concept of confidence sets that either contain or are contained within an excursion set of the spatial response with a specified probability level. We seek such confidence sets in a parametric family of nested candidate sets defined as a parametric family of sublevel or superlevel sets of a membership function. We show that the problem of identifying a confidence set with a given probability level in such a parametric family is equivalent to a problem of estimating a quantile of a random variable obtained as a global extremum of the membership function over the complement of the excursion set. To construct such confidence sets, we propose a computationally efficient bifidelity method that exploits a spectral representation of this random variable to reduce the required number of evaluations of the computational model. We show the interest of this concept of confidence sets and the efficiency gain of the proposed bifidelity method in an illustration relevant to the retreat of the grounded portion of the Antarctic ice sheet.

show abstract

Section: 33mentioning

confidence: 99%