Related papers: A Bayesian approach for global sensitivity analysi…
Scientists often express their understanding of the world through a computationally demanding simulation program. Analyzing the posterior distribution of the parameters given observations (the inverse problem) can be extremely challenging.…
Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…
In the framework of the estimation of safety margins in nuclear accident analysis, a quantitative assessment of the uncertainties tainting the results of computer simulations is essential. Accurate uncertainty propagation (estimation of…
Global sensitivity analysis is a powerful set of ideas and heuristics for understanding the importance and interplay between uncertain parameters in a computational model. Such a model is characterized by a set of input parameters and an…
We propose to estimate a metamodel and the sensitivity indices of a complex model m in the Gaussian regression framework. Our approach combines methods for sensitivity analysis of complex models and statistical tools for sparse…
Gaussian process regression is widely applied in computational science and engineering for surrogate modeling owning to its kernel-based and probabilistic nature. In this work, we propose a Bayesian approach that integrates the variability…
Global sensitivity analysis aims at quantifying respective effects of input random variables (or combinations thereof) onto variance of a physical or mathematical model response. Among the abundant literature on sensitivity measures, Sobol'…
Making good predictions of a physical system using a computer code requires the inputs to be carefully specified. Some of these inputs called control variables have to reproduce physical conditions whereas other inputs, called parameters,…
Many fields of science and engineering rely on running simulations with complex and computationally expensive models to understand the involved processes in the system of interest. Nevertheless, the high cost involved hamper reliable and…
Inverse problems are prevalent in both scientific research and engineering applications. In the context of Bayesian inverse problems, sampling from the posterior distribution can be particularly challenging when the forward models are…
In the continual effort to improve product quality and decrease operations costs, computational modeling is increasingly being deployed to determine feasibility of product designs or configurations. Surrogate modeling of these computer…
In this paper, we consider a regression model built on dependent variables. This regression modelizes an input output relationship. Under boundedness assumptions on the joint distribution function of the input variables, we show that a…
Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…
This paper deals with the Gaussian process based approximation of a code which can be run at different levels of accuracy. This method, which is a particular case of co-kriging, allows us to improve a surrogate model of a complex computer…
Predictions from science and engineering models depend on several input parameters. Global sensitivity analysis quantifies the importance of each input parameter, which can lead to insight into the model and reduced computational cost;…
The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…
Surrogate models have become ubiquitous in science and engineering for their capability of emulating expensive computer codes, necessary to model and investigate complex phenomena. Bayesian emulators based on Gaussian processes adequately…
In the context of computer code experiments, sensitivity analysis of a complicated input-output system is often performed by ranking the so-called Sobol indices. One reason of the popularity of Sobol's approach relies on the simplicity of…
Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a…
We develop a new efficient methodology for Bayesian global sensitivity analysis for large-scale multivariate data. The focus is on computationally demanding models with correlated variables. A multivariate Gaussian process is used as a…