相关论文: Asymptotic normality of a Sobol index estimator in…

Models with high-dimensional parameter spaces are common in many applications. Global sensitivity analyses can provide insights on how uncertain inputs and interactions influence the outputs. Many sensitivity analysis methods face…

Global sensitivity analysis (GSA) of functional-output models is usually performed by combining statistical techniques, such as basis expansions, metamodeling and sampling based estimation of sensitivity indices. By neglecting truncation…

Variance-based Sobol' sensitivity is one of the most well-known measures in global sensitivity analysis (GSA). However, uncertainties with certain distributions, such as highly skewed distributions or those with a heavy tail, cannot be…

Let $X:=(X_1, \ldots, X_p)$ be random objects (the inputs), defined on some probability space $(\Omega,{\mathcal{F}}, \mathbb P)$ and valued in some measurable space $E=E_1\times\ldots \times E_p$. Further, let $Y:=Y = f(X_1, \ldots, X_p)$…

Linear thresholding models postulate that the conditional distribution of a response variable in terms of covariates differs on the two sides of a (typically unknown) hyperplane in the covariate space. A key goal in such models is to learn…

The presence of uncertainties are inevitable in engineering design and analysis, where failure in understanding their effects might lead to the structural or functional failure of the systems. The role of global sensitivity analysis in this…

Consider estimation of the regression function based on a model with equidistant design and measurement errors generated from a fractional Gaussian noise process. In previous literature, this model has been heuristically linked to an…

Given a bivariate random pair $(X,Y)$, a natural problem is to estimate, from a single sample $(X_i,Y_i)_{1\le i\le n}$, quantities such as $\mathbb{E}\left[ \mathbb{E}[ Y\mid X ]^2 \right]$. More broadly, sensitivity indices are designed…

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…

Many standard estimators, when applied to adaptively collected data, fail to be asymptotically normal, thereby complicating the construction of confidence intervals. We address this challenge in a semi-parametric context: estimating the…

Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator,…

We present an HSIC-based approach for global sensitivity analysis of broad classes of models with correlated and possibly function-valued inputs and outputs. To this end, we define the total HSIC sensitivity index: a bounded, interpretable,…

The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…

High-fidelity simulations and physical experiments are essential for engineering analysis and design, yet their high cost often makes two critical tasks--global sensitivity analysis (GSA) and optimization--prohibitively expensive. This…

This chapter makes a review, in a complete methodological framework, of various global sensitivity analysis methods of model output. Numerous statistical and probabilistic tools (regression, smoothing, tests, statistical learning, Monte…

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.…

This article provides an introduction to the asymptotic analysis of covariance parameter estimation for Gaussian processes. Maximum likelihood estimation is considered. The aim of this introduction is to be accessible to a wide audience and…

This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…

Computer models, also known as simulators, can be computationally expensive to run, and for this reason statistical surrogates, known as emulators, are often used. Any statistical model, including an emulator, should be validated before…

This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally…