A second-order expansion is established for predictive distributions in Gaussian processes with estimated covariances. Particular focus is on estimating quantiles of the predictive distribution and their subsequent application to prediction intervals. Two basic approaches are considered, (a) a “plug-in” approach using the restricted maximum likelihood estimate of the covariance parameters, (b) ...

Diffusion MRI offers great potential in studying the human brain microstructure and connectivity. However, diffusion images are marred by technical problems, such as image distortions and spurious signal loss. Correcting for these problems is non-trivial and relies on having a mechanism that predicts what to expect. In this paper we describe a novel way to represent and make predictions about d...

A second-order expansion is established for predictive distributions in Gaussian processes with estimated covariances. Particular focus is on estimating quantiles of the predictive distribution and their subsequent application to prediction intervals. Two basic approaches are considered, (a) a “plug-in” approach using the restricted maximum likelihood estimate of the covariance parameters, (b) ...

Sequential simulation of a continuous variable usually requires its transformation into a binary or a Gaussian variable, giving rise to the classical algorithms of sequential indicator simulation or sequential Gaussian simulation. Journel (1994) showed that the sequential simulation of a continuous variable, without any prior transformation, succeeded in reproducing the covariance model, provid...

In the context of expensive numerical experiments, a promising solution to alleviate the computational costs consists of using partially converged simulations instead of exact solutions. The gain in computational time is at a price of precision in the response. This work addresses the issue of fitting a Gaussian process model to partially converged simulation data, for further use in prediction...

The publisher apologized for this unfortunate error, which has been corrected in the original article.

We consider the problem of constructing metamodels for computationally expensive simulation codes; that is, we construct interpolation/prediction of functions values (responses) from a finite collection of evaluations (observations). We use Gaussian process modeling and Kriging, and combine a Bayesian approach, based on a finite set of covariance functions, with the use of localized models, ind...

In many global optimization problems motivated by engineering applications, the number of function evaluations is severely limited by time or cost. To ensure that each of these evaluations contributes to the localization of good candidates for the role of global minimizer, a sequential choice of evaluation points is usually carried out. In particular, when Kriging is used to interpolate past ev...

Metamodels are widely used to facilitate the analysis and optimization of engineering systems that involve computationally expensive simulations. Kriging is a metamodelling technique that is well known for its ability to build surrogate models of responses with non-linear behaviour. However, the assumption of a stationary covariance structure underlying Kriging does not hold in situations where...