Equitable (d,m)(d,m)-edge designs

The paper addresses design of experiments for classifying the input factors of a multi-variate function into negligible, linear and other (non-linear/interaction) factors. We give constructive procedures for completing the definition of the clustered designs proposed Morris 1991, that become defined for arbitrary number of input factors and desired clusters' multiplicity. Our work is based on a representation of subgraphs of the hyper-cube by polynomials that allows the formal verification of the designs' properties. Ability to generate these designs in a systematic manner opens new perspectives for the characterisation of the behaviour of the function's derivatives over the input space that may offer increased discrimination

Model-free spatial Interpolation and error prediction for survey data acquired by mobile platforms

International audienceThe paper proposes a new randomized Cross Validation (CV) criterion specially designed for use with data acquired over non-uniformly scattered designs, like the linear transect surveys typical in environmental observation. Numerical results illustrate the impact of randomized cross-validation in real environmental datasets showing that it leads to interpolated fields with smaller error at a much lower computational load. Randomized CV enables a robust parameterization of interpolation algorithms, in a manner completely driven by the data and free of any modelling assumptions. The new method proposed here resorts to tools and concepts from Computational Geometry, in particular the Yao graph determined by the set of sampled sites. The method randomly chooses the hold-out sets such that they reflect, statistically, the geometry of the design with respect to the unobserved points of the area where the observations are to be extrapolated, minimizing biases due to the particular geometry of the designs

Extending Morris Method: identification of the interaction graph using cycle-equitabe designs

International audienceThe paper presents designs that allow detection of mixed effects when performing preliminary screening of the inputs of a scalar function of $d$ input factors, in the spirit of Morris' Elementary Effects approach. We introduce the class of $(d,c)$-cycle equitable designs as those that enable computation of exactly $c$ second order effects on all possible pairs of input factors. Using these designs, we propose a fast Mixed Effects screening method, that enables efficient identification of the interaction graph of the input variables. Design definition is formally supported on the establishment of an isometry between sub-graphs of the unit cube $Q_d$ equipped of the Manhattan metric, and a set of polynomials in $(X_1,\ldots, X_d)$ on which a convenient inner product is defined. In the paper we present systems of equations that recursively define these $(d,c)$-cycle equitable designs for generic values of $c\geq 1$, from which direct algorithmic implementations are derived. Application cases are presented, illustrating the application of the proposed designs to the estimation of the interaction graph of specific functions

Bayesian Local Kriging

<p>We consider the problem of constructing metamodels for computationally expensive simulation codes; that is, we construct interpolators/predictors of functions values (responses) from a finite collection of evaluations (observations). We use Gaussian process (GP) modeling and kriging, and combine a Bayesian approach, based on a finite set GP models, with the use of localized covariances indexed by the point where the prediction is made. Our approach is not based on postulating a generative model for the unknown function, but by letting the covariance functions depend on the prediction site, it provides enough flexibility to accommodate arbitrary nonstationary observations. Contrary to kriging prediction with plug-in parameter estimates, the resulting Bayesian predictor is constructed explicitly, without requiring any numerical optimization, and locally adjusts the weights given to the different models according to the data variability in each neighborhood. The predictor inherits the smoothness properties of the covariance functions that are used and its superiority over plug-in kriging, sometimes also called empirical-best-linear-unbiased predictor, is illustrated on various examples, including the reconstruction of an oceanographic field over a large region from a small number of observations. Supplementary materials for this article are available online.</p

Sparse spline-based shape models

NICE-BU Sciences (060882101) / SudocSudocFranceF

Incremental construction of nested designs based on two-level fractional factorial designs

The incremental construction of nested designs having good spreading properties over the d-dimensional hypercube is considered, for values of d such that the 2 d vertices of the hypercube are too numerous to be all inspected. A greedy algorithm is used, with guaranteed efficiency bounds in terms of packing and covering radii, using a 2 d−m fractional-factorial design as candidate set for the sequential selection of design points. The packing and covering properties of fractional-factorial designs are investigated and a review of the related literature is provided. An algorithm for the construction of fractional-factorial designs with maximum packing radius is proposed. The spreading properties of the obtained incremental designs, and of their lower dimensional projections, are investigated. An example with d = 50 is used to illustrate that their projection in a space of dimension close to d has a much higher packing radius than projections of more classical designs based on Latin hypercubes or low discrepancy sequences