ENBIS-8 in Athens
21 – 25 September 2008
Abstract submission: 14 March – 11 August 2008
The following abstracts have been accepted for this event:
Learning a deterministic function using a gaussian process (Kriging) relies on the selection of a covariance kernel. When some prior information is available concerning symmetries of the function to be approximated, it is clearly unreasonable not to use it in the choice of the kernel or covariance function. We propose a characterization of the kernels which associated gaussian processes have their paths invariant under the action of a finite group of transformations. We then give an example of such symmetrical processes, built on the basis of stationary gaussian processes, and having interesting regularity properties. The applicability of the latter methodology is finally demonstrated with the help of toy examples and of an industrial test-case.
23-Sep-2008 15:40 Kriging and Invariances
Kriging and Invariances
David Ginsbourger, Xavier Bay, Yann Richet, Laurent Carraro
Affiliation: Ecole des Mines de Saint-Etienne and Institut de Radioprotection et de Surete Nucleaire
Primary area of focus / application:
Submitted at 15-May-2008 22:23 by David Ginsbourger
Kriging is intensively used to interpolate costly deterministic computer experiments. Since many recent advances in simulation rely on probabilistic methods (Monte-Carlo, etc...), it becomes necessary to take their randomness into account. Here we present an adaptation of the geostatistical "observational noise" to the frame of computer experiments with tunable probabilistic noise. We propose a statistical model for such simulators, give a derivation of the associated Kriging equations, and discuss the estimation of the covariance parameters. Perspectives include the use of Kriging for noisy-simulator-based uncertainty propagation or optimization strategies. We finally rise some new challenges about optimal design of experiments for Kriging, in the input-allocation space.
The comparison of two samples is one of the most important problems in statistical testing. If it is assumed that parent distributions may differ only in location, there are many parametric and nonparametric tests. There are many tests also for the scale problem. It is well-known that under normal distributions the t test and the F test are the uniformly most powerful unbiased tests for the location and scale problem respectively, at least for one-sided alternatives; and that the t test is alfa robust for nonnormal distributions (except for very heavy-tailed ones), whereas the F test is non alfa robust (see, among others, Tiku et al. 1986 and Wilcox 2005). Therefore it may be useful to act within the rank setting, without requiring the assumption of normality. Moreover, even if the usual two-sample problem tests for a location shift, in quality control and industrial statistics situations in which location and scale shifts should be simultaneously detected arise often.
The best known and most used rank test for the location-scale problem is the Lepage (1971) test. There is also another rank test, due to Cucconi (1968) that is earlier but neither known in the literature nor applied in practice. The test is of interest since, contrary to the other location-scale tests, it is not a quadratic form of a test on location and a test on scale and it is easier to be computed than that of Lepage, and other tests. It should be noted that the power of the Lepage test, contrary to that of the Cucconi test, has been widely studied, even recently. For this reason power and size of the Cucconi test are studied, and comparisons with the Lepage test are assesed. Applications of the tests to real data sets in the context of quality control and industrial statistics are discussed.
Cucconi, O. (1968) Un nuovo test non parametrico per il confronto tra due gruppi campionari, Giornale degli Economisti, XXVII, 225-248.
Lepage, Y. (1971) A combination of Wilcoxon’s and Ansari-Bradley’s statistics, Biometrika, 58, 213-217.
Tiku, M. L., Tan, W. Y. and Balakrishnan, N. (1986) Robust inference, Marcel Dekker: New York.
Wilcox, R. R. (2005) Introduction to robust estimation and hypothesis testing, Academic Press: San Diego.
When a studied quality characteristic is zero-bound it is common that its distribution is skewed and that the specification limit is one-sided. Furthermore it is not unusual that the best value to obtain is zero and hence, the target value is zero. The traditional process capability indices based on the normality assumption cannot be used in such situations. A class of capability indices, designed for this case, has previously been suggested and studied under the assumption that the distribution of the quality characteristic is continuous. However, if the quality characteristic can attain values of exactly zero a continuous distribution is not a proper model to use. A typical situation when this might occur is during a process that handles materials where cracks can occur. No crack is the best situation, but if cracks occur they should be short or cover a small area. Then the quality characteristic can obtain the value 0, corresponding to no crack, or some strictly positive number describing the length of the crack or the size of the crack area. Furthermore, the specification interval is an upper specification limit and the target value is 0. We study this situation by using a nonstandard mixture of distributions, involving a Weibull distribution, to model the quality characteristic. Under this assumption we suggest an estimator of the index in the class of indices previously suggested. We study the asymptotic statistical properties of this estimator and suggest a suitable decision rule to be used for deeming a process capable at a given significance level. This decision rule is constructed to be simple to use for practitioners. By using simulation studies we investigate the suggested rule for moderate sample sizes. Examples will also be given to illustrate the presented result.
The EWMA chart for the standard deviation is usually used under the assumption of known parameters. However, in practice, this assumption is rarely fulfilled. The research has shown that if we consider the parameters of a process unknown and we estimate them during Phase I, then the ability of a chart to detect out of control situations is affected. In this paper we derive the run length distribution of the EWMA chart for process dispersion with estimated process parameters along with its first two moments using suitable integral equations.
Paper discuss allocation of the main factor effect in basic columns of 2^k full factorial designs, where k trends to infinity, by development of adequate formula. From there formula is expanded in interactive process of identification of all factorial interactions and their places in columns of design matrix, eider for their identification or for placement. Principle is applicable, with minor changes for both open (traditional approach) and closed (Taguchi's orthogonal arrays) full factorial designs. This enables new approach to defining generators and identification of alias structure in construction of fractional factorial designs