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Plate Splines (plate + spline)

Distribution by Scientific Domains
Mathematics and Statistics50%
Engineering33%

Kinds of Plate Splines

  • thin plate spline
    		•

    Selected Abstracts

    Evaluation of reduced rank semiparametric models to assess excess of risk in cluster analysis

    ENVIRONMETRICS, Issue 4 2009
    Marco Geraci
    Abstract The existence of multiple environmental hazards is obviously a threat to human health and, from a statistical point of view, the modeling and the detection of disease clusters potentially related to those hazards offer challenging tasks. In this paper, we consider low rank thin plate spline (TPS) models within a semiparametric approach to focused clustering for small area health data. Both the distance from a putative source and a general, unspecified clustering process are modeled in the same fashion and they are entered log-additively in mixed Poisson-Normal models. Some issues related to the identification of the random effects arising from this approach are investigated. Under different simulated scenarios, we evaluate the proposed models using conditional Akaike's weights and tests for variance components, providing a comprehensive model selection methodology easy to implement. We examine observations of lung cancer deaths taken in Ohio between 1987 and 1988. These data were analyzed on several occasions to investigate the risk associated with a putative source in Hamilton county. In our analysis, we found a strong south-eastward spatial trend which is confounded with a significant radial distance effect decreasing between 0 and 150 km from the point source. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Meshless thermo-elastoplastic analysis by triple-reciprocity boundary element method

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010
    Yoshihiro OchiaiArticle first published online: 18 SEP 200
    Abstract In general, internal cells are required to solve thermo-elastoplasticity problems by a conventional boundary element method (BEM). However, in this case, the merit of BEM, which is the easy preparation of data, is lost. A conventional multiple-reciprocity boundary element method (MRBEM) cannot be used to solve elastoplasticity problems, because the distribution of initial strain or stress cannot be determined analytically. In this study, it is shown that without the use of internal cells, two-dimensional thermo-elastoplasticity problems can be solved by a triple-reciprocity BEM using a thin plate spline. Initial strain and stress formulations are adopted and the initial strain or stress distribution is interpolated using boundary integral equations. A new computer program was developed and applied to solve several problems. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Semiparametric M -quantile regression for estimating the proportion of acidic lakes in 8-digit HUCs of the Northeastern US

    ENVIRONMETRICS, Issue 7 2008
    Monica Pratesi
    Abstract Between 1991 and 1995, the Environmental Monitoring and Assessment Program of the US Environmental Protection Agency conducted a survey of lakes in the Northeastern states of the US to determine the ecological condition of these waters. Here, to this end, we want to obtain estimates of the proportion of lakes at (high) risk of acidification or acidified already for each 8-digit hydrologic unit code (HUC) within the region of interest. Sample sizes for the 113 HUCs are very small and 27 HUCs are not even observed. Therefore, small area estimation techniques should be invoked for the estimation of the distribution function of acid neutralizing capacity (ANC) for each HUC. The procedure is based on a semiparametric M -quantile regression model in which ANC depends on elevation and the year of the survey linearly, and on the geographical position of the lake through an unknown smooth bivariate function estimated by low-rank thin plate splines. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Tests of radial basis functions in the 3D DRM-MD

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2006
    Bruno Natalini
    Abstract Several global as well as compactly supported radial basis functions were tested in the boundary element dual reciprocity method-multi domain approach (DRM-MD) applied to 3D potential problems. Compactly supported radial basis functions (CS-RBFs) showed the highest accuracy, while the augmented thin plate splines (ATPS) showed the highest consistency in terms of accuracy and convergence for the two examples considered, the Poisson and the advection,diffusion equations. A problem for implementation of the CS-RBFs is the lack of guidelines in choosing the size of the support, which showed to have large influence on the accuracy and convergence when these types of RBFs are used. The ATPS showed satisfactory accuracy and since its use does not involve any extra parameters, at the moment it is this function that is the choice of the authors for use in the DRM-MD. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Comparing the accuracy and precision of three techniques used for estimating missing landmarks when reconstructing fossil hominin crania

    AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY, Issue 1 2009
    Rudolph Neeser
    Abstract Various methodological approaches have been used for reconstructing fossil hominin remains in order to increase sample sizes and to better understand morphological variation. Among these, morphometric quantitative techniques for reconstruction are increasingly common. Here we compare the accuracy of three approaches,mean substitution, thin plate splines, and multiple linear regression,for estimating missing landmarks of damaged fossil specimens. Comparisons are made varying the number of missing landmarks, sample sizes, and the reference species of the population used to perform the estimation. The testing is performed on landmark data from individuals of Homo sapiens, Pan troglodytes and Gorilla gorilla, and nine hominin fossil specimens. Results suggest that when a small, same-species fossil reference sample is available to guide reconstructions, thin plate spline approaches perform best. However, if no such sample is available (or if the species of the damaged individual is uncertain), estimates of missing morphology based on a single individual (or even a small sample) of close taxonomic affinity are less accurate than those based on a large sample of individuals drawn from more distantly related extant populations using a technique (such as a regression method) able to leverage the information (e.g., variation/covariation patterning) contained in this large sample. Thin plate splines also show an unexpectedly large amount of error in estimating landmarks, especially over large areas. Recommendations are made for estimating missing landmarks under various scenarios. Am J Phys Anthropol 2009. © 2009 Wiley-Liss, Inc. [source]

    Low-Rank Smoothing Splines on Complicated Domains

    BIOMETRICS, Issue 1 2007
    Haonan Wang
    Summary Smoothing over a domain with irregular boundaries or interior gaps and holes is addressed. Consider the problem of estimating mercury in sediment concentrations in the estuarine waters in New Hampshire. A modified version of low-rank thin plate splines (LTPS) is introduced where the geodesic distance is applied to evaluate dissimilarity of any two data observations: loosely speaking, distances between locations are not measured as the crow flies, but as the fish swims. The method is compared with competing smoothing techniques, LTPS, and finite element L-splines. [source]