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Size Parameter (size + parameter)
Selected AbstractsRobust principal component analysis and outlier detection with ecological dataENVIRONMETRICS, Issue 2 2004Donald A. Jackson Abstract Ecological studies frequently involve large numbers of variables and observations, and these are often subject to various errors. If some data are not representative of the study population, they tend to bias the interpretation and conclusion of an ecological study. Because of the multivariate nature of ecological data, it is very difficult to identify atypical observations using approaches such as univariate or bivariate plots. This difficulty calls for the application of robust statistical methods in identifying atypical observations. Our study provides a comparison of a standard method, based on the Mahalanobis distance, used in multivariate approaches to a robust method based on the minimum volume ellipsoid as a means of determining whether data sets contain outliers or not. We evaluate both methods using simulations varying conditions of the data, and show that the minimum volume ellipsoid approach is superior in detecting outliers where present. We show that, as the sample size parameter, h, used in the robust approach increases in value, there is a decrease in the accuracy and precision of the associated estimate of the number of outliers present, in particular as the number of outliers increases. Conversely, where no outliers are present, large values for the parameter provide the most accurate results. In addition to the simulation results, we demonstrate the use of the robust principal component analysis with a data set of lake-water chemistry variables to illustrate the additional insight available. We suggest that ecologists consider that their data may contain atypical points. Following checks associated with normality, bivariate linearity and other traditional aspects, we advocate that ecologists examine their data sets using robust multivariate methods. Points identified as being atypical should be carefully evaluated based on background information to determine their suitability for inclusion in further multivariate analyses and whether additional factors explain their unusual characteristics. Copyright © 2004 John Wiley & Sons, Ltd. [source] A comparative study of efficient iterative solvers for generalized Stokes equationsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2008Maxim Larin Abstract We consider a generalized Stokes equation with problem parameters ,,0 (size of the reaction term) and ,>0 (size of the diffusion term). We apply a standard finite element method for discretization. The main topic of the paper is a study of efficient iterative solvers for the resulting discrete saddle point problem. We investigate a coupled multigrid method with Braess,Sarazin and Vanka-type smoothers, a preconditioned MINRES method and an inexact Uzawa method. We present a comparative study of these methods. An important issue is the dependence of the rate of convergence of these methods on the mesh size parameter and on the problem parameters , and ,. We give an overview of the main theoretical convergence results known for these methods. For a three-dimensional problem, discretized by the Hood,Taylor ,,2,,,1 pair, we give results of numerical experiments. Copyright © 2007 John Wiley & Sons, Ltd. [source] Extension theorems for Stokes and Lamé equations for nearly incompressible media and their applications to numerical solution of problems with highly discontinuous coefficientsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2 2002N. S. Bakhvalov Abstract We prove extension theorems in the norms described by Stokes and Lamé operators for the three-dimensional case with periodic boundary conditions. For the Lamé equations, we show that the extension theorem holds for nearly incompressible media, but may fail in the opposite limit, i.e. for case of absolutely compressible media. We study carefully the latter case and associate it with the Cosserat problem. Extension theorems serve as an important tool in many applications, e.g. in domain decomposition and fictitious domain methods, and in analysis of finite element methods. We consider an application of established extension theorems to an efficient iterative solution technique for the isotropic linear elasticity equations for nearly incompressible media and for the Stokes equations with highly discontinuous coefficients. The iterative method involves a special choice for an initial guess and a preconditioner based on solving a constant coefficient problem. Such preconditioner allows the use of well-known fast algorithms for preconditioning. Under some natural assumptions on smoothness and topological properties of subdomains with small coefficients, we prove convergence of the simplest Richardson method uniform in the jump of coefficients. For the Lamé equations, the convergence is also uniform in the incompressible limit. Our preliminary numerical results for two-dimensional diffusion problems show fast convergence uniform in the jump and in the mesh size parameter. Copyright © 2002 John Wiley & Sons, Ltd. [source] Exact Confidence Bounds Following Adaptive Group Sequential TestsBIOMETRICS, Issue 2 2009Werner Brannath Summary We provide a method for obtaining confidence intervals, point estimates, and p-values for the primary effect size parameter at the end of a two-arm group sequential clinical trial in which adaptive changes have been implemented along the way. The method is based on applying the adaptive hypothesis testing procedure of Müller and Schäfer (2001, Biometrics57, 886,891) to a sequence of dual tests derived from the stage-wise adjusted confidence interval of Tsiatis, Rosner, and Mehta (1984, Biometrics40, 797,803). In the nonadaptive setting this confidence interval is known to provide exact coverage. In the adaptive setting exact coverage is guaranteed provided the adaptation takes place at the penultimate stage. In general, however, all that can be claimed theoretically is that the coverage is guaranteed to be conservative. Nevertheless, extensive simulation experiments, supported by an empirical characterization of the conditional error function, demonstrate convincingly that for all practical purposes the coverage is exact and the point estimate is median unbiased. No procedure has previously been available for producing confidence intervals and point estimates with these desirable properties in an adaptive group sequential setting. The methodology is illustrated by an application to a clinical trial of deep brain stimulation for Parkinson's disease. [source] Nuclear morphometry and texture analysis of B-cell non-Hodgkin lymphoma: Utility in subclassification on cytosmearsDIAGNOSTIC CYTOPATHOLOGY, Issue 2 2010Shilpa Gupta M.D. Abstract Non-Hodgkin lymphoma (NHL) is a heterogeneous group of lymphoid neoplasms and accurate subclassification is an essential prerequisite for proper management of patients. This study was aimed at evaluating the utility of nuclear morphometry and textural features on cytology smears to classify the cases of NHL on aspiration cytology. Fine needle aspiration smears of 50 cases of B-cell NHL were included. Various morphometric and texture parameters were obtained by manually tracing the nuclei on digitized images in each case and discriminant analysis performed using various features taken individually as well as all together. The percentage of cells correctly classified to a particular NHL subtype using the discriminant functions so obtained was noted. Our results show that discriminant analysis done on size parameters could correctly classify a greater number of cells than on shape parameters (36.4% vs. 21.2%, respectively). Texture parameters based on single pixel values (first order texture) were inferior (42.8%) to those based on pair of pixels (58.7%) in subtyping of cells. Discriminant analysis based on color parameters was more effective (61.9%) as compared to rest of the morphometric and textural parameters. Using all the morphometric and textural parameters together, 83.3% of cells could be correctly classified to a particular NHL subtype. The present study, perhaps the first study of detailed morphometric analysis on cytosmears, shows that satisfactory classification of NHL on aspiration cytology is possible using nuclear morphometry and textural parameters considered together. These results are promising for further studies on this subject and development of automated cytodiagnosis. Diagn. Cytopathol. 2010. © 2009 Wiley-Liss, Inc. [source] Trends in aquatic macrophyte species turnover in Northern Ireland , which factors determine the spatial distribution of local species turnover?GLOBAL ECOLOGY, Issue 5 2004Einar Heegaard ABSTRACT Aim, The study examined qualitative predictions of ecological theories in relation to the spatial distribution of species turnover of aquatic macrophytes, through the following parameters: (1) distance between lakes (2) chemical conditions of the lakes (3) chemical differences between the lakes, and (4) the lake size. Location, 562 lakes dispersed throughout Northern Ireland were analysed. Methods, To obtain species turnover estimates independent of richness, the average distance between focal lakes and their five nearest neighbours in ordination space (DCA) was standardized by the species richness in a Generalized Additive Model (GAM). The relationships between species turnover and ecological (chemical condition, chemical difference, distance between lakes, and lake-size) and geographical parameters (latitude, longitude, and altitude) were analysed using GAM. Results, The results indicate that the pattern in species turnover is a combination of the chemical conditions and the distance between the lakes, including the interaction term. The effects of chemical heterogeneity and lake size parameters were both positive but weak. In general, increased distance and decreased ionic concentration contribute to increased turnover. The influence of distance on species turnover is strongest at low and high altitude, and at mid-elevation the species turnover is mainly driven by the chemical conditions. Towards the north there is an increasing influence of distance, whereas in the south the chemical conditions have their strongest influence. Conclusions, There is a need for components from several established ecological theories to explain the spatial trends in species turnover within Northern Ireland. Central theories in this particular study are the population/metapopulation dynamics, the continuum concept, and the species-pool concept. [source] Measuring egg size using digital photography: testing Hoyt's method using Florida Scrub-Jay eggsJOURNAL OF FIELD ORNITHOLOGY, Issue 1 2007Eli S. Bridge ABSTRACT Egg volumes are most often estimated using a mathematical model that incorporates length and width measurements and a species-specific shape variable. Although adequate in many respects, this technique does not account for intraspecific variation in egg shape. We developed a computer-automated technique that uses calibrated digital photographs to render precise measurements of several egg-size parameters including length, width, volume, and surface area. The system extracts egg outlines from photographs, and divides each egg into latitudinal slices that are subsequently regarded as simple geometric shapes (cylinders or cone frustra) with volumes and surface areas that can be summed to generate size parameters for the entire egg. We tested this technique using 491 eggs from Florida Scrub-Jay (Aphelocoma coerulescens) nests and compared the resulting egg volumes with volumes calculated using the preeminent method of estimating volume from linear measurements. Our method was highly accurate, and differences between the volumes from our method and the alternative method were strongly associated with variation in egg shape. Advantages of our technique include decreased handling of eggs and increased accuracy. Software resources and additional information regarding the technique are available at http://www.archbold-station.org/abs/data/birddata/Bridge-JFO-eggsize.htm. SINOPSIS El volumen de los huevos comunmente es estimado utilizando un modelo matemático en donde se incorpora el ancho y el largo del huevo y la variable de la forma de este. Aunque es un método adecuado en muchos aspectos, esta técnica no toma enconsideracion las variaciones intraespecificas de la forma de los huevos. Desarrollamos una técnica automática con computadora, que usa fotografia digital calibrada para ofrecer medidas de los huevos incluyendo largo, ancho, volumen y área superficial. El sistema extrae parámetros de los huevos de fotografías y divide cada huevo en rebanadas latitudinales, que subsecuentemente son tomadas como formas geométricas (e.g., cilindros o conos) con volumenes y áreas superficiales, que a su vez pueden ser utilizadas para obtener el largo y el ancho. Pusimos a prueba esta técnica con 491 huevos del Azulejón (Aphelocoma coerulescens) y comparamos el volumen de los huevos obtenidos con el computador con volumenes calculados con el método usual de medidas lineales. Nuestro método fue preciso y las diferencias en los volumenes usando nuestro método y las del método clásico estuvieron asociadas a la variación en la forma de los huevos. Entre las ventajas de nuestra técnica encontramos una disminución en la manipulación de los huevos y un aumento en la presición de los datos tomados. Los recursos computacionales que se necesitan e información adicional sobre esta técnica se encuentra disponible en: http://www.archbold-station.org/abs/data/birddata/Bridge-JFO-eggsize.htm. [source] Environmental and ontogenetic constraints on developmental stability in the spatangoid sea urchin Echinocardium (Echinoidea)BIOLOGICAL JOURNAL OF THE LINNEAN SOCIETY, Issue 2 2006THOMAS SAUCEDE Spatangoid irregular sea urchins are detritivorous benthic organisms particularly prone to variations of environment, and their mode of growth and plate morphology make them an appropriate model to assess the effects of environmental variations. Two populations of Echinocardium flavescens were sampled in two sites of the Norwegian coast characterized by contrasted environmental conditions. Different morphological descriptors (plate areas, interlandmarks distances, overall size, and shape of the posterior ambulacra) were used to appraise interindividual variations, and fluctuating asymmetry. The comparisons were carried out using classical fluctuating asymmetry (FA) methods, as well as Procrustean approaches. The population suspected to be less influenced by anthropic activities exhibits lower levels of FA for the size parameters (plate surfaces, interlandmarks distances, and centroid size) than the population located in a polluted area. Conversely, it shows higher FA values for the shape parameters (landmarks configuration). Interindividual variations appear to be correlated to FA. Variations are orientated according to the main growth axis of the ambulacra, and their intensity is stronger in the large posterior plates, which are also the youngest. These results are discussed with respect to architectural constraints involved in the sea urchin growth. © 2006 The Linnean Society of London, Biological Journal of the Linnean Society, 2006, 88, 165,177. [source] | |||||||||||||