Random walk and quantitative stratigraphical sequences

A sequence of digitized observations on short-normal resistivity determinations seems to show trend from higher to lower values. An appropriate statistical model proves it to have less range than expected on the distribution of its successive increments. On a two-tailed statistical procedure for testing deviations from a random walk, the series tends towards ‘stasis’ rather than trend. The random walk model is shown to be plausible for the problem considered.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73590/1/j.1365-3121.1992.tb00465.x.pd

On stability of compositional canonical variate vector components

Abstract: Canonical variate analysis (aka discriminant coordinates) is viewed from the aspect of Aitchisonian compositional data analysis and the concept of stability in canonical vectors examined in relation to their reification (i.e. providing canonical vector components with a practical interpretation). The log-ratio transformation was found to have computational and interpretational advantages over the centred log-ratio transformation. The ad hoc application of N. A. Campbell's application of the method of shrinkage estimators to multiple discrimination, and the optimal retention of discrimination power, is exemplified by two cases, one drawn from quantitative sedimentology, the other from biomolecular palaeontology, with the intention of probing the effect of instability on interpreting the relative importance of standardized canonical variate coefficients in relation to the suppression of near-redundant directions of within-groups variation. Pronounced instability in canonical vectors may endanger the validity of an analysis

Fish remains (Elasmobranchii, Actinopterygii) from the Late Cretaceous of the Benue Trough, Nigeria

International audienceSelachian and ray-finned fish remains from various Late Cretaceous localities of Nigeria are described. Each locality has yielded only a very few specimens and the diversity is therefore very low. However, some taxa are recorded for the first time in Africa. The Ashaka locality in the Upper Benue Trough (northeastern Nigeria) has yielded a small but interesting late Cenomanian assemblage of microremains, including teeth of ''Carcharias'' amonensis, Rhombopterygia zaborskii sp. nov., Hamrabatis sp., ''Stephanodus'' sp., and a possible ionoscopiform. A large prearticular dentition coming from the early Turonian beds of this locality is assigned to the large pycnodontiform Acrotemnus, a poorly known genus here regarded as a senior synonym of Macropycnodon. In the Lower Benue Trough (southeastern Nigeria), several localities ranging in age from the late Cenomanian to the early Maastrichtian have yielded various widespread taxa such as Ptychodus, Scapanorhynchus, Squalicorax, Vidalamiinae indet., cf. Protosphyraena, and Eodiaphyodus. The seaway that occupied the Benue Trough during transgressive episodes (late Cenomanian-early Turonian and Maastrichtian) created opportunities for the dispersal of many marine fish taxa into new areas, such as the proto-South Atlantic

The Morphometric Synthesis for landmarks and edge-elements in images

Over the last decade, techniques from mathematical statistics, multivariate biometrics, non-Euclidean geometry, and computer graphics have been combined in a coherent new system of tools for the biometric analysis of landmarks , or labelled points, along with the biological images in which they are seen. Multivariate analyses of samples for all the usual scientific purposes - description of mean shapes, of shape variation, and of the covariation of shape with size, group, or other causes or effects - may be carried out very effectively in the tangent space to David Kendall's shape space at the Procrustes average shape. For biometric interpretation of such analyses, we need a basis for the tangent space that is Procrustes-orthonormal, and we need graphics for visualizing mean shape differences and other segments and vectors there; both of these needs are managed by the thin-plate spline. The spline also links the biometrics of landmarks to deformation analysis of curves in the images from which the landmarks originally arose. This article reviews the principal tools of this synthesis in a typical study design involving landmarks and edge information from a microfossil.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75091/1/j.1365-3121.1995.tb00535.x.pd

Host-based identification is not supported by morphometrics in natural populations of Gyrodactylus salaris and G. thymalli (Platyhelminthes, Monogenea)

Gyrodactylus salaris is a serious pest of wild pre-smolt Atlantic salmon (Salmo salar) in Norway. The closely related G. thymalli, originally described from grayling (Thymallus thymallus), is assumed harmless to both grayling and salmon. The 2 species are difficult to distinguish using traditional, morphometric methods or molecular approaches. The aim of this study was to explore whether there is a consistent pattern of morphometrical variation between G. salaris and G. thymalli and to analyse the morphometric variation in the context of ‘diagnostic realism’ (in natural populations). Specimens from the type-material for the 2 species are also included. In total, 27 point-to-point measurements from the opisthaptoral hard parts were used and analysed by digital image processing and uni- and multivariate morphometry. All populations most closely resembled its respective type material, as expected from host species, with the exception of G. thymalli from the Norwegian river Trysilelva. We, therefore, did not find clear support in the morphometrical variation among G. salaris and G. thymalli for an a priori species delineation based on host. The present study also indicates an urgent need for more detailed knowledge on the influence of environmental factors on the phenotype of gyrodactylid populations

An EWMA control chart for the multivariate coefficient of variation

This is the peer reviewed version of the following article: Giner-Bosch, V, Tran, KP, Castagliola, P, Khoo, MBC. An EWMA control chart for the multivariate coefficient of variation. Qual Reliab Engng Int. 2019; 35: 1515-1541, which has been published in final form at https://doi.org/10.1002/qre.2459. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.[EN] Monitoring the multivariate coefficient of variation over time is a natural choice when the focus is on stabilising the relative variability of a multivariate process, as is the case in a significant number of real situations in engineering, health sciences, and finance, to name but a few areas. However, not many tools are available to practitioners with this aim. This paper introduces a new control chart to monitor the multivariate coefficient of variation through an exponentially weighted moving average (EWMA) scheme. Concrete methodologies to calculate the limits and evaluate the performance of the chart proposed and determine the optimal values of the chart's parameters are derived based on a theoretical study of the statistic being monitored. Computational experiments reveal that our proposal clearly outperforms existing alternatives, in terms of the average run length to detect an out-of-control state. A numerical example is included to show the efficiency of our chart when operating in practice.Generalitat Valenciana, Grant/Award Number: BEST/2017/033 and GV/2016/004; Ministerio de Economia y Competitividad, Grant/Award Number: MTM2013-45381-PGiner-Bosch, V.; Tran, KP.; Castagliola, P.; Khoo, MBC. (2019). An EWMA control chart for the multivariate coefficient of variation. Quality and Reliability Engineering International. 35(6):1515-1541. https://doi.org/10.1002/qre.2459S15151541356Kang, C. W., Lee, M. S., Seong, Y. J., & Hawkins, D. M. (2007). 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The coefficient of variation biplot. Journal of Classification, 7(2), 241-256. doi:10.1007/bf01908718Boik, R. J., & Shirvani, A. (2009). Principal components on coefficient of variation matrices. Statistical Methodology, 6(1), 21-46. doi:10.1016/j.stamet.2008.02.006MacGregor, J. F., & Kourti, T. (1995). Statistical process control of multivariate processes. Control Engineering Practice, 3(3), 403-414. doi:10.1016/0967-0661(95)00014-lBersimis, S., Psarakis, S., & Panaretos, J. (2007). Multivariate statistical process control charts: an overview. Quality and Reliability Engineering International, 23(5), 517-543. doi:10.1002/qre.829Yeong, W. C., Khoo, M. B. C., Teoh, W. L., & Castagliola, P. (2015). A Control Chart for the Multivariate Coefficient of Variation. Quality and Reliability Engineering International, 32(3), 1213-1225. doi:10.1002/qre.1828Lim, A. J. X., Khoo, M. B. C., Teoh, W. L., & Haq, A. (2017). Run sum chart for monitoring multivariate coefficient of variation. 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Sparsest factor analysis for clustering variables: a matrix decomposition approach

We propose a new procedure for sparse factor analysis (FA) such that each variable loads only one common factor. Thus, the loading matrix has a single nonzero element in each row and zeros elsewhere. Such a loading matrix is the sparsest possible for certain number of variables and common factors. For this reason, the proposed method is named sparsest FA (SSFA). It may also be called FA-based variable clustering, since the variables loading the same common factor can be classified into a cluster. In SSFA, all model parts of FA (common factors, their correlations, loadings, unique factors, and unique variances) are treated as fixed unknown parameter matrices and their least squares function is minimized through specific data matrix decomposition. A useful feature of the algorithm is that the matrix of common factor scores is re-parameterized using QR decomposition in order to efficiently estimate factor correlations. A simulation study shows that the proposed procedure can exactly identify the true sparsest models. Real data examples demonstrate the usefulness of the variable clustering performed by SSFA

Distributed static linear Gaussian models using consensus

Algorithms for distributed agreement are a powerful means for formulating distributed versions of existing centralized algorithms. We present a toolkit for this task and show how it can be used systematically to design fully distributed algorithms for static linear Gaussian models, including principal component analysis, factor analysis, and probabilistic principal component analysis. These algorithms do not rely on a fusion center, require only low-volume local (1-hop neighborhood) communications, and are thus efficient, scalable, and robust. We show how they are also guaranteed to asymptotically converge to the same solution as the corresponding existing centralized algorithms. Finally, we illustrate the functioning of our algorithms on two examples, and examine the inherent cost-performance tradeoff