Discriminant analysis under the common principal components model

For two or more populations of which the covariance matrices have a common set of eigenvectors, but different sets of eigenvalues, the common principal components (CPC) model is appropriate. Pepler et al. (2015) proposed a regularised CPC covariance matrix estimator and showed that this estimator outperforms the unbiased and pooled estimators in situations where the CPC model is applicable. This paper extends their work to the context of discriminant analysis for two groups, by plugging the regularised CPC estimator into the ordinary quadratic discriminant function. Monte Carlo simulation results show that CPC discriminant analysis offers significant improvements in misclassification error rates in certain situations, and at worst performs similar to ordinary quadratic and linear discriminant analysis. Based on these results, CPC discriminant analysis is recommended for situations where the sample size is small compared to the number of variables, in particular for cases where there is uncertainty about the population covariance matrix structures

Correlation between drying defects, their parameters and moisture gradient in kiln-dried, south african grown Eucalyptus Grandis poles

Non-destructive testing for drying defects in Eucalyptus grandis utility poles would be highly advantageous. These defects can negatively affect creosote preservative treatment and in-service performance. The objective of this study was to assess correlations between drying defects such as surface checking, honeycombing, collapse, their parameters and moisture content (MC) gradient in poles, to possibly find a simple and quick but reliable method to assess internal and external drying defects. Defects and moisture content gradients were measured in 39 kiln-dried E. grandis poles. After measuring surface check length, width and depth using a measuring tape, a ruler and a depth gauge, destructive sampling at the theoretical ground line (TGL) was done to measure the MC gradient between the shell and core of poles. Digital image analysis of cross-sections of discs cut at TGL was used to measure honeycomb check width, length and area, as well as counting individual closed surface checks. Collapse was assessed using qualitative methods. Results showed that honeycombing and collapse were positively, and surface checking and MC gradient were negatively correlated. Surface check width, length and depth were also correlated. Honeycomb count, check width, length and area were strongly correlated. It was concluded that measuring any of these surface check and/or honeycomb parameters may give meaningful deductions about the extent of surface checking and honeycombing respectively

Sensitivity analysis of reactive ecological dynamics

Author Posting. © Springer, 2008. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Bulletin of Mathematical Biology 70 (2008): 1634-1659, doi:10.1007/s11538-008-9312-7.Ecological systems with asymptotically stable equilibria may exhibit significant transient dynamics following perturbations. In some cases, these transient dynamics include the possibility of excursions away from the equilibrium before the eventual return; systems that exhibit such amplification of perturbations are called reactive. Reactivity is a common property of ecological systems, and the amplification can be large and long-lasting. The transient response of a reactive ecosystem depends on the parameters of the underlying model. To investigate this dependence, we develop sensitivity analyses for indices of transient dynamics (reactivity, the amplification envelope, and the optimal perturbation) in both continuous- and discrete-time models written in matrix form. The sensitivity calculations require expressions, some of them new, for the derivatives of equilibria, eigenvalues, singular values, and singular vectors, obtained using matrix calculus. Sensitivity analysis provides a quantitative framework for investigating the mechanisms leading to transient growth. We apply the methodology to a predator-prey model and a size-structured food web model. The results suggest predator-driven and prey-driven mechanisms for transient amplification resulting from multispecies interactions.Financial support provided by NSF grant DEB-0343820, NOAA grant NA03-NMF4720491, the Ocean Life Institute of the Woods Hole Oceanographic Institution, and the Academic Programs Office of the MIT-WHOI Joint Program in Oceanography

Fungal Planet description sheets: 1284–1382

Novel species of fungi described in this study include those from various countries as follows: Antartica, Cladosporium austrolitorale from coastal sea sand. Australia, Austroboletus yourkae on soil, Crepidotus innuopurpureus on dead wood, Curvularia stenotaphri from roots and leaves of Stenotaphrum secundatum and Thecaphora stajsicii from capsules of Oxalis radicosa. Belgium, Paraxerochrysium coryli (incl. Paraxerochrysium gen. nov.) from Corylus avellana. Brazil, Calvatia nordestina on soil, Didymella tabebuiicola from leaf spots on Tabebuia aurea, Fusarium subflagellisporum from hypertrophied floral and vegetative branches of Mangifera indica and Microdochium maculosum from living leaves of Digitaria insularis. Canada, Cuphophyllus bondii fromagrassland. Croatia, Mollisia inferiseptata from a rotten Laurus nobilis trunk. Cyprus, Amanita exilis oncalcareoussoil. Czech Republic, Cytospora hippophaicola from wood of symptomatic Vaccinium corymbosum. Denmark, Lasiosphaeria deviata on pieces of wood and herbaceousdebris. Dominican Republic, Calocybella goethei among grass on a lawn. France (Corsica) , Inocybe corsica onwetground. France (French Guiana) , Trechispora patawaensis on decayed branch of unknown angiosperm tree and Trechispora subregularis on decayed log of unknown angiosperm tree. Germany, Paramicrothecium sambuci (incl. Paramicrothecium gen. nov.)ondeadstemsof Sambucus nigra. India, Aureobasidium microtermitis from the gut of a Microtermes sp. termite, Laccaria diospyricola on soil and Phylloporia tamilnadensis on branches of Catunaregam spinosa. Iran, Pythium serotinoosporum from soil under Prunus dulcis. Italy, Pluteus brunneovenosus on twigs of broad leaved trees on the ground. Japan, Heterophoma rehmanniae on leaves of Rehmannia glutinosa f. hueichingensis. Kazakhstan, Murispora kazachstanica from healthy roots of Triticum aestivum. Namibia, Caespitomonium euphorbiae (incl. Caespitomonium gen. nov.)from stems of an Euphorbia sp. Netherlands, Alfaria junci, Myrmecridium junci, Myrmecridium juncicola, Myrmecridium juncigenum, Ophioceras junci, Paradinemasporium junci (incl. Paradinemasporium gen. nov.), Phialoseptomonium junci, Sporidesmiella juncicola, Xenopyricularia junci and Zaanenomyces quadripartis (incl. Zaanenomyces gen. nov.), fromdeadculmsof Juncus effusus, Cylindromonium everniae and Rhodoveronaea everniae from Evernia prunastri, Cyphellophora sambuci and Myrmecridium sambuci from Sambucus nigra, Kiflimonium junci, Saro cladium junci, Zaanenomyces moderatricis academiae and Zaanenomyces versatilis from dead culms of Juncus inflexus, Microcera physciae from Physcia tenella, Myrmecridium dactylidis from dead culms of Dactylis glomerata, Neochalara spiraeae and Sporidesmium spiraeae from leaves of Spiraea japonica, Neofabraea salicina from Salix sp., Paradissoconium narthecii (incl. Paradissoconium gen. nov.)from dead leaves of Narthecium ossifragum, Polyscytalum vaccinii from Vaccinium myrtillus, Pseudosoloacrosporiella cryptomeriae (incl. Pseudosoloacrosporiella gen. nov.)fromleavesof Cryptomeria japonica, Ramularia pararhabdospora from Plantago lanceolata, Sporidesmiella pini from needles of Pinus sylvestris and Xenoacrodontium juglandis (incl. Xenoacrodontium gen. nov. and Xenoacrodontiaceae fam. nov.)from Juglans regia. New Zealand, Cryptometrion metrosideri from twigs of Metrosideros sp., Coccomyces pycnophyllocladi from dead leaves of Phyllocladus alpinus, Hypoderma aliforme from fallen leaves Fuscopora solandri and Hypoderma subiculatum from dead leaves Phormium tenax. Norway, Neodevriesia kalakoutskii from permafrost and Variabilispora viridis from driftwood of Picea abies. Portugal, Entomortierella hereditatis from abio film covering adeteriorated limestone wall. Russia, Colpoma junipericola from needles of Juniperus sabina, Entoloma cinnamomeum on soil in grasslands, Entoloma verae on soil in grasslands, Hyphodermella pallidostraminea on a dry dead branch of Actinidia sp., Lepiota sayanensis onlitterinamixedforest, Papiliotrema horticola from Malus communis , Paramacroventuria ribis (incl. Paramacroventuria gen. nov.)fromleaves of Ribes aureum and Paramyrothecium lathyri from leaves of Lathyrus tuberosus. South Africa, Harzia combreti from leaf litter of Combretum collinum ssp. sulvense, Penicillium xyleborini from Xyleborinus saxesenii , Phaeoisaria dalbergiae from bark of Dalbergia armata, Protocreopsis euphorbiae from leaf litter of Euphorbia ingens and Roigiella syzygii from twigs of Syzygium chordatum. Spain, Genea zamorana on sandy soil, Gymnopus nigrescens on Scleropodium touretii, Hesperomyces parexochomi on Parexochomus quadriplagiatus, Paraphoma variabilis from dung, Phaeococcomyces kinklidomatophilus from a blackened metal railing of an industrial warehouse and Tuber suaveolens in soil under Quercus faginea. Svalbard and Jan Mayen, Inocybe nivea associated with Salix polaris. Thailand, Biscogniauxia whalleyi oncorticatedwood. UK, Parasitella quercicola from Quercus robur. USA , Aspergillus arizonicus from indoor air in a hospital, Caeliomyces tampanus (incl. Caeliomyces gen. nov.)fromoffice dust, Cippumomyces mortalis (incl. Cippumomyces gen. nov.)fromatombstone, Cylindrium desperesense from air in a store, Tetracoccosporium pseudoaerium from air sample in house, Toxicocladosporium glendoranum from air in a brick room, Toxicocladosporium losalamitosense from air in a classroom, Valsonectria portsmouthensis from airinmen'slockerroomand Varicosporellopsis americana from sludge in a water reservoir. Vietnam, Entoloma kovalenkoi on rotten wood, Fusarium chuoi inside seed of Musa itinerans , Micropsalliota albofelina on soil in tropical evergreen mixed forest sand Phytophthora docyniae from soil and roots of Docynia indica. Morphological and culture characteristics are supported by DNA barcodes

A comparison of approximate confidence interval methods for the difference between two independent binomial proportions

Conventional methods to determine confidence intervals for the difference between two independent binomial proportions p1 and p2 are prone to violations of the definition interval [-1; 1] for p1-p2 and may have very poor coverage properties. In this paper several less known methods are described. A simulation study was done to compare the different confidence interval methods with respect to length, coverage, zero width interval and violation of the definition interval. The best methods were found to be Mee's and Miettinen and Nurminen's method. These methods, however, are computer intensive. The Jeffreys-Perks and Score interval methods seem to be the best of the more easily calculable methods to use in most practical situations.Conventional methods to determine confidence intervals for the difference between two independent binomial proportions p1 and p2 are prone to violations of the definition interval [-1; 1] for p1-p2 and may have very poor coverage properties. In this paper several less known methods are described. A simulation study was done to compare the different confidence interval methods with respect to length, coverage, zero width interval and violation of the definition interval. The best methods were found to be Mee's and Miettinen and Nurminen's method. These methods, however, are computer intensive. The Jeffreys-Perks and Score interval methods seem to be the best of the more easily calculable methods to use in most practical situations.Conventional methods to determine confidence intervals for the difference between two independent binomial proportions p1 and p2 are prone to violations of the definition interval [-1; 1] for p1-p2 and may have very poor coverage properties. In this paper several less known methods are described. A simulation study was done to compare the different confidence interval methods with respect to length, coverage, zero width interval and violation of the definition interval. The best methods were found to be Mee's and Miettinen and Nurminen's method. These methods, however, are computer intensive. The Jeffreys-Perks and Score interval methods seem to be the best of the more easily calculable methods to use in most practical situations.ArticleArticl

The Decomposition of the Behrens-Fisher Statistic in q-Dimensional Common Principal Component Submodels

Covariance matrices, heteroscedasticity, iterative procedure, model fitting, randomization testing, Takemura decomposition,

Regularised covariance matrix estimation under the common principal components model

The common principal components (CPC) model provides a way to model the population covariance matrices of several groups by assuming a common eigenvector structure. When appropriate, this model can provide covariance matrix estimators of which the elements have smaller standard errors than when using either the pooled covariance matrix or the per group unbiased sample covariance matrix estimators. In this paper, a regularised CPC estimator under the assumption of a common (or partially common) eigenvector structure in the populations is proposed. After estimation of the common eigenvectors using the Flury-Gautschi (or other) algorithm, the off-diagonal elements of the nearly diagonalised covariance matrices are shrunk towards zero and multiplied with the orthogonal common eigenvector matrix to obtain the regularised CPC covariance matrix estimates. The optimal shrinkage intensity per group can be estimated using cross-validation. The efficiency of these estimators compared to the pooled and unbiased estimators is investigated in a Monte Carlo simulation study, and the regularised CPC estimator is applied to a real data set to demonstrate the utility of the method

A comparison of some methods for the selection of a common eigenvector model for the covariance matrices of two groups

Two new non-parametric common principal component model selection procedures based on bootstrap distributions of the vector correlations of all combinations of the eigenvectors from two groups are proposed. The performance of these methods is compared in a simulation study to the two parametric methods previously suggested by Flury (1988), as well as modified versions of two non-parametric methods proposed by Klingenberg (1996) and Klingenberg and McIntyre (1998). The proposed bootstrap vector correlation distribution (BVD) method is shown to outperform all of the existing methods in most of the simulated situations considered