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dc.contributorAluja Banet, Tomàs
dc.contributor.authorGraffelman, Jan
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament d'Estadística i Investigació Operativa
dc.date.accessioned2011-04-12T15:16:58Z
dc.date.available2007-05-21
dc.date.issued2000-09-12
dc.date.submitted2007-04-27
dc.identifier.citationGraffelman, J. Contributions to the multivariate Analysis of Marine Environmental Monitoring. Tesi doctoral, UPC, Departament d'Estadística i Investigació Operativa, 2000. ISBN 9788469064917. DOI 10.5821/dissertation-2117-93836.
dc.identifier.isbn9788469064917
dc.identifier.otherhttp://www.tdx.cat/TDX-0427107-121733
dc.identifier.urihttp://hdl.handle.net/2117/93836
dc.description.abstractThe thesis parts from the view that statistics starts with data, and starts by introducing the data sets studied: marine benthic species counts and chemical measurements made at a set of sites in the Norwegian Ekofisk oil field, with replicates and annually repeated. An introductory chapter details the sampling procedure and shows with reliability calculations that the (transformed) chemical variables have excellent reliability, whereas the biological variables have poor reliability, except for a small subset of abundant species. Transformed chemical variables are shown to be approximately normal. Bootstrap methods are used to assess whether the biological variables follow a Poisson distribution, and lead to the conclusion that the Poisson distribution must be rejected, except for rare species. A separate chapter details more work on the distribution of the species variables: truncated and zero-inflated Poisson distributions as well as Poisson mixtures are used in order to account for sparseness and overdispersion. Species are thought to respond to environmental variables, and regressions of the abundance of a few selected species onto chemical variables are reported. For rare species, logistic regression and Poisson regression are the tools considered, though there are problems of overdispersion. For abundant species, random coefficient models are needed in order to cope with intraclass correlation. The environmental variables, mainly heavy metals, are highly correlated, leading to multicollinearity problems. The next chapters use a multivariate approach, where all species data is now treated simultaneously. The theory of correspondence analysis is reviewed, and some theoretical results on this method are reported (bounds for singular values, centring matrices). An applied chapter discusses the correspondence analysis of the species data in detail, detects outliers, addresses stability issues, and considers different ways of stacking data matrices to obtain an integrated analysis of several years of data, and to decompose variation into a within-sites and between-sites component. More than 40 % of the total inertia is due to variation within stations. Principal components analysis is used to analyse the set of chemical variables. Attempts are made to integrate the analysis of the biological and chemical variables. A detailed theoretical development shows how continuous variables can be mapped in an optimal manner as supplementary vectors into a correspondence analysis biplot. Geometrical properties are worked out in detail, and measures for the quality of the display are given, whereas artificial data and data from the monitoring survey are used to illustrate the theory developed. The theory of display of supplementary variables in biplots is also worked out in detail for principal component analysis, with attention for the different types of scaling, and optimality of displayed correlations. A theoretical chapter follows that gives an in depth theoretical treatment of canonical correspondence analysis, (linearly constrained correspondence analysis, CCA for short) detailing many mathematical properties and aspects of this multivariate method, such as geometrical properties, biplots, use of generalized inverses, relationships with other methods, etc. Some applications of CCA to the survey data are dealt with in a separate chapter, with their interpretation and indication of the quality of the display of the different matrices involved in the analysis. Weighted principal component analysis of weighted averages is proposed as an alternative for CCA. This leads to a better display of the weighted averages of the species, and in the cases so far studied, also leads to biplots with a higher amount of explained variance for the environmental data. The thesis closes with a bibliography and outlines some suggestions for further research, such as a the generalization of canonical correlation analysis for working with singular covariance matrices, the use partial least squares methods to account for the excess of predictors, and data fusion problems to estimate missing biological data.
dc.language.isoeng
dc.publisherUniversitat Politècnica de Catalunya
dc.rightsADVERTIMENT. L'accés als continguts d'aquesta tesi doctoral i la seva utilització ha de respectar els drets de la persona autora. Pot ser utilitzada per a consulta o estudi personal, així com en activitats o materials d'investigació i docència en els termes establerts a l'art. 32 del Text Refós de la Llei de Propietat Intel·lectual (RDL 1/1996). Per altres utilitzacions es requereix l'autorització prèvia i expressa de la persona autora. En qualsevol cas, en la utilització dels seus continguts caldrà indicar de forma clara el nom i cognoms de la persona autora i el títol de la tesi doctoral. No s'autoritza la seva reproducció o altres formes d'explotació efectuades amb finalitats de lucre ni la seva comunicació pública des d'un lloc aliè al servei TDX. Tampoc s'autoritza la presentació del seu contingut en una finestra o marc aliè a TDX (framing). Aquesta reserva de drets afecta tant als continguts de la tesi com als seus resums i índexs.
dc.sourceTDX (Tesis Doctorals en Xarxa)
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.otherinertia
dc.subject.othersupplementary variables
dc.subject.otherprincipal component analysis
dc.subject.othersingular values
dc.subject.otherabundance data
dc.subject.otherobservational data
dc.subject.othermultivariate analysis
dc.subject.otherweighted averages
dc.titleContributions to the multivariate Analysis of Marine Environmental Monitoring
dc.typeDoctoral thesis
dc.subject.lemacAnàlisi multivariable
dc.subject.lemacEcologia marina
dc.identifier.doi10.5821/dissertation-2117-93836
dc.identifier.dlB.33055-2007
dc.rights.accessOpen Access
dc.description.versionPostprint (published version)
dc.identifier.tdxhttp://hdl.handle.net/10803/6525


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