Numerical aspects in the data model of conceptual information systems

While most data analysis and decision support tools use numerical aspects of the data, Conceptual Information Systems focus on their conceptual structure. This paper discusses how both approaches can be combined.

Entwicklung von Interessen und Nicht-Interessen bei Kindern im Kindergarten, in der Grundschule und in der Sekundarstufe I

Zusammenfassung der Dissertation von Barbara Wieder zum Thema: Entwicklung von Interessen und Nicht-Interessen bei Kindern im Kindergarten, in der Grundschule und in der Sekundarstufe I. Die vorliegende Arbeit beschäftigt sich mit der Genese und Entwicklung von Interessen und Nicht-Interessen von Kindern im Alter von 4 bis 16 Jahren. Dazu wurden 87 Kinder sowie deren Eltern und Lehrkräfte bzw. Erzieherinnen mittels strukturierter Interviews in einem Längsschnitt etwa alle zwei Jahre wiederholt befragt. Theoretische Grundlage ist die Rahmenkonzeption einer pädagogischen Interessentheorie, die Interesse als einen Bezug zwischen einer Person und einem Gegenstand bestimmt. Dieser Bezug ist charakterisiert durch die Merkmale kognitive Ausprägung, emotionale Tönung und Wertaspekt (SCHIEFELE et al. 1983) sowie durch die Merkmale zur qualitativen Unterscheidung der PG-Bezüge zwischen Vorläufer-Interessen und Individuellen Interessen von VOGT und WIEDER (1999). Nicht-Interesse wird gemäß UPMEIER ZU BELZEN und VOGT (2001) mithilfe theoretischer Merkmale (wie z. B. Kognition, Emotion, Wertbezug) in zwei unterschiedliche Ausprägungsformen – Desinteresse und Abneigung – differenziert. Für die vorliegende Arbeit ergeben sich folgende Untersuchungsfragen: Wie entstehen Interessen und Nicht-Interessen und wie verlaufen qualitative Entwicklungen? Inwiefern werden die Interessen und Nicht-Interessen im Verlauf außerschulisch und schulisch beeinflusst? Für die Datenerhebung wurden im Rahmen der vorliegenden Studie „halbstandardisierte“ Interviewleitfäden entwickelt und mithilfe der Grundtechniken der qualitativen Inhaltsanalyse von MAYRING (2003) ausgewertet. Die Ergebnisse verdeutlichen, dass alle befragten Kinder spätestens ab dem Schuleintritt über mindestens ein gemäß der Theorie definiertes Individuelles Interesse verfügten, die bis auf eine Ausnahme im außerschulischen Bereich festgestellt wurden. Ausgelöst wurden die Interessen hauptsächlich durch die Eltern und Peers, wobei der Einfluss der Peers im Entwicklungsverlauf immer mehr an Bedeutung gewann. Mit zunehmendem Alter hatten die Kinder auch Nicht-Interessen, die vor allem durch Erlebnisse ausgelöst wurden. Zusätzlich wurde die Entwicklung der Interessen und Nicht-Interessen durch den Grad der Befriedigung der grundlegenden Bedürfnisse (basic needs gemäß DECI & RYAN 1993) nach Kompetenz, Autonomie und sozialer Eingebundenheit während der Person-Gegenstands-Auseinandersetzungen beeinflusst. Beispielsweise fehlte bei Kindern mit schulischen Nicht-Interessen häufig das Erleben von Kompetenz und Autonomie in der Schule. Um der Entstehung von Nicht-Interessen in der Schule vorbeugen zu können, sollte ein alltagsrelevanter, kognitiv und methodisch differenzierter Unterricht stattfinden, der möglichst allen Kindern ein individuelles, positives Kompetenz- und Autonomieerleben ermöglicht. Dann könnten zukünftig sogar vielleicht auch Interessen in der Schule angestoßen werden.

Learning achievements of farmers during the transition to market-oriented organic agriculture in rural Uganda

Organic agriculture requires farmers with the ability to develop profitable agro-enterprises on their own. By drawing on four years of experiences with the Enabling Rural Innovation approach in Uganda, we outline how smallholder farmers transition to organic agriculture and, at the same time, increase their entrepreneurial skills and competences through learning. In order to document this learning we operationalised the Kirkpatrick learning evaluation model, which subsequently informed the collection of qualitative data in two study sites. Our analysis suggests that the Enabling Rural Innovation approach helps farmers to develop essential capabilities for identifying organic markets and new organic commodities, for testing these organic commodities under varying organic farm management scenarios, and for negotiating contracts with organic traders. We also observed several obstacles that confront farmers’ transition to organic agriculture when using the Enabling Rural Innovation approach. These include the long duration of agronomic experimentation and seed multiplication, expensive organic certification procedures and the absence of adequate mechanism for farmers to access crop finance services. Despite prevailing obstacles we conclude that the Enabling Rural Innovation approach provides a starting point for farmers to develop entrepreneurial competences and profitable agro-enterprises on their own.

Local food security and principle of organic farming (from farm to fork) in context of food culture in Indonesia: Minangkabau's case study

The basic idea behind improving local food security consists of two paths; first, accessibility (price, stock) and second, availability (quantity and biodiversity); both are perquisites to the provision of nutrients and a continuous food supply with locally available resources. The objectives of this thesis are to investigate if indigenous knowledge still plays an important role in traditional farming in the Minangkabau`s culture, thus supporting local food security. If the indigenous knowledge still plays a role in food culture in the Minangkabau`s culture which is linked to the matrilineal role and leads to a sound nutrition. Further, it should be tested if marantau influences traditional farming and food culture in Minangkabau`s, and if the local government plays a role in changing of traditional farming systems and food culture. Furthermore this thesis wants to prove if education and gender are playing a role in changing traditional farming system and food culture, and if the mass media affects traditional farming systems and food culture for the Minangkabau. The study was completed at four locations in West Sumatera; Nagari Ulakan (NU) (coastal area), Nagari Aia Batumbuak (NAB) (hilly area), Nagari Padang Laweh Malalo (NPLM) (lake area), Nagari Pandai Sikek (NPS) (hilly area). The rainfall ranged from 1400- 4800 mm annually with fertile soils. Data was collected by using PRA (Participatory Rural Appraisal) to investigate indigenous knowledge (IK) and its interactions, which is also combining with in depth-interview, life history, a survey using semi-structured-questionnaire, pictures, mapping, and expert interview. The data was collected from June - September 2009 and June 2010. The materials are; map of area, list of names, questionnaires, voices recorder, note book, and digital camera. The sampling method was snowball sampling which resulted in the qualitative and quantitative data taken. For qualitative data, ethnography and life history was used. For quantitative, a statistical survey with a semi-structured questionnaire was used. 50 respondents per each site participated voluntarily. Data was analyzed by performing MAXQDA 10, and F4 audio analysis software (created and developed by Philip-University Marburg). The data is clustered based on causality. The results show that; the role of IK on TFS (traditional farming system) shown on NPLM which has higher food crop biodiversity in comparison to the other three places even though it has relatively similar temperature and rainfall. This high food crop biodiversity is due to the awareness of local people who realized that they lived in unfavourable climate and topography; therefore they are more prepared for any changes that may occur. Carbohydrate intake is 100 % through rice even though they are growing different staple crops. Whereas most of the people said in the interviews that not eating rice is like not really eating for them. In addition to that, mothers still play an important role in kitchen activities. But when the agriculture income is low, mothers have to decide whether to change the meals or to feel insecure about their food supply. Marantau yields positive impact through the remittances it provides to invest on the farm. On the other hand, it results in fewer workers for agriculture, and therefore a negative impact on the transfer of IK. The investigation showed that the local government has a PTS (Padi Tanam Sabatang) programme which still does not guarantee that the farmers are getting sufficient revenue from their land. The low agricultural income leads to situation of potential food insecurity. It is evident that education is equal among men and women, but in some cases women tend to leave school earlier because of arranged marriages or the distances of school from their homes. Men predominantly work in agriculture and fishing, while women work in the kitchen. In NAB, even though women work on farmland they earn less then men. Weaving (NPS) and kitchen activity is recognized as women’s work, which also supports the household income. Mass media is not yielding any changes in TFS and food culture in these days. The traditional farming system has changed because of intensive agricultural extension which has introduced new methods of agriculture for the last three decades (since the 1980’s). There is no evidence that they want to change any of their food habits because of the mass media despite the lapau activity which allows them to get more food choices, instead preparing traditional meal at home. The recommendations of this thesis are: 1) The empowerment of farmers. It is regarding the self sufficient supply of manure, cooperative seed, and sustainable farm management. Farmers should know – where are they in their state of knowledge – so they can use their local wisdom and still collaborate with new sources of knowledge. Farmers should learn the prognosis of supply and demand next prior to harvest. There is a need for farm management guidelines; that can be adopted from both their local wisdom and modern knowledge. 2) Increase of non-agricultural income Increasing the non-agricultural income is strongly recommended. The remittances can be invested on non-agricultural jobs. 3) The empowerment of the mother. The mother plays an important role in farm to fork activities; the mother can be an initiator and promoter of cultivating spices in the backyard. Improvement of nutritional knowledge through information and informal public education can be done through arisan ibu-ibu and lapau activity. The challenges to apply these recommendations are: 1) The gap between institutions and organizations of local governments. There is more than one institution involved in food security policy. 2) Training and facilities for field extension agriculture (FEA) is needed because the rapid change of interaction between local government and farmer’s dependent on this agency.

Adaptive Real-time Anomaly-based Intrusion Detection using Data Mining and Machine Learning Techniques

Die zunehmende Vernetzung der Informations- und Kommunikationssysteme führt zu einer weiteren Erhöhung der Komplexität und damit auch zu einer weiteren Zunahme von Sicherheitslücken. Klassische Schutzmechanismen wie Firewall-Systeme und Anti-Malware-Lösungen bieten schon lange keinen Schutz mehr vor Eindringversuchen in IT-Infrastrukturen. Als ein sehr wirkungsvolles Instrument zum Schutz gegenüber Cyber-Attacken haben sich hierbei die Intrusion Detection Systeme (IDS) etabliert. Solche Systeme sammeln und analysieren Informationen von Netzwerkkomponenten und Rechnern, um ungewöhnliches Verhalten und Sicherheitsverletzungen automatisiert festzustellen. Während signatur-basierte Ansätze nur bereits bekannte Angriffsmuster detektieren können, sind anomalie-basierte IDS auch in der Lage, neue bisher unbekannte Angriffe (Zero-Day-Attacks) frühzeitig zu erkennen. Das Kernproblem von Intrusion Detection Systeme besteht jedoch in der optimalen Verarbeitung der gewaltigen Netzdaten und der Entwicklung eines in Echtzeit arbeitenden adaptiven Erkennungsmodells. Um diese Herausforderungen lösen zu können, stellt diese Dissertation ein Framework bereit, das aus zwei Hauptteilen besteht. Der erste Teil, OptiFilter genannt, verwendet ein dynamisches "Queuing Concept", um die zahlreich anfallenden Netzdaten weiter zu verarbeiten, baut fortlaufend Netzverbindungen auf, und exportiert strukturierte Input-Daten für das IDS. Den zweiten Teil stellt ein adaptiver Klassifikator dar, der ein Klassifikator-Modell basierend auf "Enhanced Growing Hierarchical Self Organizing Map" (EGHSOM), ein Modell für Netzwerk Normalzustand (NNB) und ein "Update Model" umfasst. In dem OptiFilter werden Tcpdump und SNMP traps benutzt, um die Netzwerkpakete und Hostereignisse fortlaufend zu aggregieren. Diese aggregierten Netzwerkpackete und Hostereignisse werden weiter analysiert und in Verbindungsvektoren umgewandelt. Zur Verbesserung der Erkennungsrate des adaptiven Klassifikators wird das künstliche neuronale Netz GHSOM intensiv untersucht und wesentlich weiterentwickelt. In dieser Dissertation werden unterschiedliche Ansätze vorgeschlagen und diskutiert. So wird eine classification-confidence margin threshold definiert, um die unbekannten bösartigen Verbindungen aufzudecken, die Stabilität der Wachstumstopologie durch neuartige Ansätze für die Initialisierung der Gewichtvektoren und durch die Stärkung der Winner Neuronen erhöht, und ein selbst-adaptives Verfahren eingeführt, um das Modell ständig aktualisieren zu können. Darüber hinaus besteht die Hauptaufgabe des NNB-Modells in der weiteren Untersuchung der erkannten unbekannten Verbindungen von der EGHSOM und der Überprüfung, ob sie normal sind. Jedoch, ändern sich die Netzverkehrsdaten wegen des Concept drif Phänomens ständig, was in Echtzeit zur Erzeugung nicht stationärer Netzdaten führt. Dieses Phänomen wird von dem Update-Modell besser kontrolliert. Das EGHSOM-Modell kann die neuen Anomalien effektiv erkennen und das NNB-Model passt die Änderungen in Netzdaten optimal an. Bei den experimentellen Untersuchungen hat das Framework erfolgversprechende Ergebnisse gezeigt. Im ersten Experiment wurde das Framework in Offline-Betriebsmodus evaluiert. Der OptiFilter wurde mit offline-, synthetischen- und realistischen Daten ausgewertet. Der adaptive Klassifikator wurde mit dem 10-Fold Cross Validation Verfahren evaluiert, um dessen Genauigkeit abzuschätzen. Im zweiten Experiment wurde das Framework auf einer 1 bis 10 GB Netzwerkstrecke installiert und im Online-Betriebsmodus in Echtzeit ausgewertet. Der OptiFilter hat erfolgreich die gewaltige Menge von Netzdaten in die strukturierten Verbindungsvektoren umgewandelt und der adaptive Klassifikator hat sie präzise klassifiziert. Die Vergleichsstudie zwischen dem entwickelten Framework und anderen bekannten IDS-Ansätzen zeigt, dass der vorgeschlagene IDSFramework alle anderen Ansätze übertrifft. Dies lässt sich auf folgende Kernpunkte zurückführen: Bearbeitung der gesammelten Netzdaten, Erreichung der besten Performanz (wie die Gesamtgenauigkeit), Detektieren unbekannter Verbindungen und Entwicklung des in Echtzeit arbeitenden Erkennungsmodells von Eindringversuchen.

Compositional Data in Biomedical Research

Modern methods of compositional data analysis are not well known in biomedical research. Moreover, there appear to be few mathematical and statistical researchers working on compositional biomedical problems. Like the earth and environmental sciences, biomedicine has many problems in which the relevant scienti c information is encoded in the relative abundance of key species or categories. I introduce three problems in cancer research in which analysis of compositions plays an important role. The problems involve 1) the classi cation of serum proteomic pro les for early detection of lung cancer, 2) inference of the relative amounts of di erent tissue types in a diagnostic tumor biopsy, and 3) the subcellular localization of the BRCA1 protein, and it's role in breast cancer patient prognosis. For each of these problems I outline a partial solution. However, none of these problems is \solved". I attempt to identify areas in which additional statistical development is needed with the hope of encouraging more compositional data analysts to become involved in biomedical research

Modelling structural zeros in compositional data

This analysis was stimulated by the real data analysis problem of household expenditure data. The full dataset contains expenditure data for a sample of 1224 households. The expenditure is broken down at 2 hierarchical levels: 9 major levels (e.g. housing, food, utilities etc.) and 92 minor levels. There are also 5 factors and 5 covariates at the household level. Not surprisingly, there are a small number of zeros at the major level, but many zeros at the minor level. The question is how best to model the zeros. Clearly, models that try to add a small amount to the zero terms are not appropriate in general as at least some of the zeros are clearly structural, e.g. alcohol/tobacco for households that are teetotal. The key question then is how to build suitable conditional models. For example, is the sub-composition of spending excluding alcohol/tobacco similar for teetotal and non-teetotal households? In other words, we are looking for sub-compositional independence. Also, what determines whether a household is teetotal? Can we assume that it is independent of the composition? In general, whether teetotal will clearly depend on the household level variables, so we need to be able to model this dependence. The other tricky question is that with zeros on more than one component, we need to be able to model dependence and independence of zeros on the different components. Lastly, while some zeros are structural, others may not be, for example, for expenditure on durables, it may be chance as to whether a particular household spends money on durables within the sample period. This would clearly be distinguishable if we had longitudinal data, but may still be distinguishable by looking at the distribution, on the assumption that random zeros will usually be for situations where any non-zero expenditure is not small. While this analysis is based on around economic data, the ideas carry over to many other situations, including geological data, where minerals may be missing for structural reasons (similar to alcohol), or missing because they occur only in random regions which may be missed in a sample (similar to the durables)

Markov chain montecarlo method applied to rounding zeros of compositional data: first approach

As stated in Aitchison (1986), a proper study of relative variation in a compositional data set should be based on logratios, and dealing with logratios excludes dealing with zeros. Nevertheless, it is clear that zero observations might be present in real data sets, either because the corresponding part is completely absent –essential zeros– or because it is below detection limit –rounded zeros. Because the second kind of zeros is usually understood as “a trace too small to measure”, it seems reasonable to replace them by a suitable small value, and this has been the traditional approach. As stated, e.g. by Tauber (1999) and by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000), the principal problem in compositional data analysis is related to rounded zeros. One should be careful to use a replacement strategy that does not seriously distort the general structure of the data. In particular, the covariance structure of the involved parts –and thus the metric properties– should be preserved, as otherwise further analysis on subpopulations could be misleading. Following this point of view, a non-parametric imputation method is introduced in Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000). This method is analyzed in depth by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2003) where it is shown that the theoretical drawbacks of the additive zero replacement method proposed in Aitchison (1986) can be overcome using a new multiplicative approach on the non-zero parts of a composition. The new approach has reasonable properties from a compositional point of view. In particular, it is “natural” in the sense that it recovers the “true” composition if replacement values are identical to the missing values, and it is coherent with the basic operations on the simplex. This coherence implies that the covariance structure of subcompositions with no zeros is preserved. As a generalization of the multiplicative replacement, in the same paper a substitution method for missing values on compositional data sets is introduced

A Factor analysis of hidrochemical composition of Llobregat river basin

Hydrogeological research usually includes some statistical studies devised to elucidate mean background state, characterise relationships among different hydrochemical parameters, and show the influence of human activities. These goals are achieved either by means of a statistical approach or by mixing models between end-members. Compositional data analysis has proved to be effective with the first approach, but there is no commonly accepted solution to the end-member problem in a compositional framework. We present here a possible solution based on factor analysis of compositions illustrated with a case study. We find two factors on the compositional bi-plot fitting two non-centered orthogonal axes to the most representative variables. Each one of these axes defines a subcomposition, grouping those variables that lay nearest to it. With each subcomposition a log-contrast is computed and rewritten as an equilibrium equation. These two factors can be interpreted as the isometric log-ratio coordinates (ilr) of three hidden components, that can be plotted in a ternary diagram. These hidden components might be interpreted as end-members. We have analysed 14 molarities in 31 sampling stations all along the Llobregat River and its tributaries, with a monthly measure during two years. We have obtained a bi-plot with a 57% of explained total variance, from which we have extracted two factors: factor G, reflecting geological background enhanced by potash mining; and factor A, essentially controlled by urban and/or farming wastewater. Graphical representation of these two factors allows us to identify three extreme samples, corresponding to pristine waters, potash mining influence and urban sewage influence. To confirm this, we have available analysis of diffused and widespread point sources identified in the area: springs, potash mining lixiviates, sewage, and fertilisers. Each one of these sources shows a clear link with one of the extreme samples, except fertilisers due to the heterogeneity of their composition. This approach is a useful tool to distinguish end-members, and characterise them, an issue generally difficult to solve. It is worth note that the end-member composition cannot be fully estimated but only characterised through log-ratio relationships among components. Moreover, the influence of each endmember in a given sample must be evaluated in relative terms of the other samples. These limitations are intrinsic to the relative nature of compositional data

CODAPACK3D. A new version of Compositional Data Package

The statistical analysis of compositional data should be treated using logratios of parts, which are difficult to use correctly in standard statistical packages. For this reason a freeware package, named CoDaPack was created. This software implements most of the basic statistical methods suitable for compositional data. In this paper we describe the new version of the package that now is called CoDaPack3D. It is developed in Visual Basic for applications (associated with Excel©), Visual Basic and Open GL, and it is oriented towards users with a minimum knowledge of computers with the aim at being simple and easy to use. This new version includes new graphical output in 2D and 3D. These outputs could be zoomed and, in 3D, rotated. Also a customization menu is included and outputs could be saved in jpeg format. Also this new version includes an interactive help and all dialog windows have been improved in order to facilitate its use. To use CoDaPack one has to access Excel© and introduce the data in a standard spreadsheet. These should be organized as a matrix where Excel© rows correspond to the observations and columns to the parts. The user executes macros that return numerical or graphical results. There are two kinds of numerical results: new variables and descriptive statistics, and both appear on the same sheet. Graphical output appears in independent windows. In the present version there are 8 menus, with a total of 38 submenus which, after some dialogue, directly call the corresponding macro. The dialogues ask the user to input variables and further parameters needed, as well as where to put these results. The web site http://ima.udg.es/CoDaPack contains this freeware package and only Microsoft Excel© under Microsoft Windows© is required to run the software. Kew words: Compositional data Analysis, Software

A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel density estimation techniques in the context of compositional data analysis. Indeed, they gave two options for the choice of the kernel to be used in the kernel estimator. One of these kernels is based on the use the alr transformation on the simplex SD jointly with the normal distribution on RD-1. However, these authors themselves recognized that this method has some deficiencies. A method for overcoming these dificulties based on recent developments for compositional data analysis and multivariate kernel estimation theory, combining the ilr transformation with the use of the normal density with a full bandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu- Figueras (2006). Here we present an extensive simulation study that compares both methods in practice, thus exploring the finite-sample behaviour of both estimators

Compositions in life science data

The aim of this talk is to convince the reader that there are a lot of interesting statistical problems in presentday life science data analysis which seem ultimately connected with compositional statistics. Key words: SAGE, cDNA microarrays, (1D-)NMR, virus quasispecies

Elemental analysis of New Zealand Nephrite Jade (pounamu) for forensic purposes

Pounamu (NZ jade), or nephrite, is a protected mineral in its natural form following the transfer of ownership back to Ngai Tahu under the Ngai Tahu (Pounamu Vesting) Act 1997. Any theft of nephrite is prosecutable under the Crimes Act 1961. Scientific evidence is essential in cases where origin is disputed. A robust method for discrimination of this material through the use of elemental analysis and compositional data analysis is required. Initial studies have characterised the variability within a given nephrite source. This has included investigation of both in situ outcrops and alluvial material. Methods for the discrimination of two geographically close nephrite sources are being developed. Key Words: forensic, jade, nephrite, laser ablation, inductively coupled plasma mass spectrometry, multivariate analysis, elemental analysis, compositional data analysis

Coherent forecasting of multiple-decrement life tables: a test using Japanese cause of death data

Planners in public and private institutions would like coherent forecasts of the components of age-specic mortality, such as causes of death. This has been di cult to achieve because the relative values of the forecast components often fail to behave in a way that is coherent with historical experience. In addition, when the group forecasts are combined the result is often incompatible with an all-groups forecast. It has been shown that cause-specic mortality forecasts are pessimistic when compared with all-cause forecasts (Wilmoth, 1995). This paper abandons the conventional approach of using log mortality rates and forecasts the density of deaths in the life table. Since these values obey a unit sum constraint for both conventional single-decrement life tables (only one absorbing state) and multiple-decrement tables (more than one absorbing state), they are intrinsically relative rather than absolute values across decrements as well as ages. Using the methods of Compositional Data Analysis pioneered by Aitchison (1986), death densities are transformed into the real space so that the full range of multivariate statistics can be applied, then back-transformed to positive values so that the unit sum constraint is honoured. The structure of the best-known, single-decrement mortality-rate forecasting model, devised by Lee and Carter (1992), is expressed in compositional form and the results from the two models are compared. The compositional model is extended to a multiple-decrement form and used to forecast mortality by cause of death for Japan

CODAMAT: a modern analogue techinque for compositional data

The quantitative estimation of Sea Surface Temperatures from fossils assemblages is a fundamental issue in palaeoclimatic and paleooceanographic investigations. The Modern Analogue Technique, a widely adopted method based on direct comparison of fossil assemblages with modern coretop samples, was revised with the aim of conforming it to compositional data analysis. The new CODAMAT method was developed by adopting the Aitchison metric as distance measure. Modern coretop datasets are characterised by a large amount of zeros. The zero replacement was carried out by adopting a Bayesian approach to the zero replacement, based on a posterior estimation of the parameter of the multinomial distribution. The number of modern analogues from which reconstructing the SST was determined by means of a multiple approach by considering the Proxies correlation matrix, Standardized Residual Sum of Squares and Mean Squared Distance. This new CODAMAT method was applied to the planktonic foraminiferal assemblages of a core recovered in the Tyrrhenian Sea. Kew words: Modern analogues, Aitchison distance, Proxies correlation matrix, Standardized Residual Sum of Squares