Alternative ways to estimate change points in multinomial sequences. An application to an authorship attribution problem

The statistical analysis of literary style is the part of stylometry that compares measurable characteristics in a text that are rarely controlled by the author, with those in other texts. When the goal is to settle authorship questions, these characteristics should relate to the author’s style and not to the genre, epoch or editor, and they should be such that their variation between authors is larger than the variation within comparable texts from the same author. For an overview of the literature on stylometry and some of the techniques involved, see for example Mosteller and Wallace (1964, 82), Herdan (1964), Morton (1978), Holmes (1985), Oakes (1998) or Lebart, Salem and Berry (1998). Tirant lo Blanc, a chivalry book, is the main work in catalan literature and it was hailed to be “the best book of its kind in the world” by Cervantes in Don Quixote. Considered by writters like Vargas Llosa or Damaso Alonso to be the first modern novel in Europe, it has been translated several times into Spanish, Italian and French, with modern English translations by Rosenthal (1996) and La Fontaine (1993). The main body of this book was written between 1460 and 1465, but it was not printed until 1490. There is an intense and long lasting debate around its authorship sprouting from its first edition, where its introduction states that the whole book is the work of Martorell (1413?-1468), while at the end it is stated that the last one fourth of the book is by Galba (?-1490), after the death of Martorell. Some of the authors that support the theory of single authorship are Riquer (1990), Chiner (1993) and Badia (1993), while some of those supporting the double authorship are Riquer (1947), Coromines (1956) and Ferrando (1995). For an overview of this debate, see Riquer (1990). Neither of the two candidate authors left any text comparable to the one under study, and therefore discriminant analysis can not be used to help classify chapters by author. By using sample texts encompassing about ten percent of the book, and looking at word length and at the use of 44 conjunctions, prepositions and articles, Ginebra and Cabos (1998) detect heterogeneities that might indicate the existence of two authors. By analyzing the diversity of the vocabulary, Riba and Ginebra (2000) estimates that stylistic boundary to be near chapter 383. Following the lead of the extensive literature, this paper looks into word length, the use of the most frequent words and into the use of vowels in each chapter of the book. Given that the features selected are categorical, that leads to three contingency tables of ordered rows and therefore to three sequences of multinomial observations. Section 2 explores these sequences graphically, observing a clear shift in their distribution. Section 3 describes the problem of the estimation of a suden change-point in those sequences, in the following sections we propose various ways to estimate change-points in multinomial sequences; the method in section 4 involves fitting models for polytomous data, the one in Section 5 fits gamma models onto the sequence of Chi-square distances between each row profiles and the average profile, the one in Section 6 fits models onto the sequence of values taken by the first component of the correspondence analysis as well as onto sequences of other summary measures like the average word length. In Section 7 we fit models onto the marginal binomial sequences to identify the features that distinguish the chapters before and after that boundary. Most methods rely heavily on the use of generalized linear models

Interactions between grain size and composition of sediments: two examples

Two contrasting case studies of sediment and detrital mineral composition are investigated in order to outline interactions between chemical composition and grain size. Modern glacial sediments exhibit a strong dependence of the two parameters due to the preferential enrichment of mafic minerals, especially biotite, in the fine-grained fractions. On the other hand, the composition of detrital heavy minerals (here: rutile) appears to be not systematically related to grain-size, but is strongly controlled by location, i.e. the petrology of the source rocks of detrital grains. This supports the use of rutile as a well-suited tracer mineral for provenance studies. The results further suggest that (i) interpretations derived from whole-rock sediment geochemistry should be flanked by grain-size observations, and (ii) a more sound statistical evaluation of these interactions require the development of new tailor-made statistical tools to deal with such so-called two-way compositions

Analysis of Pleistocene paleodrainage evolution in the Po Basin (Italy) by multivariate statistical techniques

In order to obtain a high-resolution Pleistocene stratigraphy, eleven continuously cored boreholes, 100 to 220m deep were drilled in the northern part of the Po Plain by Regione Lombardia in the last five years. Quantitative provenance analysis (QPA, Weltje and von Eynatten, 2004) of Pleistocene sands was carried out by using multivariate statistical analysis (principal component analysis, PCA, and similarity analysis) on an integrated data set, including high-resolution bulk petrography and heavy-mineral analyses on Pleistocene sands and of 250 major and minor modern rivers draining the southern flank of the Alps from West to East (Garzanti et al, 2004; 2006). Prior to the onset of major Alpine glaciations, metamorphic and quartzofeldspathic detritus from the Western and Central Alps was carried from the axial belt to the Po basin longitudinally parallel to the SouthAlpine belt by a trunk river (Vezzoli and Garzanti, 2008). This scenario rapidly changed during the marine isotope stage 22 (0.87 Ma), with the onset of the first major Pleistocene glaciation in the Alps (Muttoni et al, 2003). PCA and similarity analysis from core samples show that the longitudinal trunk river at this time was shifted southward by the rapid southward and westward progradation of transverse alluvial river systems fed from the Central and Southern Alps. Sediments were transported southward by braided river systems as well as glacial sediments transported by Alpine valley glaciers invaded the alluvial plain. Kew words: Detrital modes; Modern sands; Provenance; Principal Components Analysis; Similarity, Canberra Distance; palaeodrainage

Filogeografia de la truita comuna (Salmo trutta) basada en la diversitat molecular del DNA mitocondrial

Les anàlisis realitzades en cent deu poblacions de truita comuna (Salmo trutta) que abarquen el seu rang natural de distribució indiquen que el patró filogenètic es relaciona amb les tres grans vessants on es troba distribuïda l'espècie: ponto-càspia, atlàntica i mediterrània. Aquesta diferenciació estaria associada a l'aïllament de les vessants durant el Quaternari. L'origen de l'espècie es relaciona amb la vessant ponto-càspia, d'acord amb els models biogeogràfics que postulen l'origen asiàtic de la ictiofauna europea. S'ha detectat també un segon nivell de divergència dins de cada vessant que dóna com a resultat l'existència de sis llinatges evolutius: Atlàntic i Duero a la vessant atlàntica, els llinatges Adriàtic, Mediterrani i Marmoratus als rius mediterranis, i el llinatge Danubi a la zona ponto-càspia. Les glaciacions del Pleistocè han modificat profundament el rang de distribució de la truita comuna, especialment a la vessant atlàntica, on s'han proposat quatre grans refugis glacials: a l'est de la capa de gel, a Europa central, a l'entorn del canal de la Mànega i a l'entorn del golf de Biscaia; tot i que només els tres primers haurien participat en la recolonització del nord d'Europa al final de l'última glaciació. El quart refugi, que inclou el sud de França i el Cantàbric hauria estat l'origen de l'expansió cap al sud durant el Pleistocè Superior d'un grup de poblacions distribuïdes actualment a la vessant atlàntica ibèrica, i també hauria servit de base per a l'expansió cap al nord d'altres grups de truita durant interglacials anteriors. A la vessant atlàntica de la peninsula Ibèrica, l'estructura poblacional es troba associada a la xarxa hidrogràfica i es determinen fins a cinc unitats poblacionals: les truites dels rius Cantàbrics, les del Miño, les del Duero, les del Tajo i les del Guadalquivir. Les poblacions del Guadalquivir pertanyerien a un grup d'influència mediterrània. Els marcadors d'al·lozims i de DNA mitocondrial es troben fortament correlacionats en aquesta vessant, on apunten cap als mateixos grups de poblacions. Per contra, els rius de la vessant mediterrània haurien estat colonitzats pels llinatges Adriàtic i Mediterrani i s'hauria produït una intensa intergradació secundària entre aquests llinatges durant els períodes glacials a partir de l'expansió de les poblacions retingudes a les capçaleres durant els interglacials. Els grups de hibridació, l'aïllament i la deriva en el període interglacial fa que els grups de poblacions identificats pels marcadors d'al·lozims i de DNA mitocondrial no coincideixin.