Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Centralnotations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform.In this way very elaborated aspects of mathematical statistics can be understoodeasily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating,combination of likelihood and robust M-estimation functions are simple additions/perturbations in A2(Pprior). Weighting observations corresponds to a weightedaddition of the corresponding evidence.Likelihood based statistics for general exponential families turns out to have aparticularly easy interpretation in terms of A2(P). Regular exponential families formfinite dimensional linear subspaces of A2(P) and they correspond to finite dimensionalsubspaces formed by their posterior in the dual information space A2(Pprior).The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P.The discussion of A2(P) valued random variables, such as estimation functionsor likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Some last thoughts on compositional data analysis

One of the disadvantages of old age is that there is more past than future: this,however, may be turned into an advantage if the wealth of experience and, hopefully,wisdom gained in the past can be reflected upon and throw some light on possiblefuture trends. To an extent, then, this talk is necessarily personal, certainly nostalgic,but also self critical and inquisitive about our understanding of the discipline ofstatistics. A number of almost philosophical themes will run through the talk: searchfor appropriate modelling in relation to the real problem envisaged, emphasis onsensible balances between simplicity and complexity, the relative roles of theory andpractice, the nature of communication of inferential ideas to the statistical layman, theinter-related roles of teaching, consultation and research. A list of keywords might be:identification of sample space and its mathematical structure, choices betweentransform and stay, the role of parametric modelling, the role of a sample spacemetric, the underused hypothesis lattice, the nature of compositional change,particularly in relation to the modelling of processes. While the main theme will berelevance to compositional data analysis we shall point to substantial implications forgeneral multivariate analysis arising from experience of the development ofcompositional data analysis…

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 researchersworking on compositional biomedical problems. Like the earth and environmental sciences,biomedicine has many problems in which the relevant scienti c information isencoded in the relative abundance of key species or categories. I introduce three problemsin cancer research in which analysis of compositions plays an important role. Theproblems involve 1) the classi cation of serum proteomic pro les for early detection oflung cancer, 2) inference of the relative amounts of di erent tissue types in a diagnostictumor biopsy, and 3) the subcellular localization of the BRCA1 protein, and it'srole in breast cancer patient prognosis. For each of these problems I outline a partialsolution. However, none of these problems is \solved". I attempt to identify areas inwhich additional statistical development is needed with the hope of encouraging morecompositional data analysts to become involved in biomedical research

Compositions in life science data

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

Experimental design on the simplex

Optimum experimental designs depend on the design criterion, the model andthe design region. The talk will consider the design of experiments for regressionmodels in which there is a single response with the explanatory variables lying ina simplex. One example is experiments on various compositions of glass such asthose considered by Martin, Bursnall, and Stillman (2001).Because of the highly symmetric nature of the simplex, the class of models thatare of interest, typically Scheff´e polynomials (Scheff´e 1958) are rather differentfrom those of standard regression analysis. The optimum designs are also ratherdifferent, inheriting a high degree of symmetry from the models.In the talk I will hope to discuss a variety of modes for such experiments. ThenI will discuss constrained mixture experiments, when not all the simplex is availablefor experimentation. Other important aspects include mixture experimentswith extra non-mixture factors and the blocking of mixture experiments.Much of the material is in Chapter 16 of Atkinson, Donev, and Tobias (2007).If time and my research allows, I would hope to finish with a few comments ondesign when the responses, rather than the explanatory variables, lie in a simplex.ReferencesAtkinson, A. C., A. N. Donev, and R. D. Tobias (2007). Optimum ExperimentalDesigns, with SAS. Oxford: Oxford University Press.Martin, R. J., M. C. Bursnall, and E. C. Stillman (2001). Further results onoptimal and efficient designs for constrained mixture experiments. In A. C.Atkinson, B. Bogacka, and A. Zhigljavsky (Eds.), Optimal Design 2000,pp. 225–239. Dordrecht: Kluwer.Scheff´e, H. (1958). Experiments with mixtures. Journal of the Royal StatisticalSociety, Ser. B 20, 344–360.1

Art i part :la figura del/la professional de l'educació social en processos de desenvolupament cultural comunitari

Anàlisi de la figura de l'educador/a social en processos de desenvolupament comunitari a partir d'experiències diverses a Catalunya

Les biblioteques populars de la Mancomunitat: un projecte polític i un projecte bibliotecari

Les biblioteques populars o públiques que impulsà la Mancomunitat de Catalunya, creades a imatge i semblança de les pioneres biblioteques anglosaxones, foren un modelinnovador dins del panorama bibliotecari d'Espanya. Al seu èxit contribuí tant la figura d'Eugeni d'Ors, responsable del projecte inicial que establí com havien de ser les biblioteques i quina havia de ser la formació del personal a l'Escola de Bibliotecàries, com la de Jordi Rubió, director de la Biblioteca de Catalunya, que el succeí com a director de la xarxa de biblioteques que implantà definitivament un sistema bibliotecari a Catalunya.

Gombrich i la història cultural

The recent death of the art historian motives this approach to his works. Gombrich studies connected art with many other fields of human knowledge. In this article the author focused the Gombrich conception of the relationship between art and cultural history.

La història cultural i l'intel·lectual professional. Una visió personal

The author exposes the main research lines in the history of local culture. He briefly considers the main lines in cultural contemporary history investigation. The author studies the introduction and development of cultural history based on the concept of intellectual professional in Catalan historiography at a moment when economical and social research were preferred by a large part of local historians.

Els antecedents de la crisi de l'estat liberal a Espanya i a Itàlia: una visió comparada (1875-1895)

The author proposes a comparative study in the frame of a macroarea formed by the south European countries. He points out the characteristics and difficulties of the liberal state establishment in the Mediterranean countries. At the same time he underlines the new importance of the intellectuals roll as one of the main consequences of that crisis.

Literatura i política catalanista: Josep Maria Valls i Vicens als inicis de la Restauració

Joseph Maria Valls i Vicens was an important Catalan intellectual who had an important performance in literature, politics , sociology, pedagogy and several cultural initiatives. The author focalizes the study of the young writer's thought as a common character of a wide sector of intellectuals that had developed an important activity in local politics and culture all through the period.

Joan Estelrich i l'Expansió Catalana. La traducció de Prat de la Riba i Cambó en la Itàlia feixista

El text presenta la important tasca de Joan Estelrich en projectar el problema nacional català a l'estranger entre els anys 1919-1926. Se subratlla l'empenta que dóna a la traducció d'obres de la cultura catalana en altres idiomes i especialment a l'italià. En aquest marc s'expliquen les relacions entre aquest intel·lectual català i l'italià Cesare Giardini. Seguint l'epistolari inèdit entre els dos, el text explica els rerefons en què es va fer la traducció de dos obres significatives com La nacionalitat catalana d'Enric Prat de la Riba i Entorn del feixisme italià de Francesc Cambó. En aquest marc, el text reflexiona i critica les interpretacions historiogràfiques que han llegit l'experiència de Cambó com la d'un autor proper al feixisme.