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

Vital Statistics of Iowa, 2005

This publication is an historical recording of the most requested statistics on vital events and is a source of information that can be used in further analysis.

Vital Statistics of Iowa, 2004

This publication is an historical recording of the most requested statistics on vital events and is a source of information that can be used in further analysis.

Vital Statistics of Iowa in Brief, 2005

This publication is an historical recording of the most requested statistics on vital events and is a source of information that can be used in further analysis.

Resolució de problemes i mètode de raonament en l'educació matemàtica

Des del principi dels temps històrics, la Matemàtica s'ha generat en totes les civilitzacions sobre la base de la resolució de problemes pràctics.Tanmateix, a partir del període grec la Història ens mostra la necessitat de fer un pas més endavant: l'evolució històrica de la Matemàtica situa els mètodes de raonament com a eix central de la recerca en Matemàtica. A partir d'una ullada als objectius i mètodes de treball d'alguns autors cabdals en la Història dels conceptes matemàtics postulem l'aprenentatge de les formes de raonament matemàtic com l'objectiu central de l'educació matemàtica, i la resolució de problemes com el mitjà més eficient per a coronar aquest objectiu.English version.From the beginning of the historical times, mathematics has been generated in all the civilizations on the base of the resolution of practical problems. Nevertheless, from the greek period History shows us the necessity to take one more step: the historical evolution of mathematics locates the methods of reasoning as the central axis of the research in mathematics. Glancing over the objectives and methods of work used bysome fundamental authors in the History of the mathematical concepts we postulated the learning of the forms of mathematical reasoning like the central objective of the mathematical education, and the resolution of problems as the most efficient way to carry out this objective.

A subsampling approach to estimating the distribution of diversing statistics with application to assessing financial market risks

In this paper we propose a subsampling estimator for the distribution ofstatistics diverging at either known rates when the underlying timeseries in strictly stationary abd strong mixing. Based on our results weprovide a detailed discussion how to estimate extreme order statisticswith dependent data and present two applications to assessing financialmarket risk. Our method performs well in estimating Value at Risk andprovides a superior alternative to Hill's estimator in operationalizingSafety First portofolio selection.

The impact of "early" nineteenth-century globalization on foreign trade in the Southern Cone: A study of British trade statistics

This paper deals with the impact of "early" nineteenth-century globalization (c.1815-1860) on foreign trade in the Southern Cone (SC). Most of the evidence is drawn from bilateral trades between Britain and the SC, at a time when Britain was the main commercial partner of the new republics. The main conclusion drawn is that early globalization had a positive impact on foreign trade in the SC, and this was due to: improvements in the SC's terms of trade during this period; the SC's per capita consumption of textiles (the main manufacture traded on world markets at that time) increased substantially during this period, at a time when clothing was one of the main items of SC household budgets; British merchants brought with them capital, shipping, insurance, and also facilitated the formation of vast global networks, which further promoted the SC's exports to a wider range of outlets.

Combined analysis of grey matter voxel-based morphometry and white matter tract-based spatial statistics in late-life bipolar disorder.

Background: Previous magnetic resonance imaging (MRI) studies in young patients with bipolar disorder indicated the presence of grey matter concentration changes as well as microstructural alterations in white matter in various neocortical areas and the corpus callosum. Whether these structural changes are also present in elderly patients with bipolar disorder with long-lasting clinical evolution remains unclear. Methods: We performed a prospective MRI study of consecutive elderly, euthymic patients with bipolar disorder and healthy, elderly controls. We conducted a voxel-based morphometry (VBM) analysis and a tract-based spatial statistics (TBSS) analysis to assess fractional anisotropy and longitudinal, radial and mean diffusivity derived by diffusion tensor imaging (DTI). Results: We included 19 patients with bipolar disorder and 47 controls in our study. Fractional anisotropy was the most sensitive DTI marker and decreased significantly in the ventral part of the corpus callosum in patients with bipolar disorder. Longitudinal, radial and mean diffusivity showed no significant between-group differences. Grey matter concentration was reduced in patients with bipolar disorder in the right anterior insula, head of the caudate nucleus, nucleus accumbens, ventral putamen and frontal orbital cortex. Conversely, there was no grey matter concentration or fractional anisotropy increase in any brain region in patients with bipolar disorder compared with controls. Limitations: The major limitation of our study is the small number of patients with bipolar disorder. Conclusion: Our data document the concomitant presence of grey matter concentration decreases in the anterior limbic areas and the reduced fibre tract coherence in the corpus callosum of elderly patients with long-lasting bipolar disorder.

Vital Statistics of Iowa in Brief, 2006

This publication is an historical recording of the most requested statistics on vital events and is a source of information that can be used in further analysis.

Statistics in archaeology: New directions

Connections between Statistics and Archaeology have always appeared veryfruitful. The objective of this paper is to offer an outlook of somestatistical techniques that are being developed in the most recentyears and that can be of interest for archaeologists in the short run.

Geographical deviations in foreign trade statistics: A study into European trade with Latin American Countries, 1925

We have analyzed the spatial accuracy of European foreign trade statistics compared to Latin American. We have also included USA s data because of the importance of this country in Latin American trade. We have developed a method for mapping discrepancies between exporters and importers, trying to isolate systematic spatial deviations. Although our results don t allow a unique explanation, they present some interesting clues to the distribution channels in the Latin American Continent as well as some spatial deviations for statistics in individual countries. Connecting our results with the literature specialized in the accuracy of foreign trade statistics; we can revisit Morgernstern (1963) as well as Federico and Tena (1991). Morgernstern had had a really pessimistic view on the reliability of this statistic source, but his main alert was focused on the trade balances, not in gross export or import values. Federico and Tena (1991) have demonstrated howaccuracy increases by aggregation, geographical and of product at the same time. But they still have a pessimistic view with relation to distribution questions, remarking that perhaps it will be more accurate to use import sources in this latest case. We have stated that the data set coming from foreign trade statistics for a sample in 1925, being it exporters or importers, it s a valuable tool for geography of trade patterns, although in some specific cases it needs some spatial adjustments.

On the accuracy of Latin American trade statistics: A nonparametric test for 1925

This paper proposes a nonparametric test in order to establish the level of accuracy of theforeign trade statistics of 17 Latin American countries when contrasted with the trade statistics of the main partners in 1925. The Wilcoxon Matched-Pairs Ranks test is used to determine whether the differences between the data registered by exporters and importers are meaningful, and if so, whether the differences are systematic in any direction. The paper tests for the reliability of the data registered for two homogeneous products, petroleum and coal, both in volume and value. The conclusion of the several exercises performed is that we cannot accept the existence of statistically significant differences between the data provided by the exporters and the registered by the importing countries in most cases. The qualitative historiography of Latin American describes its foreign trade statistics as mostly unusable. Our quantitative results contest this view.

Improving small area estimation by combining surveys: new perspectives in regional statistics

A national survey designed for estimating a specific population quantity is sometimes used for estimation of this quantity also for a small area, such as a province. Budget constraints do not allow a greater sample size for the small area, and so other means of improving estimation have to be devised. We investigate such methods and assess them by a Monte Carlo study. We explore how a complementary survey can be exploited in small area estimation. We use the context of the Spanish Labour Force Survey (EPA) and the Barometer in Spain for our study.

La lettera dellisole che ha trovato nuovamente el re di Spagna ([Reprod.]) / [Giuliano Dati]

Collection : Italian books before 1601 ; 103.1