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. Central notations 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 understood easily 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 weighted addition of the corresponding evidence. Likelihood based statistics for general exponential families turns out to have a particularly easy interpretation in terms of A2(P). Regular exponential families form finite dimensional linear subspaces of A2(P) and they correspond to finite dimensional subspaces 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 functions or likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Incongruence between test statistics and P values in medical papers

Given an observed test statistic and its degrees of freedom, one may compute the observed P value with most statistical packages. It is unknown to what extent test statistics and P values are congruent in published medical papers. Methods: We checked the congruence of statistical results reported in all the papers of volumes 409–412 of Nature (2001) and a random sample of 63 results from volumes 322–323 of BMJ (2001). We also tested whether the frequencies of the last digit of a sample of 610 test statistics deviated from a uniform distribution (i.e., equally probable digits).Results: 11.6% (21 of 181) and 11.1% (7 of 63) of the statistical results published in Nature and BMJ respectively during 2001 were incongruent, probably mostly due to rounding, transcription, or type-setting errors. At least one such error appeared in 38% and 25% of the papers of Nature and BMJ, respectively. In 12% of the cases, the significance level might change one or more orders of magnitude. The frequencies of the last digit of statistics deviated from the uniform distribution and suggested digit preference in rounding and reporting.Conclusions: this incongruence of test statistics and P values is another example that statistical practice is generally poor, even in the most renowned scientific journals, and that quality of papers should be more controlled and valued

Proceso penal de menores: especialidades derivadas del interés de los menores y opciones de política criminal

El presente trabajo se concibió con la vocación de devenir una aportación al estudio del proceso penal de menores. Por ello, originariamente, se planteó como un análisis de todas y cada una de las fases de dicho proceso. Sin embargo, rápidamente este objetivo se demostró inalcanzable por cuanto, de una primera aproximación a los preceptos de la norma, se aprecia que en la misma, se contiene «algo más» que algunas especialidades o especificidades con respecto a los procesos penales de adultos. Como premisa de partida, cabe considerar que el proceso diseñado por la L.O. 5/2000, al estar concebido exclusivamente para el enjuiciamiento de las conductas delictivas presuntamente cometidas por menores de edad, puede incardinarse en la categoría de los procesos especiales. Esta constatación, sin embargo, no era suficiente, a nuestro juicio, para justificar un proceso en el que aparecían figuras e instituciones procesales hasta el momento inéditas en el ordenamiento jurídico español. Por ello el planteamiento inicial al que se aludía fue sustancialmente modificado, sin que a la postre, ello haya supuesto una alteración sustancial del objetivo primigenio. El trabajo de investigación se inicia con un interrogante, que podría formularse como sigue: Aceptando que la edad es el elemento determinante de la existencia de una rama del derecho penal específicamente dedicada a los menores, ¿hasta qué punto dicho elemento condiciona la acción del legislador en el sentido de establecer un cuerpo normativo significativamente diferenciado del previsto para los adultos?