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

Multilevel multitrait-multimethod model: application to the measurement of egocentered social networks

Our goal in this paper is to assess reliability and validity of egocentered network data using multilevel analysis (Muthen, 1989, Hox, 1993) under the multitrait-multimethod approach. The confirmatory factor analysis model for multitrait-multimethod data (Werts & Linn, 1970; Andrews, 1984) is used for our analyses. In this study we reanalyse a part of data of another study (Kogovšek et al., 2002) done on a representative sample of the inhabitants of Ljubljana. The traits used in our article are the name interpreters. We consider egocentered network data as hierarchical; therefore a multilevel analysis is required. We use Muthen's partial maximum likelihood approach, called pseudobalanced solution (Muthen, 1989, 1990, 1994) which produces estimations close to maximum likelihood for large ego sample sizes (Hox & Mass, 2001). Several analyses will be done in order to compare this multilevel analysis to classic methods of analysis such as the ones made in Kogovšek et al. (2002), who analysed the data only at group (ego) level considering averages of all alters within the ego. We show that some of the results obtained by classic methods are biased and that multilevel analysis provides more detailed information that much enriches the interpretation of reliability and validity of hierarchical data. Within and between-ego reliabilities and validities and other related quality measures are defined, computed and interpreted

Selecting Scientific Papers for Publication via Citation Auctions

The scientific community has been suffering from peer review for decades. This process (also called refereeing) subjects an author's scientific work or ideas to the scrutiny of one or more experts in the field. Publishers use it to select and screen manuscript submissions, and funding agencies use it to award research funds. The goal is to get authors to meet their discipline's standards and thus achieve scientific objectivity. Publications and awards that haven't undergone peer review are often regarded with suspicion by scholars and professionals in many fields. However, peer review, although universally used, has many drawbacks. We propose replacing peer review with an auction-based approach: the better the submitted paper, the more scientific currency the author likely bid to have it published. If the bid correctly reflects the paper's quality, the author is rewarded in this new scientific currency; otherwise, the author loses this currency. We argue that citations are an appropriate currency for all scientists. We believe that citation auctions encourage scientists to better control their submissions' quality. It also inspire them to prepare more exciting talks for accepted papers and to invite discussion of their results at congresses and conferences and among their colleagues. In the long run, citation auctions could have the power to greatly improve scientific research

Citation auctions as a method to improve selection of scientific papers

This paper describes the basis of citation auctions as a new approach to selecting scientific papers for publication. Our main idea is to use an auction for selecting papers for publication through - differently from the state of the art - bids that consist of the number of citations that a scientist expects to receive if the paper is published. Hence, a citation auction is the selection process itself, and no reviewers are involved. The benefits of the proposed approach are two-fold. First, the cost of refereeing will be either totally eliminated or significantly reduced, because the process of citation auction does not need prior understanding of the paper's content to judge the quality of its contribution. Additionally, the method will not prejudge the content of the paper, so it will increase the openness of publications to new ideas. Second, scientists will be much more committed to the quality of their papers, paying close attention to distributing and explaining their papers in detail to maximize the number of citations that the paper receives. Sample analyses of the number of citations collected in papers published in years 1999-2004 for one journal, and in years 2003-2005 for a series of conferences (in a totally different discipline), via Google scholar, are provided. Finally, a simple simulation of an auction is given to outline the behaviour of the citation auction approach