Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible consideration of densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended the Euclidean structure of the simplex to a Hilbert space structure of the set of densities within a bounded interval, and van den Boogaart (2005) generalized this to the set of densities bounded by an arbitrary reference density. From the many variations of the Hilbert structures available, we work with three cases. For bounded variables, a basis derived from Legendre polynomials is used. For variables with a lower bound, we standardize them with respect to an exponential distribution and express their densities as coordinates in a basis derived from Laguerre polynomials. Finally, for unbounded variables, a normal distribution is used as reference, and coordinates are obtained with respect to a Hermite-polynomials-based basis. To get the coordinates, several approaches can be considered. A numerical accuracy problem occurs if one estimates the coordinates directly by using discretized scalar products. Thus we propose to use a weighted linear regression approach, where all k- order polynomials are used as predictand variables and weights are proportional to the reference density. Finally, for the case of 2-order Hermite polinomials (normal reference) and 1-order Laguerre polinomials (exponential), one can also derive the coordinates from their relationships to the classical mean and variance. Apart of these theoretical issues, this contribution focuses on the application of this theory to two main problems in sedimentary geology: the comparison of several grain size distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock or sediment, like their composition

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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