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

The preceding two editions of CoDaWork included talks on the possible considerationof densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended theEuclidean structure of the simplex to a Hilbert space structure of the set of densitieswithin a bounded interval, and van den Boogaart (2005) generalized this to the setof densities bounded by an arbitrary reference density. From the many variations ofthe Hilbert structures available, we work with three cases. For bounded variables, abasis derived from Legendre polynomials is used. For variables with a lower bound, westandardize them with respect to an exponential distribution and express their densitiesas coordinates in a basis derived from Laguerre polynomials. Finally, for unboundedvariables, a normal distribution is used as reference, and coordinates are obtained withrespect to a Hermite-polynomials-based basis.To get the coordinates, several approaches can be considered. A numerical accuracyproblem occurs if one estimates the coordinates directly by using discretized scalarproducts. 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 thereference density. Finally, for the case of 2-order Hermite polinomials (normal reference)and 1-order Laguerre polinomials (exponential), one can also derive the coordinatesfrom their relationships to the classical mean and variance.Apart of these theoretical issues, this contribution focuses on the application of thistheory to two main problems in sedimentary geology: the comparison of several grainsize 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 orsediment, like their composition

Detection of ingested cocaine-filled packets: comparison of filtered back projection CT with adaptive statistical iterative reconstructed images

Purpose: To evaluate the diagnostic value and image quality of CT with filtered back projection (FBP) compared with adaptive statistical iterative reconstructed images (ASIR) in body stuffers with ingested cocaine-filled packets.Methods and Materials: Twenty-nine body stuffers (mean age 31.9 years, 3 women) suspected for ingestion of cocaine-filled packets underwent routine-dose 64-row multidetector CT with FBP (120kV, pitch 1.375, 100-300 mA and automatic tube current modulation (auto mA), rotation time 0.7sec, collimation 2.5mm), secondarily reconstructed with 30 % and 60 % ASIR. In 13 (44.83%) out of the body stuffers cocaine-filled packets were detected, confirmed by exact analysis of the faecal content including verification of the number (range 1-25). Three radiologists independently and blindly evaluated anonymous CT examinations (29 FBP-CT and 68 ASIR-CT) for the presence and number of cocaine-filled packets indicating observers' confidence, and graded them for diagnostic quality, image noise, and sharpness. Sensitivity, specificity, area under the receiver operating curve (ROC) Az and interobserver agreement between the 3 radiologists for FBP-CT and ASIR-CT were calculated.Results: The increase of the percentage of ASIR significantly diminished the objective image noise (p<0.001). Overall sensitivity and specificity for the detection of the cocaine-filled packets were 87.72% and 76.15%, respectively. The difference of ROC area Az between the different reconstruction techniques was significant (p= 0.0101), that is 0.938 for FBP-CT, 0.916 for 30 % ASIR-CT, and 0.894 for 60 % ASIR-CT.Conclusion: Despite the evident image noise reduction obtained by ASIR, the diagnostic value for detecting cocaine-filled packets decreases, depending on the applied ASIR percentage.

Statistical modeling on (α, +∞)

Observations in daily practice are sometimes registered as positive values larger then a given threshold α. The sample space is in this case the interval (α,+∞), α & 0, which can be structured as a real Euclidean space in different ways. This fact opens the door to alternative statistical models depending not only on the assumed distribution function, but also on the metric which is considered as appropriate, i.e. the way differences are measured, and thus variability

Statistical modeling on coordinates

This paper is a first draft of the principle of statistical modelling on coordinates. Several causes —which would be long to detail—have led to this situation close to the deadline for submitting papers to CODAWORK’03. The main of them is the fast development of the approach along thelast months, which let appear previous drafts as obsolete. The present paper contains the essential parts of the state of the art of this approach from my point of view. I would like to acknowledge many clarifying discussions with the group of people working in this field in Girona, Barcelona, Carrick Castle, Firenze, Berlin, G¨ottingen, and Freiberg. They have given a lot of suggestions and ideas. Nevertheless, there might be still errors or unclear aspects which are exclusively my fault. I hope this contribution serves as a basis for further discussions and new developments

A compositional statistical analysis of capital stock

Most of economic literature has presented its analysis under the assumption of homogeneous capital stock.However, capital composition differs across countries. What has been the pattern of capital compositionassociated with World economies? We make an exploratory statistical analysis based on compositional datatransformed by Aitchinson logratio transformations and we use tools for visualizing and measuring statisticalestimators of association among the components. The goal is to detect distinctive patterns in the composition.As initial findings could be cited that:1. Sectorial components behaved in a correlated way, building industries on one side and , in a lessclear view, equipment industries on the other.2. Full sample estimation shows a negative correlation between durable goods component andother buildings component and between transportation and building industries components.3. Countries with zeros in some components are mainly low income countries at the bottom of theincome category and behaved in a extreme way distorting main results observed in the fullsample.4. After removing these extreme cases, conclusions seem not very sensitive to the presence ofanother isolated cases

Modeling stochasticity and robustness in gene regulatory networks.

MOTIVATION: Understanding gene regulation in biological processes and modeling the robustness of underlying regulatory networks is an important problem that is currently being addressed by computational systems biologists. Lately, there has been a renewed interest in Boolean modeling techniques for gene regulatory networks (GRNs). However, due to their deterministic nature, it is often difficult to identify whether these modeling approaches are robust to the addition of stochastic noise that is widespread in gene regulatory processes. Stochasticity in Boolean models of GRNs has been addressed relatively sparingly in the past, mainly by flipping the expression of genes between different expression levels with a predefined probability. This stochasticity in nodes (SIN) model leads to over representation of noise in GRNs and hence non-correspondence with biological observations. RESULTS: In this article, we introduce the stochasticity in functions (SIF) model for simulating stochasticity in Boolean models of GRNs. By providing biological motivation behind the use of the SIF model and applying it to the T-helper and T-cell activation networks, we show that the SIF model provides more biologically robust results than the existing SIN model of stochasticity in GRNs. AVAILABILITY: Algorithms are made available under our Boolean modeling toolbox, GenYsis. The software binaries can be downloaded from http://si2.epfl.ch/ approximately garg/genysis.html.

Modern statistical models for forensic fingerprint examinations : a critical review

Over the last decade, the development of statistical models in support of forensic fingerprint identification has been the subject of increasing research attention, spurned on recently by commentators who claim that the scientific basis for fingerprint identification has not been adequately demonstrated. Such models are increasingly seen as useful tools in support of the fingerprint identification process within or in addition to the ACE-V framework. This paper provides a critical review of recent statistical models from both a practical and theoretical perspective. This includes analysis of models of two different methodologies: Probability of Random Correspondence (PRC) models that focus on calculating probabilities of the occurrence of fingerprint configurations for a given population, and Likelihood Ratio (LR) models which use analysis of corresponding features of fingerprints to derive a likelihood value representing the evidential weighting for a potential source.

Applications of stochastic analysis in finance and statistical inference

First: A continuous-time version of Kyle's model (Kyle 1985), known as the Back's model (Back 1992), of asset pricing with asymmetric information, is studied. A larger class of price processes and of noise traders' processes are studied. The price process, as in Kyle's model, is allowed to depend on the path of the market order. The process of the noise traders' is an inhomogeneous Lévy process. Solutions are found by the Hamilton-Jacobi-Bellman equations. With the insider being risk-neutral, the price pressure is constant, and there is no equilibirium in the presence of jumps. If the insider is risk-averse, there is no equilibirium in the presence of either jumps or drifts. Also, it is analised when the release time is unknown. A general relation is established between the problem of finding an equilibrium and of enlargement of filtrations. Random announcement time is random is also considered. In such a case the market is not fully efficient and there exists equilibrium if the sensitivity of prices with respect to the global demand is time decreasing according with the distribution of the random time. Second: Power variations. it is considered, the asymptotic behavior of the power variation of processes of the form _integral_0^t u(s-)dS(s), where S_ is an alpha-stable process with index of stability 0&alpha&2 and the integral is an Itô integral. Stable convergence of corresponding fluctuations is established. These results provide statistical tools to infer the process u from discrete observations. Third: A bond market is studied where short rates r(t) evolve as an integral of g(t-s)sigma(s) with respect to W(ds), where g and sigma are deterministic and W is the stochastic Wiener measure. Processes of this type are particular cases of ambit processes. These processes are in general not of the semimartingale kind.

Effective diagnosis of Alzheimer's disease by means of large margin-based methodology.

BACKGROUND Functional brain images such as Single-Photon Emission Computed Tomography (SPECT) and Positron Emission Tomography (PET) have been widely used to guide the clinicians in the Alzheimer's Disease (AD) diagnosis. However, the subjectivity involved in their evaluation has favoured the development of Computer Aided Diagnosis (CAD) Systems. METHODS It is proposed a novel combination of feature extraction techniques to improve the diagnosis of AD. Firstly, Regions of Interest (ROIs) are selected by means of a t-test carried out on 3D Normalised Mean Square Error (NMSE) features restricted to be located within a predefined brain activation mask. In order to address the small sample-size problem, the dimension of the feature space was further reduced by: Large Margin Nearest Neighbours using a rectangular matrix (LMNN-RECT), Principal Component Analysis (PCA) or Partial Least Squares (PLS) (the two latter also analysed with a LMNN transformation). Regarding the classifiers, kernel Support Vector Machines (SVMs) and LMNN using Euclidean, Mahalanobis and Energy-based metrics were compared. RESULTS Several experiments were conducted in order to evaluate the proposed LMNN-based feature extraction algorithms and its benefits as: i) linear transformation of the PLS or PCA reduced data, ii) feature reduction technique, and iii) classifier (with Euclidean, Mahalanobis or Energy-based methodology). The system was evaluated by means of k-fold cross-validation yielding accuracy, sensitivity and specificity values of 92.78%, 91.07% and 95.12% (for SPECT) and 90.67%, 88% and 93.33% (for PET), respectively, when a NMSE-PLS-LMNN feature extraction method was used in combination with a SVM classifier, thus outperforming recently reported baseline methods. CONCLUSIONS All the proposed methods turned out to be a valid solution for the presented problem. One of the advances is the robustness of the LMNN algorithm that not only provides higher separation rate between the classes but it also makes (in combination with NMSE and PLS) this rate variation more stable. In addition, their generalization ability is another advance since several experiments were performed on two image modalities (SPECT and PET).

Use of DNA profiles for investigation using a simulated national DNA database: Part II. Statistical and ethical considerations on familial searching.

Familial searching consists of searching for a full profile left at a crime scene in a National DNA Database (NDNAD). In this paper we are interested in the circumstance where no full match is returned, but a partial match is found between a database member's profile and the crime stain. Because close relatives share more of their DNA than unrelated persons, this partial match may indicate that the crime stain was left by a close relative of the person with whom the partial match was found. This approach has successfully solved important crimes in the UK and the USA. In a previous paper, a model, which takes into account substructure and siblings, was used to simulate a NDNAD. In this paper, we have used this model to test the usefulness of familial searching and offer guidelines for pre-assessment of the cases based on the likelihood ratio. Siblings of "persons" present in the simulated Swiss NDNAD were created. These profiles (N=10,000) were used as traces and were then compared to the whole database (N=100,000). The statistical results obtained show that the technique has great potential confirming the findings of previous studies. However, effectiveness of the technique is only one part of the story. Familial searching has juridical and ethical aspects that should not be ignored. In Switzerland for example, there are no specific guidelines to the legality or otherwise of familial searching. This article both presents statistical results, and addresses criminological and civil liberties aspects to take into account risks and benefits of familial searching.

JULIDE: a software tool for 3D reconstruction and statistical analysis of autoradiographic mouse brain sections.

In this article we introduce JULIDE, a software toolkit developed to perform the 3D reconstruction, intensity normalization, volume standardization by 3D image registration and voxel-wise statistical analysis of autoradiographs of mouse brain sections. This software tool has been developed in the open-source ITK software framework and is freely available under a GPL license. The article presents the complete image processing chain from raw data acquisition to 3D statistical group analysis. Results of the group comparison in the context of a study on spatial learning are shown as an illustration of the data that can be obtained with this tool.

Statistical discrimination of steroid profiles in doping control with support vector machines.

Due to their performance enhancing properties, use of anabolic steroids (e.g. testosterone, nandrolone, etc.) is banned in elite sports. Therefore, doping control laboratories accredited by the World Anti-Doping Agency (WADA) screen among others for these prohibited substances in urine. It is particularly challenging to detect misuse with naturally occurring anabolic steroids such as testosterone (T), which is a popular ergogenic agent in sports and society. To screen for misuse with these compounds, drug testing laboratories monitor the urinary concentrations of endogenous steroid metabolites and their ratios, which constitute the steroid profile and compare them with reference ranges to detect unnaturally high values. However, the interpretation of the steroid profile is difficult due to large inter-individual variances, various confounding factors and different endogenous steroids marketed that influence the steroid profile in various ways. A support vector machine (SVM) algorithm was developed to statistically evaluate urinary steroid profiles composed of an extended range of steroid profile metabolites. This model makes the interpretation of the analytical data in the quest for deviating steroid profiles feasible and shows its versatility towards different kinds of misused endogenous steroids. The SVM model outperforms the current biomarkers with respect to detection sensitivity and accuracy, particularly when it is coupled to individual data as stored in the Athlete Biological Passport.

Statistical Analysis of Eco-Toxicologic Data of Mammals from a Polluted Area

Several eco-toxicological studies have shown that insectivorous mammals, due to theirfeeding habits, easily accumulate high amounts of pollutants in relation to other mammal species. To assess the bio-accumulation levels of toxic metals and their in°uenceon essential metals, we quantified the concentration of 19 elements (Ca, K, Fe, B, P,S, Na, Al, Zn, Ba, Rb, Sr, Cu, Mn, Hg, Cd, Mo, Cr and Pb) in bones of 105 greaterwhite-toothed shrews (Crocidura russula) from a polluted (Ebro Delta) and a control(Medas Islands) area. Since chemical contents of a bio-indicator are mainly compositional data, conventional statistical analyses currently used in eco-toxicology can givemisleading results. Therefore, to improve the interpretation of the data obtained, weused statistical techniques for compositional data analysis to define groups of metalsand to evaluate the relationships between them, from an inter-population viewpoint.Hypothesis testing on the adequate balance-coordinates allow us to confirm intuitionbased hypothesis and some previous results. The main statistical goal was to test equalmeans of balance-coordinates for the two defined populations. After checking normality,one-way ANOVA or Mann-Whitney tests were carried out for the inter-group balances

MDCT Arthrography of the Hip: Value of the Adaptive Statistical Iterative Reconstruction Technique and Potential for Radiation Dose Reduction

Au cours des deux dernières décennies, la technique d'imagerie arthro-scanner a bénéficié de nombreux progrès technologiques et représente aujourd'hui une excellente alternative à l'imagerie par résonance magnétique (IRM) et / ou arthro-IRM dans l'évaluation des pathologies de la hanche. Cependant, elle reste limitée par l'exposition aux rayonnements ionisants importante. Les techniques de reconstruction itérative (IR) ont récemment été mis en oeuvre avec succès en imagerie ; la littérature montre que l'utilisation ces dernières contribue à réduire la dose d'environ 40 à 55%, comparativement aux protocoles courants utilisant la rétroprojection filtrée (FBP), en scanner de rachis. A notre connaissance, l'utilisation de techniques IR en arthro-scanner de hanche n'a pas été évaluée jusqu'à présent. Le but de notre étude était d'évaluer l'impact de la technique ASIR (GE Healthcare) sur la qualité de l'image objective et subjective en arthro-scanner de hanche, et d'évaluer son potentiel en terme de réduction de dose. Pour cela, trente sept patients examinés par arthro-scanner de hanche ont été randomisés en trois groupes : dose standard (CTDIvol = 38,4 mGy) et deux groupes de dose réduite (CTDIvol = 24,6 ou 15,4 mGy). Les images ont été reconstruites en rétroprojection filtrée (FBP) puis en appliquant différents pourcentages croissants d'ASIR (30, 50, 70 et 90%). Le bruit et le rapport contraste sur bruit (CNR) ont été mesurés. Deux radiologues spécialisés en imagerie musculo-squelettique ont évalué de manière indépendante la qualité de l'image au niveau de plusieurs structures anatomiques en utilisant une échelle de quatre grades. Ils ont également évalué les lésions labrales et du cartilage articulaire. Les résultats révèlent que le bruit augmente (p = 0,0009) et le CNR diminue (p = 0,001) de manière significative lorsque la dose diminue. A l'inverse, le bruit diminue (p = 0,0001) et le contraste sur bruit augmente (p < 0,003) de manière significative lorsque le pourcentage d'ASIR augmente ; on trouve également une augmentation significative des scores de la qualité de l'image pour le labrum, le cartilage, l'os sous-chondral, la qualité de l'image globale (au delà de ASIR 50%), ainsi que le bruit (p < 0,04), et une réduction significative pour l'os trabuculaire et les muscles (p < 0,03). Indépendamment du niveau de dose, il n'y a pas de différence significative pour la détection et la caractérisation des lésions labrales (n=24, p = 1) et des lésions cartilagineuses (n=40, p > 0,89) en fonction du pourcentage d'ASIR. Notre travail a permis de montrer que l'utilisation de plus de 50% d'ASIR permet de reduire de manière significative la dose d'irradiation reçue par le patient lors d'un arthro-scanner de hanche tout en maintenant une qualité d'image diagnostique comparable par rapport à un protocole de dose standard utilisant la rétroprojection filtrée.