Symmetric measures via moments

Algebraic tools in statistics have recently been receiving special attention and a number of interactions between algebraic geometry and computational statistics have been rapidly developing. This paper presents another such connection, namely, one between probabilistic models invariant under a finite group of (non-singular) linear transformations and polynomials invariant under the same group. Two specific aspects of the connection are discussed: generalization of the (uniqueness part of the multivariate) problem of moments and log-linear, or toric, modeling by expansion of invariant terms. A distribution of minuscule subimages extracted from a large database of natural images is analyzed to illustrate the above concepts.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ6144 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Predicting blunt cerebrovascular injury in pediatric trauma: Validation of the Utah Score

Risk factors for blunt cerebrovascular injury (BCVI) may differ between children and adults, suggesting that children at low risk for BCVI after trauma receive unnecessary computed tomography angiography (CTA) and high-dose radiation. We previously developed a score for predicting pediatric BCVI based on retrospective cohort analysis. Our objective is to externally validate this prediction score with a retrospective multi-institutional cohort. We included patients who underwent CTA for traumatic cranial injury at four pediatric Level I trauma centers. Each patient in the validation cohort was scored using the “Utah Score” and classified as high or low risk. Before analysis, we defined a misclassification rate <25% as validating the Utah Score. Six hundred forty-five patients (mean age 8.6 ± 5.4 years; 63.4% males) underwent screening for BCVI via CTA. The validation cohort was 411 patients from three sites compared with the training cohort of 234 patients. Twenty-two BCVIs (5.4%) were identified in the validation cohort. The Utah Score was significantly associated with BCVIs in the validation cohort (odds ratio 8.1 [3.3, 19.8], p < 0.001) and discriminated well in the validation cohort (area under the curve 72%). When the Utah Score was applied to the validation cohort, the sensitivity was 59%, specificity was 85%, positive predictive value was 18%, and negative predictive value was 97%. The Utah Score misclassified 16.6% of patients in the validation cohort. The Utah Score for predicting BCVI in pediatric trauma patients was validated with a low misclassification rate using a large, independent, multicenter cohort. Its implementation in the clinical setting may reduce the use of CTA in low-risk patients