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We investigate the convergence rates of uniform bias-corrected confidence intervals for a smooth curve using local polynomial regression for both the interior and boundary region. We discuss the cases when the degree of the polynomial is odd and even. The uniform confidence intervals are based on the volume-of-tube formula modified for biased estimators. We empirically show that the proposed uniform confidence intervals attain, at least approximately, nominal coverage. Finally, we investigate the performance of the volume-of-tube based confidence intervals for independent non-Gaussian errors. [ABSTRACT FROM AUTHOR]

There is an apparent paradox that the likelihood ratio (LR) approach is an appropriate measure of the weight of evidence when forensic findings have to be evaluated in court, while it is typically not used by bloodstain pattern analysis (BPA) experts. This commentary evaluates how the scope and methods of BPA relate to several types of evaluative propositions and methods to which LRs are applicable. As a result of this evaluation, we show how specificities in scope (BPA being about activities rather than source identification), gaps in the underlying science base, and the reliance on a wide range of methods render the use of LRs in BPA more complex than in some other forensic disciplines. Three directions are identified for BPA research and training, which would facilitate and widen the use of LRs: research in the underlying physics; the development of a culture of data sharing; and the development of training material on the required statistical background. An example of how recent fluid dynamics research in BPA can lead to the use of LR is provided. We conclude that an LR framework is fully applicable to BPA, provided methodic efforts and significant developments occur along the three outlined directions., (© 2021 The Authors. Journal of Forensic Sciences published by Wiley Periodicals LLC on behalf of American Academy of Forensic Sciences.)

Cast-off spatter patterns exhibit linear trails of elliptical stains. These characteristic patterns occur by centrifugal forces that detach drops from a swinging object covered with blood or other liquid. This manuscript describes a method to reconstruct the motion, or swing, of the object. The method is based on stain inspection and Euclidean geometry. The reconstructed swing is represented as a three-dimensional region of statistical likelihood. The reconstruction uncertainty corresponds to the volume of the reconstructed region, which is specific to the uncertainties of the case at hand. Simple numerical examples show that the reconstruction method is able to reconstruct multiple swings that are either intersecting or adjacent to each other. The robustness, spatial convergence, computing time of the reconstruction method is characterized. For the purpose of this study, about 20 cast-off experiments are produced, with motion of the swinging object documented using video and/or accelerometers. The swings follow circular or arbitrary paths, and are either human- or machine-made. The reconstruction results are compared with the experimentally documented swings. Agreement between measured and reconstructed swings is very good, typically within less than 10 cm. The method used in this study is implemented as a numerical code written in an open source language, provided in an open access repository, for purposes of transparency and access., Competing Interests: Declaration of Competing Interest There are no conflicts of interest., (Copyright © 2020 Elsevier B.V. All rights reserved.)

The forensics discipline of bloodstain pattern analysis plays an important role in crime scene analysis and reconstruction. One reconstruction question is whether the blood has been spattered via gunshot or blunt impact such as beating or stabbing. This paper proposes an automated framework to classify bloodstain spatter patterns generated under controlled conditions into either gunshot or blunt impact classes. Classification is performed using machine learning. The study is performed with 94 blood spatter patterns which are available as public data sets, designs a set of features with possible relevance to classification, and uses the random forests method to rank the most useful features and perform classification. The study shows that classification accuracy decreases with the increasing distance between the target surface collecting the stains and the blood source. Based on the data set used in this study, the model achieves 99% accuracy in classifying spatter patterns at distances of 30 cm, 93% accuracy at distances of 60 cm, and 86% accuracy at distances of 120 cm. Results with 10 additional backspatter patterns also show that the presence of muzzle gases can reduce classification accuracy., (© 2020 American Academy of Forensic Sciences.)

This is a data set of blood spatter patterns scanned at high resolution, generated in controlled experiments. The spatter patterns were generated with a rifle or a handgun with varying ammunition. The resulting atomized blood droplets travelled opposite to the bullet direction, generating a gunshot backspatter on a poster board target sheet. Fresh blood with anticoagulants was used; its hematocrit and temperature were measured. The main parameters of the study were the bullet shape, size and speed, and the distance between the blood source and target sheet. Several other parameters were explored in a less systematic way. This new and original data set is suitable for training or research purposes in the forensic discipline of bloodstain pattern analysis.

This is a data set of 61 blood spatter patterns scanned at high resolution, generated by controlled impact events corresponding to forensic beating situations. The spatter patterns were realized with two test rigs, to vary the geometry and speed of the impact of a solid object on a blood source - a pool of blood. The resulting atomized blood droplets travelled a set distance towards a poster board sheet, creating a blood spatter. Fresh swine blood was used; its hematocrit and temperature were measured. Main parameters of the study were the impact velocity and the distance between blood source and target sheet, and several other parameters were explored in a less systematic way. This new and original data set is suitable for training or research purposes in the forensic discipline of bloodstain pattern analysis.

Background: Clinical data, such as patient history, laboratory analysis, ultrasound parameters-which are the basis of day-to-day clinical decision support-are often used to guide the clinical management of cancer in the presence of microarray data. Several data fusion techniques are available to integrate genomics or proteomics data, but only a few studies have created a single prediction model using both gene expression and clinical data. These studies often remain inconclusive regarding an obtained improvement in prediction performance. To improve clinical management, these data should be fully exploited. This requires efficient algorithms to integrate these data sets and design a final classifier. LS-SVM classifiers and generalized eigenvalue/singular value decompositions are successfully used in many bioinformatics applications for prediction tasks. While bringing up the benefits of these two techniques, we propose a machine learning approach, a weighted LS-SVM classifier to integrate two data sources: microarray and clinical parameters., Results: We compared and evaluated the proposed methods on five breast cancer case studies. Compared to LS-SVM classifier on individual data sets, generalized eigenvalue decomposition (GEVD) and kernel GEVD, the proposed weighted LS-SVM classifier offers good prediction performance, in terms of test area under ROC Curve (AUC), on all breast cancer case studies., Conclusions: Thus a clinical classifier weighted with microarray data set results in significantly improved diagnosis, prognosis and prediction responses to therapy. The proposed model has been shown as a promising mathematical framework in both data fusion and non-linear classification problems.

Background: DNA microarrays are potentially powerful technology for improving diagnostic classification, treatment selection, and prognostic assessment. The use of this technology to predict cancer outcome has a history of almost a decade. Disease class predictors can be designed for known disease cases and provide diagnostic confirmation or clarify abnormal cases. The main input to this class predictors are high dimensional data with many variables and few observations. Dimensionality reduction of these features set significantly speeds up the prediction task. Feature selection and feature transformation methods are well known preprocessing steps in the field of bioinformatics. Several prediction tools are available based on these techniques., Results: Studies show that a well tuned Kernel PCA (KPCA) is an efficient preprocessing step for dimensionality reduction, but the available bandwidth selection method for KPCA was computationally expensive. In this paper, we propose a new data-driven bandwidth selection criterion for KPCA, which is related to least squares cross-validation for kernel density estimation. We propose a new prediction model with a well tuned KPCA and Least Squares Support Vector Machine (LS-SVM). We estimate the accuracy of the newly proposed model based on 9 case studies. Then, we compare its performances (in terms of test set Area Under the ROC Curve (AUC) and computational time) with other well known techniques such as whole data set + LS-SVM, PCA + LS-SVM, t-test + LS-SVM, Prediction Analysis of Microarrays (PAM) and Least Absolute Shrinkage and Selection Operator (Lasso). Finally, we assess the performance of the proposed strategy with an existing KPCA parameter tuning algorithm by means of two additional case studies., Conclusion: We propose, evaluate, and compare several mathematical/statistical techniques, which apply feature transformation/selection for subsequent classification, and consider its application in medical diagnostics. Both feature selection and feature transformation perform well on classification tasks. Due to the dynamic selection property of feature selection, it is hard to define significant features for the classifier, which predicts classes of future samples. Moreover, the proposed strategy enjoys a distinctive advantage with its relatively lesser time complexity.

Bias-corrected approximate 100(1-α)% pointwise and simultaneous confidence and prediction intervals for least squares support vector machines are proposed. A simple way of determining the bias without estimating higher order derivatives is formulated. A variance estimator is developed that works well in the homoscedastic and heteroscedastic case. In order to produce simultaneous confidence intervals, a simple Šidák correction and a more involved correction (based on upcrossing theory) are used. The obtained confidence intervals are compared to a state-of-the-art bootstrap-based method. Simulations show that the proposed method obtains similar intervals compared to the bootstrap at a lower computational cost.