On automorphisms of monotone transformation posemigroups

In this paper, we provide a simple generalization of results of Sullivan for [Formula: see text] the full transformation monotone pomonoid and for [Formula: see text] the partial transformation monotone pomonoid by showing that every automorphism of [Formula: see text] and [Formula: see text] is inner induced by the elements of [Formula: see text] the pogroup of all ordered bijections on [Formula: see text]. We also show that [Formula: see text] is isomorphic to [Formula: see text]. Finally, we apply these results to get some more results in this direction.

Non-monotone transformation of biomarkers

We comment here on a recent paper in this journal, on a non-monotone transformation of biomarkers aimed at improving diagnostic accuracy. We highlight that, in a binary classification problem, the proposed transformation finds its motivation in the Neyman–Pearson lemma, so that the underlying approach is very general and it is applicable to many parametric families, other than the normal one.

A likelihood analysis of quantile-matching transformations

Summary Quantile matching is a strictly monotone transformation that sends the observed response values to the quantiles of a given target distribution. A profile likelihood-based criterion is developed for comparing one target distribution with another in a linear-model setting.

Identification of Li-ion battery models through monotonic echo serial networks for coarse data

Monotone transformation models are extended to inaccurate data and are combined with recurrent neural networks in a new battery model that is able to ascertain the health of rechargeable batteries for automotive applications. The presented method exploits the information contained in the vehicle’s operational records better than other cutting-edge models and uses a minimum amount of human expert knowledge. The experimental validation of the technique includes a comparative analysis of batteries in different health conditions, comprising first-principles models and different machine learning procedures.

Non-monotone transformation of biomarkers to improve diagnostic and screening accuracy in a DNA methylation study with trichotomous phenotypes

We propose a non-monotone transformation to biomarkers in order to improve the diagnostic and screening accuracy. The proposed quadratic transformation only involves modeling the distribution means and variances of the biomarkers and is therefore easy to implement in practice. Mathematical justification was rigorously established to support the validity of the proposed transformation. We conducted extensive simulation studies to assess the performance of the proposed method and compared the new method with the traditional methods. Case studies on real biomedical and epigenetics data were provided to illustrate the proposed transformation. In particular, the proposed method improved the AUC values for a large number of markers in a DNA methylation study and consequently led to the identification of greater number of important biomarkers and biologically meaningful genetic pathways.

Residual Probability Function, Associated Orderings, and Related Aging Classes

The concept of residual probability plays an important role in reliability and life testing. In this investigation, we study further the residual probability order and its related aging classes. Several characterizations and preservation properties of this order under some statistical and reliability operations of monotone transformation, mixture, weighted distributions, and order statistics are discussed. In addition, by comparing the original distribution with its associated equilibrium distribution with respect to the residual probability order, new aging classes of life distributions are proposed and studied. Finally, a test of exponentiality against such classes is derived and sets of real data are used as examples to elucidate the use of the proposed test for practical problems.

Lehmann Family of ROC Curves

Receiver operating characteristic (ROC) curves evaluate the discriminatory power of a continuous marker to predict a binary outcome. The most popular parametric model for an ROC curve is the binormal model, which assumes that the marker, after a monotone transformation, is normally distributed conditional on the outcome. Here, the authors present an alternative to the binormal model based on the Lehmann family, also known as the proportional hazards specification. The resulting ROC curve and its functionals (such as the area under the curve and the sensitivity at a given level of specificity) have simple analytic forms. Closed-form expressions for the functional estimates and their corresponding asymptotic variances are derived. This family accommodates the comparison of multiple markers, covariate adjustments, and clustered data through a regression formulation. Evaluation of the underlying assumptions, model fitting, and model selection can be performed using any off-the-shelf proportional hazards statistical software package.