Automatic robust Box–Cox and extended Yeo–Johnson transformations in regression

The paper introduces an automatic procedure for the parametric transformation of the response in regression models to approximate normality. We consider the Box–Cox transformation and its generalization to the extended Yeo–Johnson transformation which allows for both positive and negative responses. A simulation study illuminates the superior comparative properties of our automatic procedure for the Box–Cox transformation. The usefulness of our procedure is demonstrated on four sets of data, two including negative observations. An important theoretical development is an extension of the Bayesian Information Criterion (BIC) to the comparison of models following the deletion of observations, the number deleted here depending on the transformation parameter.

Computational methods on food contact chemicals: Big data and in silico screening on nuclear receptors family

According to Eurostat, the EU production of chemicals hazardous to health reached 211 million tonnes in 2019. Thus, the possibility that some of these chemical compounds interact negatively with the human endocrine system has received, especially in the last decade, considerable attention from the scientific community. It is obvious that given the large number of chemical compounds it is impossible to use in vitro/in vivo tests for identifying all the possible toxic interactions of these chemicals and their metabolites. In addition, the poor availability of highly curated databases from which to retrieve and download the chemical, structure, and regulative information about all food contact chemicals has delayed the application of in silico methods. To overcome these problems, in this study we use robust computational approaches, based on a combination of highly curated databases and molecular docking, in order to screen all food contact chemicals against the nuclear receptor family in a cost and time-effective manner.

Constrained parsimonious model-based clustering

A new methodology for constrained parsimonious model-based clustering is introduced, where some tuning parameter allows to control the strength of these constraints. The methodology includes the 14 parsimonious models that are often applied in model-based clustering when assuming normal components as limit cases. This is done in a natural way by filling the gap among models and providing a smooth transition among them. The methodology provides mathematically well-defined problems and is also useful to prevent us from obtaining spurious solutions. Novel information criteria are proposed to help the user in choosing parameters. The interest of the proposed methodology is illustrated through simulation studies and a real-data application on COVID data.

Semiautomatic robust regression clustering of international trade data

The purpose of this paper is to show in regression clustering how to choose the most relevant solutions, analyze their stability, and provide information about best combinations of optimal number of groups, restriction factor among the error variance across groups and level of trimming. The procedure is based on two steps. First we generalize the information criteria of constrained robust multivariate clustering to the case of clustering weighted models. Differently from the traditional approaches which are based on the choice of the best solution found minimizing an information criterion (i.e. BIC), we concentrate our attention on the so called optimal stable solutions. In the second step, using the monitoring approach, we select the best value of the trimming factor. Finally, we validate the solution using a confirmatory forward search approach. A motivating example based on a novel dataset concerning the European Union trade of face masks shows the limitations of the current existing procedures. The suggested approach is initially applied to a set of well known datasets in the literature of robust regression clustering. Then, we focus our attention on a set of international trade datasets and we provide a novel informative way of updating the subset in the random start approach. The Supplementary material, in the spirit of the Special Issue, deepens the analysis of trade data and compares the suggested approach with the existing ones available in the literature.

Statistical and Proactive Analysis of an Inter-Laboratory Comparison: The Radiocarbon Dating of the Shroud of Turin

We review the sampling and results of the radiocarbon dating of the archaeological cloth known as the Shroud of Turin, in the light of recent statistical analyses of both published and raw data. The statistical analyses highlight an inter-laboratory heterogeneity of the means and a monotone spatial variation of the ages of subsamples that suggest the presence of contaminants unevenly removed by the cleaning pretreatments. We consider the significance and overall impact of the statistical analyses on assessing the reliability of the dating results and the design of correct sampling. These analyses suggest that the 1988 radiocarbon dating does not match the current accuracy requirements. Should this be the case, it would be interesting to know the accurate age of the Shroud of Turin. Taking into account the whole body of scientific data, we discuss whether it makes sense to date the Shroud again.

Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis

Minimum density power divergence estimation provides a general framework for robust statistics, depending on a parameter α , which determines the robustness properties of the method. The usual estimation method is numerical minimization of the power divergence. The paper considers the special case of linear regression. We developed an alternative estimation procedure using the methods of S-estimation. The rho function so obtained is proportional to one minus a suitably scaled normal density raised to the power α . We used the theory of S-estimation to determine the asymptotic efficiency and breakdown point for this new form of S-estimation. Two sets of comparisons were made. In one, S power divergence is compared with other S-estimators using four distinct rho functions. Plots of efficiency against breakdown point show that the properties of S power divergence are close to those of Tukey's biweight. The second set of comparisons is between S power divergence estimation and numerical minimization. Monitoring these two procedures in terms of breakdown point shows that the numerical minimization yields a procedure with larger robust residuals and a lower empirical breakdown point, thus providing an estimate of α leading to more efficient parameter estimates.

Role of noise in image processing by the human perceptive system

Two psychophysics experiments are described, pointing out the significant role played by stochastic resonance in recognition of capital stylized noisy letters by the human perceptive apparatus. The first experiment shows that an optimal noise level exists at which the letter is recognized for a minimum threshold contrast. A simple two-parameter model that best fits the experimental data is also discussed. In the second experiment we show that a dramatically increased ability of the visual system in letter recognition occurs in an extremely narrow range of increasing noise. Possible interesting future investigations suggested by these experimental results and based on functional imaging techniques are discussed.

Ambiguity and structural information in the perception of reversible figures

The perspective reversals elicited by a set of drawings based on the Mach truncated pyramid are examined. We obtained each pattern of the set from the previous one by adding to it some graphic cues, which were easily integrated into one of the two competing interpretations, thus reducing step by step the ambiguity of the basic pattern. The phenomenological model, proposed to link the mean times of both alternative interpretations with their complexities, is in close agreement with our experimental data. Furthermore, different aspects of such data are well described by the model equations: The measure of the prevalence of the supported interpretation is well correlated with the difference in complexity between the two alternative interpretations; the two different trends of the mean time of the unfavored interpretation, found in the data obtained from different observers as a function of the various patterns of the set, are well fitted by the model without the need for any specific additional hypothesis.

Perceptual ambiguity and stability of reversible figures

In this work, the results of two experiments on ambiguous patterns are reported, which have been obtained by presenting a series of stimuli designed, in both cases, to reduce gradually the ambiguity of the patterns. Such reduction has been performed by respectively increasing or decreasing the amount of graphic details in the experiments. Data of both experiments show a lengthening of mean reversal time. The increase in the stability of one percept can be regarded as associated with the increasing difficulties encountered by an observer in organizing and restating the alternative "hypothesis" through the perceptual mechanisms. The loss of balance in the durations of percepts is discussed in terms of their different informational contents. Finally, in Exp. 1 an analysis is made to evaluate to what extent an addition of perceptual cues, designed to reinforce a three-dimensional interpretation of a pattern, can influence its figure-ground alternation.

Effect of luminance on perceptual alternation of ambiguous patterns

The perceptual alternation of the Necker cube, in its stationary phase, is studied as a function of the stimulus luminance down to the extreme condition in which the cones are completely inactivated so that the pattern of neural excitation reaching the primary visual cortex is very different from the normal one. No evident effect of luminance was found under passive observation either on the reversal rate or on the features of data distributions. Moreover, the complementary situation in which perception is based only on the cones does not affect the phenomenon either. These results permit the assumption that the perceptual alternation in its stationary phase, is a passive and automatic process, that is affected neither by a satiation of the first levels of the visual system nor by the psychological attitude of the subject consequent on dazzling the retina.

Effects of visual angle on perspective reversal for ambiguous patterns

Reversal rates of an ambiguous figure (the Necker cube) were studied for different pattern sizes covering a range of visual angles theta from approximately 1 to 62 deg. A large number of reversals was obtained for each observer and each pattern in order to examine the statistical distributions of reversal times. A pronounced flattening of the statistical distributions (represented throughout by a gamma distribution) and a growth of the mean duration of each percept, with increasing pattern size was found. A plateau in the range of theta between 5 and 20-30 deg was observed. For larger values of theta two kinds of observers have been identified: for 'fast' observers the inversion rate is little affected by theta, whilst for 'slow' observers, the mean reversal time increases strongly with theta. A tentative model, based on three different contributions to the duration of the alternation process, is proposed: a constant term, independent of theta, and two terms dependent on theta--a retinal term, and a cortical one. The last term is interpreted as due to the spreading of excitation with the characteristic of a filling-in process.