Estimating the risk of SARS-CoV-2 deaths using a Markov switching-volatility model combined with heavy-tailed distributions for South Africa.

BACKGROUND: SARS-CoV-2 (Covid-19 virus) infection exposed the unpreparedness of African countries to health-related issues, South Africa included. Africa recorded more than 211 853 deaths as a consequence of Covid-19. When rare and deadly diseases require urgent hospitalisation strikes, governments and healthcare providers are usually caught unprepared, resulting in huge loss of lives. Usually, at the beginning of such pandemics, there is no rich data for health practitioners and academics to be able to forecast the number of patients or deaths related to the pandemic. This study aims to predict the number of deaths associated with Covid-19 infection. With the availability of the number of deaths on a daily basis, the results stemming from this study are important to inform and plan health policy. METHODS: This study uses the daily number of deaths due to Covid-19 infection. Exploratory data analysis reveals that the data exhibits non-normality, three structural breaks and volatility clustering characteristics. The Markov switching (MS)-generalized autoregressive conditional heteroscedasticity (GARCH)-type model combined with heavy-tailed distributions is fitted to the returns of the data. Using available daily reported Covid-19-related deaths up until 26 August 2021, we report 10-day ahead forecasts of deaths. All forecasts are compared to the actual observed values in the forecasting period. RESULTS: The Anderson-Darling Goodness of fit test confirms that the fitted models are adequate for the data. The Kupiec likelihood ratio test and the root mean square error (RMSE) were used to select the robust model at different risk levels. At 95% the MS(3)-GARCH(1,1) combined with Pearson's type IV distribution (PIVD) is the best model. This indicates that the proposed best-fitting model is reasonable and can be used for predicting the daily number of deaths due to Covid-19. CONCLUSION: The MS(3)-GARCH(1,1)-PIVD model provides a reliable and accurate method for predicting the minimum number of death due to Covid-19. The accuracy of the proposed model will assist policymakers, academics and health practitioners in forecasting the volatility of future health-related deaths in which the predictability of volatility plays an integral role in health risk management.

Shannon Entropy: An Econophysical Approach to Cryptocurrency Portfolios.

Cryptocurrency markets have attracted many interest for global investors because of their novelty, wide on-line availability, increasing capitalization, and potential profits. In the econophysics tradition, we show that many of the most available cryptocurrencies have return statistics that do not follow Gaussian distributions, instead following heavy-tailed distributions. Entropy measures are applied, showing that portfolio diversification is a reasonable practice for decreasing return uncertainty.

Heavy-tailed distributions in haptic perception of wielded rods.

Humans identify properties (e.g., the length or weight) of objects through touch using somatosensory perceptions in the limbs. Humans identify these properties by manipulating an object to access its inertial qualities. However, there is little work evidencing a unifying pattern of movements humans use to access these inertial properties. The current study examined if participants' wielding movements followed a systematic distribution-specifically, a Lévy-like distribution that is characterized by heavy-tails and is often seen in efficient foraging behavior. Participants wielded rods they could not see and were tasked to identify whether the rod they were wielding was the longer or shorter of two rods. While participants wielded the rod, the rod's motion was captured. Results demonstrate that the sampling of angular accelerations produced heavy-tailed distributions. Since angular acceleration has a distinct physical-mathematical relationship with inertia, this finding is consistent with the interpretation that the haptic subsystems are sensitive to the inertial properties of an object. Angular acceleration from wielding motions appear to follow a similar distribution as optimal foraging strategies-perhaps it is the case that humans are foraging for information about the inertia of an object through changes in angular acceleration and wielding movements.

COVID-19 X-ray images classification based on enhanced fractional-order cuckoo search optimizer using heavy-tailed distributions.

Classification of COVID-19 X-ray images to determine the patient's health condition is a critical issue these days since X-ray images provide more information about the patient's lung status. To determine the COVID-19 case from other normal and abnormal cases, this work proposes an alternative method that extracted the informative features from X-ray images, leveraging on a new feature selection method to determine the relevant features. As such, an enhanced cuckoo search optimization algorithm (CS) is proposed using fractional-order calculus (FO) and four different heavy-tailed distributions in place of the Lévy flight to strengthen the algorithm performance during dealing with COVID-19 multi-class classification optimization task. The classification process includes three classes, called normal patients, COVID-19 infected patients, and pneumonia patients. The distributions used are Mittag-Leffler distribution, Cauchy distribution, Pareto distribution, and Weibull distribution. The proposed FO-CS variants have been validated with eighteen UCI data-sets as the first series of experiments. For the second series of experiments, two data-sets for COVID-19 X-ray images are considered. The proposed approach results have been compared with well-regarded optimization algorithms. The outcomes assess the superiority of the proposed approach for providing accurate results for UCI and COVID-19 data-sets with remarkable improvements in the convergence curves, especially with applying Weibull distribution instead of Lévy flight.

Allometric analysis using the multivariate shifted exponential normal distribution.

In allometric studies, the joint distribution of the log-transformed morphometric variables is typically elliptical and with heavy tails. To account for these peculiarities, we introduce the multivariate shifted exponential normal (MSEN) distribution , an elliptical heavy-tailed generalization of the multivariate normal (MN). The MSEN belongs to the family of MN scale mixtures (MNSMs) by choosing a convenient shifted exponential as mixing distribution. The probability density function of the MSEN has a simple closed-form characterized by only one additional parameter, with respect to the nested MN, governing the tail weight. The first four moments exist and the excess kurtosis can assume any positive value. The membership to the family of MNSMs allows us a simple computation of the maximum likelihood (ML) estimates of the parameters via the expectation-maximization (EM) algorithm; advantageously, the M-step is computationally simplified by closed-form updates of all the parameters. We also evaluate the existence of the ML estimates. Since the parameter governing the tail weight is estimated from the data, robust estimates of the mean vector of the nested MN distribution are automatically obtained by downweighting; we show this aspect theoretically but also by means of a simulation study. We fit the MSEN distribution to multivariate allometric data where we show its usefulness also in comparison with other well-established multivariate elliptical distributions.

Black swans in space: modeling spatiotemporal processes with extremes.

In ecological systems, extremes can happen in time, such as population crashes, or in space, such as rapid range contractions. However, current methods for joint inference about temporal and spatial dynamics (e.g., spatiotemporal modeling with Gaussian random fields) may perform poorly when underlying processes include extreme events. Here we introduce a model that allows for extremes to occur simultaneously in time and space. Our model is a Bayesian predictive-process GLMM (generalized linear mixed-effects model) that uses a multivariate-t distribution to describe spatial random effects. The approach is easily implemented with our flexible R package glmmfields. First, using simulated data, we demonstrate the ability to recapture spatiotemporal extremes, and explore the consequences of fitting models that ignore such extremes. Second, we predict tree mortality from mountain pine beetle (Dendroctonus ponderosae) outbreaks in the U.S. Pacific Northwest over the last 16 yr. We show that our approach provides more accurate and precise predictions compared to traditional spatiotemporal models when extremes are present. Our R package makes these models accessible to a wide range of ecologists and scientists in other disciplines interested in fitting spatiotemporal GLMMs, with and without extremes.

Central limit theorems under special relativity.

Several relativistic extensions of the Maxwell-Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior.

Use of robust multivariate linear mixed models for estimation of genetic parameters for carcass traits in beef cattle.

Assumptions of normality of residuals for carcass evaluation may make inferences vulnerable to the presence of outliers, but heavy-tail densities are viable alternatives to normal distributions and provide robustness against unusual or outlying observations when used to model the densities of residual effects. We compare estimates of genetic parameters by fitting multivariate Normal (MN) or heavy-tail distributions (multivariate Student's t and multivariate Slash, MSt and MS) for residuals in data of hot carcass weight (HCW), longissimus muscle area (REA) and 12th to 13th rib fat (FAT) traits in beef cattle using 2475 records from 2007 to 2008 from a large commercial operation in Nebraska. Model comparisons using deviance information criteria (DIC) favoured MSt over MS and MN models, respectively. The posterior means (and 95% posterior probability intervals, PPI) of v for the MSt and MS models were 5.89 ± 0.90 (4.35, 7.86) and 2.04 ± 0.18 (1.70, 2.41), respectively. Smaller values of posterior densities of v for MSt and MS models confirm that the assumption of normally distributed residuals is not adequate for the analysis of the data set. Posterior mean (PM) and posterior median (PD) estimates of direct genetic variances were variable with MSt having the highest mean value followed by MS and MN, respectively. Posterior inferences on genetic variance were, however, comparable among the models for FAT. Posterior inference on additive heritabilities for HCW, REA and FAT using MN, MSt and MS models indicated similar and moderate heritability comparable with the literature. Posterior means of genetic correlations for carcass traits were variable but positive except for between REA and FAT, which showed an antagonistic relationship. We have demonstrated that genetic evaluation and selection strategies will be sensitive to the assumed model for residuals.

Measuring income inequality via percentile relativities.

The adage "the rich are getting richer" refers to increasingly skewed and heavily-tailed income distributions. For such distributions, the mean is not the best measure of the center, but the classical indices of income inequality, including the celebrated Gini index, are mean based. In view of this, it has been proposed in the literature to incorporate the median into the definition of the Gini index. In the present paper we make a further step in this direction and, to acknowledge the possibility of differing viewpoints, investigate three median-based indices of inequality. These indices overcome past limitations, such as: (1) they do not rely on the mean as the center of, or a reference point for, income distributions, which are skewed, and are getting even more heavily skewed; (2) they are suitable for populations of any degree of tail heaviness, and income distributions are becoming increasingly such; and (3) they are unchanged by, and even discourage, transfers among the rich persons, but they encourage transfers from the rich to the poor, as well as among the poor to alleviate their hardship. We study these indices analytically and numerically using various income distribution models. Real-world applications are showcased using capital incomes from 2001 and 2018 surveys from fifteen European countries.

Improving Likert scale big data analysis in psychometric health economics: reliability of the new compositional data approach.

Bipolar psychometric scales data are widely used in psychologic healthcare. Adequate psychological profiling benefits patients and saves time and costs. Grant funding depends on the quality of psychotherapeutic measures. Bipolar Likert scales yield compositional data because any order of magnitude of agreement towards an item assertion implies a complementary order of magnitude of disagreement. Using an isometric log-ratio (ilr) transformation the bivariate information can be transformed towards the real valued interval scale yielding unbiased statistical results increasing the statistical power of the Pearson correlation significance test if the Central Limit Theorem (CLT) of statistics is satisfied. In practice, however, the applicability of the CLT depends on the number of summands (i.e., the number of items) and the variance of the data generating process (DGP) of the ilr transformed data. Via simulation we provide evidence that the ilr approach also works satisfactory if the CLT is violated. That is, the ilr approach is robust towards extremely large or infinite variances of the underlying DGP increasing the statistical power of the correlation test. The study generalizes former results pointing out the universality and reliability of the ilr approach in psychometric big data analysis affecting psychometric health economics, patient welfare, grant funding, economic decision making and profits.

Multiple scaled symmetric distributions in allometric studies.

In allometric studies, the joint distribution of the log-transformed morphometric variables is typically symmetric and with heavy tails. Moreover, in the bivariate case, it is customary to explain the morphometric variation of these variables by fitting a convenient line, as for example the first principal component (PC). To account for all these peculiarities, we propose the use of multiple scaled symmetric (MSS) distributions. These distributions have the advantage to be directly defined in the PC space, the kind of symmetry involved is less restrictive than the commonly considered elliptical symmetry, the behavior of the tails can vary across PCs, and their first PC is less sensitive to outliers. In the family of MSS distributions, we also propose the multiple scaled shifted exponential normal distribution, equivalent of the multivariate shifted exponential normal distribution in the MSS framework. For the sake of parsimony, we also allow the parameter governing the leptokurtosis on each PC, in the considered MSS distributions, to be tied across PCs. From an inferential point of view, we describe an EM algorithm to estimate the parameters by maximum likelihood, we illustrate how to compute standard errors of the obtained estimates, and we give statistical tests and confidence intervals for the parameters. We use artificial and real allometric data to appreciate the advantages of the MSS distributions over well-known elliptically symmetric distributions and to compare the robustness of the line from our models with respect to the lines fitted by well-established robust and non-robust methods available in the literature.

Regression models with asymmetric data for estimating thyroglobulin levels one year after the ablation of thyroid cancer.

A key biomarker in the study of differentiated thyroid cancer is thyroglobulin. Measurements of the levels of this protein in the blood are determined using laboratory instruments that cannot detect very small concentrations below a threshold, generating left-censored measurements. In the presence of censoring, ordinary least-squares regression models generate biased parameter estimates; therefore, it is necessary to resort to more complex models that consider the censored observations and the behavior of the distribution of the response variable, such as censored and mixed regression models. These techniques were used to model the relationship between thyroglobulin levels in individuals with differentiated thyroid cancer before and after treatment with radioactive iodine (I-131). Log-normal, log-skew-normal, log-power-normal, and log-generalized-gamma probability distributions were used to model the behavior of errors in the adjusted models. Log-generalized-gamma distribution yielded the best results according to the established model selection criteria.