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This research project aims to promote ethical principles among designers engaged in adaptive-XR by providing tools for self-assessment. We introduce a Design-Based Research (DBR) methodology to build bRight-XR, a framework including a heuristic evaluation matrix and based on learning theory.

Machine learning and deep learning have been celebrating many successes in the application to biological problems, especially in the domain of protein folding. Another equally complex and important question has received relatively little attention by the machine learning community, namely the one of prediction of complex traits from genetics. Tackling this problem requires in-depth knowledge of the related genetics literature and awareness of various subtleties associated with genetic data. In this guide, we provide an overview for the machine learning community on current state of the art models and associated subtleties which need to be taken into consideration when developing new models for phenotype prediction. We use height as an example of a continuous-valued phenotype and provide an introduction to benchmark datasets, confounders, feature selection, and common metrics.

In this paper, using inverse integral transforms, we derive the exact distribution of the random variable $X$ that is involved in the ratio $Z \stackrel{d}{=} X/(X+Y)$ where $X$ and $Y$ are independent random variables having the same support, and $Z$ and $Y$ have known distributions. We introduce new distributions this way. As applications of the obtained results, several examples are presented., Comment: 15 pages

Univariate normal regression models are statistical tools widely applied in many areas of economics. Nevertheless, income data have asymmetric behavior and are best modeled by non-normal distributions. The modeling of income plays an important role in determining workers' earnings, as well as being an important research topic in labor economics. Thus, the objective of this work is to propose parametric quantile regression models based on two important asymmetric income distributions, namely, Dagum and Singh-Maddala distributions. The proposed quantile models are based on reparameterizations of the original distributions by inserting a quantile parameter. We present the reparameterizations, some properties of the distributions, and the quantile regression models with their inferential aspects. We proceed with Monte Carlo simulation studies, considering the maximum likelihood estimation performance evaluation and an analysis of the empirical distribution of two residuals. The Monte Carlo results show that both models meet the expected outcomes. We apply the proposed quantile regression models to a household income data set provided by the National Institute of Statistics of Chile. We showed that both proposed models had a good performance both in terms of model fitting. Thus, we conclude that results were favorable to the use of Singh-Maddala and Dagum quantile regression models for positive asymmetric data, such as income data., Comment: 22 pages, 11 figures

The primary goal of this paper is to introduce a novel frailty model based on the weighted Lindley (WL) distribution for modeling clustered survival data. We study the statistical properties of the proposed model. In particular, the amount of unobserved heterogeneity is directly parameterized on the variance of the frailty distribution such as gamma and inverse Gaussian frailty models. Parametric and semiparametric versions of the WL frailty model are studied. A simple expectation-maximization (EM) algorithm is proposed for parameter estimation. Simulation studies are conducted to evaluate its finite sample performance. Finally, we apply the proposed model to a real data set to analyze times after surgery in patients diagnosed with colorectal cancer and compare our results with classical frailty models carried out in this application, which shows the superiority of the proposed model. We implement an R package that includes estimation for fitting the proposed model based on the EM-algorithm.

We study with some details a lifetime model of the class of beta generalized models, called the beta inverse Rayleigh distribution, which is a special case of the Beta Fr\'echet distribution. We provide a better foundation for some properties including quantile function, moments, mean deviations, Bonferroni and Lorenz curves, R\'enyi and Shannon entropies and order statistics. We fit the proposed model using maximum likelihood estimation to a real data set to illustrate its flexibility and potentiality.

Motivated by the case fatality rate (CFR) of COVID-19, in this paper, we develop a fully parametric quantile regression model based on the generalized three-parameter beta (GB3) distribution. Beta regression models are primarily used to model rates and proportions. However, these models are usually specified in terms of a conditional mean. Therefore, they may be inadequate if the observed response variable follows an asymmetrical distribution, such as CFR data. In addition, beta regression models do not consider the effect of the covariates across the spectrum of the dependent variable, which is possible through the conditional quantile approach. In order to introduce the proposed GB3 regression model, we first reparameterize the GB3 distribution by inserting a quantile parameter and then we develop the new proposed quantile model. We also propose a simple interpretation of the predictor-response relationship in terms of percentage increases/decreases of the quantile. A Monte Carlo study is carried out for evaluating the performance of the maximum likelihood estimates and the choice of the link functions. Finally, a real COVID-19 dataset from Chile is analyzed and discussed to illustrate the proposed approach., Comment: 30 pages, 8 figures

In extreme values theory, for a sufficiently large block size, the maxima distribution is approximated by the generalized extreme value (GEV) distribution. The GEV distribution is a family of continuous probability distributions, which has wide applicability in several areas including hydrology, engineering, science, ecology and finance. However, the GEV distribution is not suitable to model extreme bimodal data. In this paper, we propose an extension of the GEV distribution that incorporate an additional parameter. The additional parameter introduces bimodality and to vary tail weight, i.e., this proposed extension is more flexible than the GEV distribution. Inference for the proposed distribution were performed under the likelihood paradigm. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the results. Finally, the proposed distribution is applied to environmental data sets, illustrating their capabilities in challenging cases in extreme value theory., Comment: 21 pages, 7 figures

The beta model is the most important distribution for fitting data with the unit interval. However, the beta distribution is not suitable to model bimodal unit interval data. In this paper, we propose a bimodal beta distribution constructed by using an approach based on the alpha-skew-normal model. We discuss several properties of this distribution such as bimodality, real moments, entropy measures and identifiability. Furthermore, we propose a new regression model based on the proposed model and discuss residuals. Estimation is performed by maximum likelihood. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the results. An application is provided to show the modelling competence of the proposed distribution when the data sets show bimodality., Comment: 22 pages, 5 figures

The Gumbel model is a very popular statistical model due to its wide applicability for instance in the course of certain survival, environmental, financial or reliability studies. In this work, we have introduced a bimodal generalization of the Gumbel distribution that can be an alternative to model bimodal data. We derive the analytical shapes of the corresponding probability density function and the hazard rate function and provide graphical illustrations. Furthermore, We have discussed the properties of this density such as mode, bimodality, moment generating function and moments. Our results were verified using the Markov chain Monte Carlo simulation method. The maximum likelihood method is used for parameters estimation. Finally, we also carry out an application to real data that demonstrates the usefulness of the proposed distribution., Comment: 23 pages, 17 figures

In this paper, we develop two fully parametric quantile regression models, based on power Johnson SB distribution Cancho et al. (2020), for modeling unit interval response at different quantiles. In particular, the conditional distribution is modelled by the power Johnson SB distribution. The maximum likelihood method is employed to estimate the model parameters. Simulation studies are conducted to evaluate the performance of the maximum likelihood estimators in finite samples. Furthermore, we discuss residuals and influence diagnostic tools. The effectiveness of our proposals is illustrated with two data set given by the mortality rate of COVID-19 in different countries., Comment: 17 pag

In this paper, we propose a new greedy algorithm for sparse approximation, called SLS for Single L_1 Selection. SLS essentially consists of a greedy forward strategy, where the selection rule of a new component at each iteration is based on solving a least-squares optimization problem, penalized by the L_1 norm of the remaining variables. Then, the component with maximum amplitude is selected. Simulation results on difficult sparse deconvolution problems involving a highly correlated dictionary reveal the efficiency of the method, which outperforms popular greedy algorithms and Basis Pursuit Denoising when the solution is sparse., Comment: in Proceedings of iTWIST'20, Paper-ID: 24, Nantes, France, December, 2-4, 2020

We consider several detection situations where, under the alternative hypothesis, the signal admits a low complexity model and, under both the null and the alternative hypotheses, the distribution of the background noise is {unknown}. We present several detection strategies for such cases, whose design relies on exogenous or on endogenous data. These testing procedures have been inspired by and are applied to two specific problems in Astrophysics, namely the detection of exoplanets from radial velocity curves and of distant galaxies in hyperspectral datacubes., Comment: in Proceedings of iTWIST'20, Paper-ID: 34, Nantes, France, December, 2-4, 2020

In this paper, we consider the beta prime regression model recently proposed by \cite{bour18}, which is tailored to situations where the response is continuous and restricted to the positive real line with skewed and long tails and the regression structure involves regressors and unknown parameters. We consider two different strategies of bias correction of the maximum-likelihood estimators for the parameters that index the model. In particular, we discuss bias-corrected estimators for the mean and the dispersion parameters of the model. Furthermore, as an alternative to the two analytically bias-corrected estimators discussed, we consider a bias correction mechanism based on the parametric bootstrap. The numerical results show that the bias correction scheme yields nearly unbiased estimates. An example with real data is presented and discussed.

This paper introduces a cure rate survival model by assuming that the time to the event of interest follows a beta prime distribution and that the number of competing causes of the event of interest follows a negative binomial distribution. This model provides a novel alternative to the existing cure rate regression models due to its flexibility, as the beta prime model can exhibit greater levels of skewness and kurtosis than those of the gamma and inverse Gaussian distributions. Moreover, the hazard rate of this model can have an upside-down bathtub or an increasing shape. We approach both parameter estimation and local influence based on likelihood methods. In special, three perturbation schemes are considered for local influence. Numerical evaluation of the proposed model is performed by Monte Carlo simulations. In order to illustrate the potential for practice of our model we apply it to a real data set., Comment: 13 pages, 2 figures

The Hapke model has been widely used to describe the photometrical behavior of planetary surface through the Bi-directional Reflectance Distribution Function (BRDF), but the uncertainties about retrieved parameters has been difficult to handle so far. A recent study proposed to estimate the uncertainties using a Bayesian approach (Schmidt et al., Icarus 2015). In the present article, we first propose an improved numerical implementation to speed up the uncertainties estimation. Then, we conduct two synthetic studies about photometric measurements in order to analyze the influence of observation geometry: First, we introduce the concept of "efficiency" of a set of geometries to sample the photometric behavior. A set of angular sampling elements (noted as geometry) is efficient if the retrieved Hapke parameters are close to the expected ones. We compared different geometries and found that the principal plane with high incidence is the most efficient geometry among the tested ones. In particular, such geometries are better than poorly sampled full BRDF. Second, we test the analysis scheme of a collection of photometric data acquired from various locations in order to answer the question: are these locations photometrically homogeneous or not? For instance, this question arises when combining data from an entire planetary body, where each spatial position is sampled at a single geometry. We tested the ability of the Bayesian method to decipher two situations, in the presence of noise: (i) a photometrically homogeneous surface (all observations with the same photometric behavior), or (ii) an heterogeneous surface with two distinct photometrical properties (half observations with photometric behavior 1, other half with photometric behavior 2). We show that the naive interpretation of the results provided by Bayesian method is not able to solve this problem., Comment: 32 pages, 5 figures

In this paper, we propose a regression model where the response variable is beta prime distributed using a new parameterization of this distribution that is indexed by mean and precision parameters. The proposed regression model is useful for situations where the variable of interest is continuous and restricted to the positive real line and is related to other variables through the mean and precision parameters. The variance function of the proposed model has a quadratic form. In addition, the beta prime model has properties that its competitor distributions of the exponential family do not have. Estimation is performed by maximum likelihood. Furthermore, we discuss residuals and influence diagnostic tools. Finally, we also carry out an application to real data that demonstrates the usefulness of the proposed model., Comment: 20 pages and 11 figures