The outbreak of the new COVID-19 disease is a serious health problem that has affected a large part of the world population, especially older adults and people who suffer from a previous comorbidity. In this work, we proposed a classifier model that allows for deciding whether or not a patient might suffer from the COVID-19 disease, considering spatio-temporal variables, physical characteristics of the patients and the presence of previous diseases. We used XGBoost to maximize the likelihood function of the multivariate logistic regression model. The estimated and observed values of percentage occurrence of cases were very similar, and indicated that the proposed model was suitable to predict new cases (AUC = 0.75). The main results revealed that patients without comorbidities are less likely to be COVID-19 positive, unlike people with diabetes, obesity and pneumonia. The distribution function by age group showed that, during the first and second wave of COVID-19, young people aged ≤20 were the least affected by the pandemic, while the most affected were people between 20 and 40 years, followed by adults older than 40 years. In the case of the third and fourth wave, there was an increased risk for young individuals (under 20 years), while older adults over 40 years decreased their chances of infection. Estimates of positive COVID cases with both the XGBoost-LR model and the multivariate logistic regression model were used to create maps to visualize the spatial distribution of positive cases across the country. Spatial analysis was carried out to determine, through the data, the main geographical areas where a greater number of positive cases occurred. The results showed that the areas most affected by COVID-19 were in the central and northern regions of Mexico.
We introduced a novel spatial model based on the distribution of generalized extreme values (GEV) to analyze the maximum intensity levels of earthquakes with incomplete data (randomly censored) on the Pacific coast of southern Mexico using a random censorship approach. Spatiotemporal trends were modeled through a non-stationary GEV model. We used a multivariate smoothing function as a linear predictor of GEV parameters to approximate nonlinear trends. The model was fitted using a flexible semi-parametric Bayesian approach and the parameters are estimated via Markov chain Monte-Carlo (MCMC). Through a rigorous simulation study, we showed the robustness of both the model and the estimation method used. Maps of the location parameter on the spatial plane for different periods of time show the existence of local variations in the extreme values of seismicity in the study area. The results indicate strong evidence of an increase in the magnitude of earthquakes over time. A spatial map of risk with maximum intensity of earthquakes in a period of 25 years was elaborated.
Air pollution by carbon monoxide is a serious problem that affects many cities around the world, and the theory of extreme values has played a crucial role in the study of this issue. In this paper, we proposed a Bayesian hierarchical spatial model of extreme values to evaluate the risk of extreme events of air pollution due to carbon monoxide in the metropolitan area of Mexico City. Spatial trends are modeled through of a Gaussian process for the generalized extreme value (GEV) distribution parameters, and prediction maps are produced for each of these. The results show a marginal spatial behavior for the location, scale, and shape parameters of GEV distribution, which indicate the existence of local variations that would not be possible to model using only stationary models. A return map of the maximum concentrations with a return period of one year is obtained. We found that the return levels for a one-year return period of CO concentration above 8 ppm in the Metropolitan Area of the Valley of Mexico are concentrated in the central part of this region, and the areas with the lowest estimates are distributed in the periphery. In addition, a quantile-quantile (QQ) plot between the theoretical and empirical quantiles was provided, which showed a very good fit of data to the proposed model.
Prediction about the failure probability of a product or system is essential in reliability engineering, where a decision‐making process is carried out on a regular basis. This paper proposes a novel index, that allows to predict the failure rate on products recently launched into the market; its calculation is based on sales information and failure reports. Maximum likelihood method is used to derive a mathematical expression for this index, and prediction intervals are obtained throughout a bootstrap approach. A good performance regarding the mean square error and coverage probability is observed in the simulation study included here. Monthly sales data and mobile phone failure reports, provided by the company in charge of the warranty policy process, were used to illustrate our proposal that emerged from an academic‐industry collaboration.
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