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Given the fast spread of the novel coronavirus (COVID-19) worldwide and its classification by the World Health Organization (WHO) as being one of the worst pandemics in history, several scientific studies are carried out using various statistical and mathematical models to predict and study the likely evolution of this pandemic in the world. In the present research paper, we present a brief study aiming to predict the probability of reaching a new record number of COVID-19 cases in Lebanon, based on the record theory, giving more insights about the rate of its quick spread in Lebanon. The main advantage of the records theory resides in avoiding several statistical constraints concerning the choice of the underlying distribution and the quality of the residuals. In addition, this theory could be used, in cases where the number of available observations is somehow small. Moreover, this theory offers an alternative solution in case where machine learning techniques and long-term memory models are inapplicable because they need a considerable amount of data to be performant. The originality of this paper lies in presenting a new statistical approach allowing the early detection of unexpected phenomena such as the new pandemic COVID-19. For this purpose, we used epidemiological data from Johns Hopkins University to predict the trend of COVID-2019 in Lebanon. Our method is useful in calculating the probability of reaching a new record as well as studying the propagation of the disease. It also computes the probabilities of the waiting time to observe the future COVID-19 record. Our results obviously confirm the quick spread of the disease in Lebanon over a short time.

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Stochastic blockmodels have been widely proposed as a probabilistic random graph model for the analysis of networks data as well as for detecting community structure in these networks. In a number of real-world networks, not all ties among nodes have the same weight. Ties among networks nodes are often associated with weights that differentiate them in terms of their strength, intensity, or capacity. In this paper, we provide an inference method through a variational expectation maximization algorithm to estimate the parameters in binomial stochastic blockmodels for weighted networks. To prove the validity of the method and to highlight its main features, we set some applications of the proposed approach by using some simulated data and then some real data sets. Stochastic blockmodels belong to latent classes models. Classes defines a node's clustering. We compare the clustering found through binomial stochastic blockmodels with the ones found fitting a stochastic blockmodel with Poisson distributed edges. Inferred Poisson and binomial stochastic blockmodels mainly differs. Moreover, in our examples, the statistical error is lower for binomial stochastic blockmodels.

During the last decades, air pollution has become a serious environmental hazard. Its impact on public health and safety, as well as on the ecosystem, has been dramatic. Forecasting the levels of air pollution to maintain the climatic conditions and environmental protection becomes crucial for government authorities to develop strategies for the prevention of pollution. This study aims to evaluate the atmospheric air pollution of the city of Zahleh located in the geographic zone of Bekaa. The study aims to determine a relationship between variations in ambient particulate concentrations during a short time. The data was collected from June 2017 to June 2018. In order to predict the Air Quality Index (AQI), Naïve, Exponential Smoothing, TBATS (a forecasting method to model time series data), and Seasonal Autoregressive Integrated Moving Average (SARIMA) models were implemented. The performance of these models for predicting air quality is measured using the Mean Absolute Error (MAE), the Root Mean Square Error (RMSE), and the Relative Error (RE). SARIMA model is the most accurate in prediction of AQI (RMSE = 38.04, MAE = 22.52 and RE = 0.16). The results reveal that SARIMA can be applied to cities like Zahleh to assess the level of air pollution and to prevent harmful impacts on health. Furthermore, the authorities responsible for controlling the air quality may use this model to measure the level of air pollution in the nearest future and establish a mechanism to identify the high peaks of air pollution.