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.
Fitting of the exponential modified Gaussian distribution to model reaction times and drawing conclusions from its estimated parameter values is one of the most popular method used in psychology. This paper aims to develop a Bayesian approach to estimate the parameters of the ex-Gaussian distribution. Since the chosen priors yield to posterior densities that are not of known form and that they are not always log-concave, we suggest to use the adaptive rejection Metropolis sampling method. Applications on simulated data and on real data are provided to compare this method to the standard maximum likelihood estimation method as well as the quantile maximum likelihood estimation. Results shows the effectiveness of the proposed Bayesian method by computing the root mean square error of the estimated parameters using the three methods.
Water pollution is a major global environmental problem. In Lebanon, water pollution threatens public health and biological diversity. In this work, a non-classical classification method was used to assess water pollution in a Mediterranean River. A clustering proposal method based on the stochastic block model (SBM) was used as an application on physicochemical parameters in three stations of the Litani River to regroup these parameters in different clusters and identify the evolution of the physicochemical parameters between the stations. Results showed that the used method gave advanced findings on the distribution of parameters between inter and intra stations. This was achieved by calculating the estimated connection matrices between the obtained clusters and the probability vector of belonging of the physicochemical parameters to each cluster in the different stations. In each of the three stations, the same two clusters were obtained, the difference between them was in the estimated connection matrices and the estimated cluster membership vectors. The power of SBM proposed methods is demonstrated in simulation studies and a new real application to the sampling physicochemical parameters in Litani River. First, we compare the proposed method to the classical principal component analysis (PCA) method then to the Hierarchical and the K-means clustering methods. Results showed that these classical methods gave the same two clusters as the proposed method. However, unlike the proposed SBM method, classical approaches are not able to show the blocks structure of the three stations.
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