## 1 Introduction and Related Works  
In recent years, there has been major progress in Statistical Machine Learning (SML) with unsupervised learning problems such as clustering, classification and recognition for both univariate and multivariate data. The success of statistical models depends on their capacity to model and build an effective representation that holds the underlying distribution of the data. SML has been used in various areas of research, such as knowledge discovery, computer vision and pattern recognition. Over the last decades, there has been extensive state-of-the-art related to these problems. In particular, there has been an increasing interest in the use of both supervised and unsupervised learning methods to assign or group similar objects into homogeneous and disjoint clusters. Such methods are also used for constructing classifiers to effectively recognize objects on the basis of discriminative visual features. A typical broadly used learning method is the so-called statistical mixture model [1; 2; 3; 4; 5], which has the advantage of offering a tractable and flexible basis for statistical inference. It is noted that statistical modelling has much to contribute to machine learning and data science. In particular, mixture models are widely used in scientific problems, where multidimensional objects are to be clustered or classified. In this situation, the data should be modelled in terms of a mixture of many components. The well-principled Finite mixture models (FMM) are used with success to partition multimodal data points and to learn cluster membership of observations with unknown cluster labels [6]. For instance, finite Gaussian mixture models were employed successfully in many applications [7; 8]. However, assuming Gaussian form density implies a strong assumption about the clusters' shape and may lead to overfitting the number of components, as well as a poor recognition (or classification) rate. A difficult aspect when considering finite mixture models is the determining of the exact component numbers, which help to avoid the issues of over- and under-fitting and minimizing the approximation errors, especially when we are trying to model complex real-world data problems (such as multimodal data) [9]. For instance, Laplace and Normal densities fail to fit many complex shapes with multi-dimensional data and when describing the heavier tails caused by specific patterns [10; 11]. In this context, non-Gaussian data modelling plays an essential role in accurate data clustering and classification. This problem can be addressed with more flexible statistical models, such as generalized Gaussian mixtures [11]. For this purpose, extensive research efforts have been developed; nevertheless, many of them still fail to achieve high accuracy for many applications [12]. On the other hand, several deterministic approaches have been implemented to deal with model parameters estimation [13; 14]. These approaches (also known as likelihood-based approaches) are well documented but they suffer from local optimality. In recent years, there has been increasing interest in Bayesian approaches (both parametric and nonparametric), which are seen as an attractive alternative for dealing with the limitations of deterministic methods such as dependency on initialization [11; 15; 16]. Indeed, the availability of prior knowledge about the parameters helps to accurately estimate these parameters from the data using a fully Bayesian approach. This approach is becoming more and more popular due to its flexibility and potential to include prior information. In previous work [10], authors have shown that Bayesian estimation of multivariate generalized Gaussian (Normal) mixture can offer good flexibility in terms of data fitting. The proposed method allows for the flexible modeling of both multidimensional and multivariate data (i.e., correlated data) by considering the relationship between attributes.