Solving the binary classification problem for an application involves solving a data driven modeling problem. Such problems entail multiple and coupled sources of errors. Two communities of practice have approached this problem with different sets of assumptions and resulting limitations. The statistical community assumes that data is generated by a given stochastic model with parameter estimates based on the given class of models. On the other hand, the machine learning or algorithmic modeling community uses algorithmic modeling methods that treat data mechanisms as unknown. Machine learning methods have been successfully used on large data sets and offer a more accurate alternative to data modeling on small data sets. In this talk we consider the hard margin support vector algorithm applied to several bivariate Gaussian data sets with common covariance matrices.