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Model selection via exponentially embedded families (EEF) of probability models has been shown to perform well on many practical problems of interest. A key component in utilizing this approach is the definition of a model origin (i.e. null hypothesis) which is embedded individually within each competing model. In this correspondence we give a geometrical interpretation of the EEF and study the sensitivity of the EEF approach to the choice of model origin in a Gaussian hypothesis testing framework. We introduce the information center (I-center) of competing models as an origin in this procedure and compare this to using the standard null hypothesis. Finally we derive optimality conditions for which the EEF using I-center achieves optimal performance in the Gaussian hypothesis testing framework.