Bayesian Model Averaging (BMA) methodology is applied for evaluating newborn brain maturity from sleep EEG. In theory this methodology provides the most accurate assessments of uncertainty in decisions. However, existing BMA techniques have been shown to provide biased evaluations in the absence of some prior information that allows the model parameter space to be explored in detail within a reasonable time. The lack of detail leads to disproportionate sampling from the posterior distribution. In the case of EEG assessment of brain maturity, BMA results may be biased due to the absence of information on the importance of EEG features. In this article, we explore how to use posterior information about EEG features to reduce the negative impact of disproportionate sampling on BMA performance. We use EEG data recorded from sleeping infants to test the efficiency of the proposed BMA technique. Evaluation of brain maturity can be achieved by estimating the age of the newborn from sleep EEG [1] - [3]. This approach is based on clinical evidence that the postconceptional and EEG-estimated ages of healthy newborns typically match each other, and the brain maturity of the newborn is most likely abnormal if the ages do not match [2], [4 ]. Therefore, the mismatch signals abnormal brain development. Established assessment methodologies are based on learning patterns from EEGs recorded from sleeping infants whose brain maturity had already been assessed by doctors. Regression models are enabled to map brain maturity into the EEG-based index [5]. Classification models are made capable of distinguishing maturity levels: at least one with normal brain maturity and the other with abnormal brain maturity [4], [6]. The established method... half of the document... its impact on the result is negligible. Conversely, when the number of weak attributes is large, the disproportionality in the models becomes significant. Therefore we could improve BMA results by reducing disproportionate sampling. In this research we aim to explore whether discarding models using weak EEG attributes will reduce bias in assessing brain maturity. A trivial strategy of using posterior information for feature selection within the BMA is to use this information to learn a new ensemble from a dataset in which weak attributes have been eliminated. This strategy reduces the parameter space of the model and therefore allows this space to be explored in greater detail. The other strategy that can be thought of is to refine the set by discarding models that use weak attributes. We expect that such refinement will improve the performance of the BMA.