The Hierarchical Redundancy Eliminated Tree Augmented Naive Bayes (HRE-TAN) classifier is a semi-naive Bayesian model that learns a type of hierarchical redundancy-free tree-like feature representation to estimate the data distribution. In this work, we propose two new types of positive feature values prioritized hierarchical redundancy eliminated tree augmented naive Bayes classifiers that focus on features bearing positive instance values. The two newly proposed methods are applied to 28 real-world bioinformatics datasets showing better predictive performance than the conventional HRE-TAN classifier.