We apply a Bayesian network-based approach for determining the structure of consumers' brand concept maps, and we further extend this approach in order to provide a precise delineation of the set of cognitive variations of that brand concept map structure which can simultaneously coexist within the data. This methodology can operate with nonlinear as well as linear relationships between the variables, and utilizes simple Likert-style marketing survey data as input. In addition, the method can operate without any a priori hypothesized structures or relations among the brand associations in the model. The resulting brand concept map structures delineate directional (as opposed to simply correlational) relations among the brand associations, and differentiates between the predictive and the diagnostic directions within each link. Further, we determine a Bayesian network-based link strength measure, and apply it to a comparison of the strengths of the connections between different semantic categories of brand association descriptors, as well as between different strategically important drivers of brand differentiation. Finally, we apply a precise form of information propagation through the predictive and diagnostic links within the network in order to evaluate the effect of introducing new information to the brand concept network. This overall methodology operates via a factorization of the joint distribution of the brand association variables via conditional independence properties and an application of the causal Markov condition, and as such, it represents an alternative approach to correlation-based structural determination methods. By using conditional independence as a core structural construct, the methods utilized here are especially well- suited for determining and analyzing asymmetric or directional beliefs about brand or product attributes. This methodology builds on the pioneering Brand Concept Mapping approach of Roedder John et al. (2006). Similar to that approach, the Bayesian network-based method derives the specific link-by-link structure among a brand's associations, and also allows for a precise quantitative determination of the likely effects that manipulation of specific brand associations will have upon other strategically important associations within that brand image. In addition, the method's precise informational semantics and specific structural measures allow for a greater understanding of the structure of these brand associations.