The DARTS approach manifests the advantages of relaxing the discrete problem of network architecture search (NAS) to the continuous domain such that network weights and architecture parameters can be optimized properly. However, it falls short in providing a justifiable and reliable solution for deciding the target architecture. In particular, the design choice of a certain operation at each layer/edge is determined without considering the distribution of operations over the overall architecture or even the neighboring layers. Our method explores such dependencies from the viewpoint of maximum a posterior (MAP) estimation. The consideration takes account of both local and global information by learning transition probabilities of network operations while enabling a greedy scheme to uncover a MAP estimate of optimal target architecture. The experiments show that our method achieves state-of-the-art results on popular benchmark datasets and also can be conveniently plugged into DARTS-related techniques to boost their performance. Our code is available at https://github.com/MAP-DARTS/MAP-DARTS.