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Radar constant false alarm rate (CFAR) detection is addressed in this correspondence. Motivated by the frequently encountered problem of clutter-edge heterogeneity, we model the secondary data as a probability mixture and impose a hierarchical model for the inference problem. A two-stage CFAR detector structure is proposed. Empirical Bayesian inference is adopted in the first stage for training data selection followed by a CFAR processor using the identified homogeneous training set for target detection. One of the advantages of the proposed algorithm is its inherent adaptivity; i.e., the threshold setting is much less sensitive to the nonstationary environment compared with other standard CFAR procedures.