We develop a mathematical modeling approach to evaluate the effectiveness of a Bayesian search for objects in cases where the target exhibits ancillary dependencies. These dependencies occur in situations where there are multiple search passes of the same region, and they represent a change in search probability from that predicted using an assumption of independent scans. This variation from independent scans is typically found in situations of advanced detection processing due to fusion and/or collaboration between searchers. The framework developed is based upon the evaluation of a recursion process over spatial search cells, and the dependencies appear as additive utility components within the recursion. We derive expressions for evaluating this utility and illustrate in detail some specific instantiations of the dependency. Computational examples are provided to demonstrate the capabilities of the method.
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