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In this paper, we introduce an automated Bayesian visual inspection framework for printed circuit board (PCB) assemblies, which is able to simultaneously deal with various shaped circuit elements (CEs) on multiple scales. We propose a novel hierarchical multi-marked point process model for this purpose and demonstrate its efficiency on the task of solder paste scooping detection and scoop area estimation, which are important factors regarding the strength of the joints. A global optimization process attempts to find the optimal configuration of circuit entities, considering the observed image data, prior knowledge, and interactions between the neighboring CEs. The computational requirements are kept tractable by a data-driven stochastic entity generation scheme. The proposed method is evaluated on real PCB data sets containing 125 images with more than 10 000 splice entities.