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This paper introduces an experimental paradigm for systematically generating increasingly hard instances for Bayesian networks inference. The approach allows us to control the level of difficulty of the Bayesian network inference problem, providing benchmark Bayesian networks for more systematic experimentation. We investigate two families of synthetic Bayesian networks, in which we study a few structural and distributional parameters and show how changing them (while maintaining network size) can change the hardness of the problem from a very simple inference problem to one that existing algorithms cannot handle. Among the parameters we study are the ratio of the number of root nodes to the number of non-root nodes in the network, the irregularity of the graph and the distributional nature of the conditional probability tables. The hardness of the networks is investigated experimentally using one of the most successful commercial inference algorithms, Hugin, along with a stochastic local search algorithm that we have developed, Stochastic Greedy Search. While both algorithms break down as the hardness of the problem increases we show that they vary significantly along some of the dimensions and that, surprisingly, the performance of the stochastic search algorithm degrades more gracefully in many cases.