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The capability of local smart sensing based on IoT devices is typically limited due to due to the inherent limitations of computational and storage capabilities. Recently, collaborative inference among multiple devices has been considered as an effective way to improve the sensing capabilities of individual IoT devices. However, the collaborative inference process still faces the challenges of data privacy leakage and inefficient collaboration. To alleviate the above issues, we design a blockchainbased collaborative inference system in this paper, called CoBC, which allows each heterogeneous device node on the blockchain to customize a personalized local machine learning model according to its own hardware constraint and performance, thus improving the efficiency of resource utilization of the whole system. Meanwhile, each device node only needs to complete training locally, which significantly reduces the risk of privacy leakage due to the remote transmission of local data. CoBC improves the sensing capability of single device nodes by using collaborative inference that can obtain a more robust global inference. In addition, CoBC employs a Bayesian approximation training approach to evaluate the output uncertainty of each device node to further improve the efficiency of collaborative inference. To evaluate the performance, we deploy CoBC in a real environment and conduct a large number of simulations to evaluate the efficiency of CoBC. The simulation results demonstrate that CoBC exhibits good performance and good practicality in various criteria.