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A significant challenge in this context is the large computational cost of simulating data from complex models, and the fact that this cost often depends on parameter values. We therefore propose \\textit{cost-aware SBI methods} which can significantly reduce the cost of existing sampling-based SBI methods, such as neural SBI and approximate Bayesian computation. This is achieved through a combination of rejection and self-normalised importance sampling, which significantly reduces the number of expensive simulations needed. 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