I'm doing simple rejection sampling within the Approximate Bayesian Computation framework, and I use regression adjustments (i.e., non-parametric multiple linear regression) to get closer to the true posterior. For some datasets, the parameter values inferred are outside the prior range.
Is that making these analyzes invalid? It seems to me that from the point of view of the Bayesian inference, the prior belief is something important, that cannot be avoided. I would like to build my intuition here about this situation, any insight?
Clearly, the extrapolation made by the non-parametric multiple linear regression is less informed, and consequently, the extrapolation should be less accurate. But from a practical point of view, expending the prior range also potentially necessitate to increase the sampling size to get as accurate and re-do the calibration step where the model error was estimated using that first prior range.
