How spiking networks are able to perform probabilistic inference is an intriguing question, not only for understanding information processing in the brain, but also for transferring these computational principles to neuromorphic silicon circuits. A number of computationally powerful spiking network models have been proposed, but most of them have only been tested, under ideal conditions, in software simulations. Any implementation in an analog, physical system, be it in vivo or in silico, will generally lead to distorted dynamics due to the physical properties of the underlying substrate. In this paper, we discuss several such distortive effects that are difficult or impossible to remove by classical calibration routines or parameter training. We then argue that hierarchical networks of leaky integrate-and-fire neurons can offer the required robustness for physical implementation and demonstrate this with both software simulations and emulation on an accelerated analog neuromorphic device.