Bayesian models have been successful in explaining sensorimotor behavior in humans and animals, yet it remains unclear whether they can also explain neural activity. Testing them using neural data is complicated by the fact that linking them to neural activity requires two key moving parts: (1) a hypothesis about which latent variable is represented by a neuron, or neural population (``generative model'') and (2) a hypothesis about how beliefs about a latent variable (``posterior'') are represented by neural responses. Here, we present two new methods that in conjunction allow us to, first, falsify the generative model without making any assumption about the representation and, then, given a generative model, test whether the representation is compatible with a neural sampling code (NSC), and if not, whether it is linear distributional like a distributed distributional code (DDC), or whether it is nonlinear like a probabilistic population code (PPC). Briefly, the first (``Metamer'') method, tests whether the neural responses and posteriors share the same invariances in stimulus space, i.e. whether two different stimuli that imply the same posterior also entail the same neural response. This test only relies on the same posterior being represented by the same response, and holds regardless of whether the representation is a NSC, DDC or PPC. The second method is an extension of representational similarity analysis (RSA). It tests whether the relationships between the posteriors for different stimuli match the relationships between the neural responses to the same stimuli. Applied to the entire (stochastic) response distribution for each stimulus, these relationships among model posterior, and among neural response distributions, are only expected to match for a NSC. When applied to the average neural response to each stimulus, they are expected to match for both NSCs and DDCs, but not for PPCs. Finally, we illustrate our method using a recently proposed Bayesian model of motion processing.