The characterization of brain activity has become a cornerstone of neuroscience to study cognition and neuropathologies. Here we focus on models of neural masses that aim to fit neurophysiological signals like EEG and MEG, in particular by optimizing interactions between brain regions, following previous work on the dynamic causal model (DCM) . We compare several modern Bayesian inference schemes for model inversion on simulated data . We benchmark the identifiability of local parameters governing the interplay between several neuronal populations in each region, as well as global parameters that relate to the connections between the cortical regions like weights and delays. We test the model inversion methods on MEG data to assess their similarities and differences with real data. Importantly we explore the role of anatomical connectivity as a prior in the Bayesian estimation. Our work provides a quantitative comparison between Bayesian methods in terms of estimation accuracy as well as required data size and computational power. David O, Kiebel SJ, Harrison LM, Mattout J, Kilner JM, Friston KJ (2006) Neuroimage, 30(4):1255-1272 Lemaréchal JD, George N, David O (2018) Neuroimage, 173:623-631 Hashemi M, Vattikonda AN, Jha J, Sip V, Woodman MM, Bartolomei F, Jirsa VK (2023) Neural Netw, 163:178-194 Gilson M, Zamora-López G, Pallarés V, Adhikari MH, Senden M, Campo AT, Mantini D, Corbetta M, Deco G, Insabato A (2020) Netw Neurosci, 4(2):338-373