Embodiments of the invention relate to a scalable neural hardware for the noisy-OR model of Bayesian networks. One embodiment comprises a neural core circuit including a pseudo-random number generator for generating random numbers. The neural core circuit further comprises a plurality of incoming electronic axons, a plurality of neural modules, and a plurality of electronic synapses interconnecting the axons to the neural modules. Each synapse interconnects an axon with a neural module. Each neural module receives incoming spikes from interconnected axons. Each neural module represents a noisy-OR gate. Each neural module spikes probabilistically based on at least one random number generated by the pseudo-random number generator unit.