  The seemingly stochastic transient dynamics of neocortical circuits observed
in vivo have been hypothesized to represent a signature of ongoing stochastic
inference. In vitro neurons, on the other hand, exhibit a highly deterministic
response to various types of stimulation. We show that an ensemble of
deterministic leaky integrate-and-fire neurons embedded in a spiking noisy
environment can attain the correct firing statistics in order to sample from a
well-defined target distribution. We provide an analytical derivation of the
activation function on the single cell level; for recurrent networks, we
examine convergence towards stationarity in computer simulations and
demonstrate sample-based Bayesian inference in a mixed graphical model. This
establishes a rigorous link between deterministic neuron models and functional
stochastic dynamics on the network level.
