A distributed, reconfigurable statistical signal processing apparatus comprises an array of discrete-time analog signal processing circuitry for statistical signal processing based on a local message-passing algorithm and digital configuration circuitry for controlling the functional behavior of the array of analog circuitry. The input signal to the apparatus may be expressed as a probabilistic representation. The analog circuitry may comprise computational elements arranged in a network, with a receiving module that assigns probability values when an input signal arrives and communicates the probability values to one of the computational elements, the computational elements producing outputs based on the assigned probability values. The signal processing apparatus may be an analog logic automata cell or an array of cells, wherein each cell is able to communicate with all neighboring cells.