1. A distributed, reconfigurable statistical signal processing apparatus, comprising: an array of discrete-time analog signal processing circuits for statistical signal processing, wherein the analog signal processing circuits are arranged into a network such that each analog signal processing circuit is configured to communicate with neighboring analog signal processing circuits according to a local message-passing algorithm and wherein each analog signal processing circuit comprises: at least one computational element; and at least one digital configuration circuit, each digital configuration circuit being configured for programming a logic function implemented by the analog signal processing circuit; and a receiving module connected to the array of analog signal processing circuits, the receiving module being configured for assigning probability values when an input signal arrives at the array of analog signal processing circuits and for communicating the assigned probability values to at least a first one of the analog signal processing circuits in the array, wherein the computational elements are configured by the digital configuration circuits to produce outputs based on assigned probability values.