  One of the major problems in adaptive filtering is the problem of system
identification. It has been studied extensively due to its immense practical
importance in a variety of fields. The underlying goal is to identify the
impulse response of an unknown system. This is accomplished by placing a known
system in parallel and feeding both systems with the same input. Due to initial
disparity in their impulse responses, an error is generated between their
outputs. This error is set to tune the impulse response of known system in a
way that every change in impulse response reduces the magnitude of prospective
error. This process is repeated until the error becomes negligible and the
responses of both systems match. To specifically minimize the error, numerous
adaptive algorithms are available. They are noteworthy either for their low
computational complexity or high convergence speed. Recently, a method, known
as Markov Chain Monte Carlo (MCMC), has gained much attention due to its
remarkably low computational complexity. But despite this colossal advantage,
properties of MCMC method have not been investigated for adaptive system
identification problem. This article bridges this gap by providing a complete
treatment of MCMC method in the aforementioned context.
