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We present a flexible stochastic model for a class of cooperative wireless relay networks, in which the relay processing functionality is not known at the destination. In addressing this problem, we develop efficient algorithms to perform relay identification in a wireless relay network. We first construct a statistical model based on a representation of the system using Gaussian processes (GPs) in a nonstandard manner due to the way we treat the imperfect channel-state information. We then formulate the estimation problem to perform system identification, taking into account complexity and computational efficiency. Next, we develop a set of three algorithms to solve the identification problem, each of decreasing complexity, trading off the estimation bias for computational efficiency. The joint optimization problem is tackled through a Bayesian framework using the iterated conditioning on the modes (ICM) methodology. We develop a lower bound and several suboptimal computationally efficient solutions to the identification problem for comparison. We illustrate the estimation performance of our methodology for a range of widely used relay functionalities. The relative total error attained by our algorithm compared to the lower bound is found to be at worst 9% for low signal-to-noise ratio values under all functions considered. The effect of the relay functional estimation error is also studied through BER simulations and is shown to be less than 2 dB worse than the lower bound.