We consider the use of the Wiener system to perform nonlinear prediction. In this paper we propose a technique to retain the simplicity of the linear prediction by including a memoryless nonlinear function. The design of this later is approached from a Bayesian perspective: we look for the conditional mean of the predicted value, given the output of the linear predictor. Two techniques are proposed: the first one makes use of a closed form solution where some higher-order statistics are to be estimated. The second one is a direct sample estimate of the conditional mean given a data training set. The techniques are applied to improve the signal to noise ratio in the automatic detection of fire by infrared signal processing.