A speech processing method and arrangement are described. A dynamic noise adaptation (DNA) model characterizes a speech input reflecting effects of background noise. A null noise DNA model characterizes the speech input based on reflecting a null noise mismatch condition. A DNA interaction model performs Bayesian model selection and re-weighting of the DNA model and the null noise DNA model to realize a modified DNA model characterizing the speech input for automatic speech recognition and compensating for noise to a varying degree depending on relative probabilities of the DNA model and the null noise DNA model.