In this paper we develop different mathematical models in the framework of the multi-stream paradigm for noise robust ASR, and discuss their close relationship with human speech perception. Largely inspired by Fletcher's "product-of-errors" rule in psychoacoustics, multi-band ASR aims for robustness to data mismatch through the exploitation of spectral redundancy, while making minimum assumptions about noise type. Previous ASR tests have shown that independent sub-band processing can lead to decreased recognition performance with clean speech. We have overcome this problem by considering every combination of data sub-bands as an independent data stream. After introducing the background to multi-band ASR, we show how this "full combination" approach can be formalised, in the context of HMM/ANN based ASR, by introducing a latent variable to specify which data sub-bands in each data frame are free from data mismatch. This enables us to decompose the posterior probability for each phoneme into a reliability weighted integral over all possible positions of clean data. This approach offers great potential for adaptation to rapidly changing and unpredictable noise.