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Latent variable decomposition permits factorisation of posterior probability based, or likelihood based, speech unit discriminant functions into a composition of simpler functions which can be analysed separately and evaluated more accurately in the presence of band-limited noise, or other source of data mismatch. See [2,7] for a more self contained introduction to this subject. In this report we present the essential theoretical issues, and implementation details, for the key points concerning this approach to multiband ASR. In particular, we show that the posteriors and likelihood based multiband decompositions are very closely linked.