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Speech recognition is formulated as a problem of maximum likelihood decoding. This formulation requires statistical models of the speech production process. In this paper, we describe a number of statistical models for use in speech recognition. We give special attention to determining the parameters for such models from sparse data. We also describe two decoding methods, one appropriate for constrained artificial languages and one appropriate for more realistic decoding tasks. To illustrate the usefulness of the methods described, we review a number of decoding results that have been obtained with them.