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The polynomial segment model (PSM), which was first proposed in Gish et al. (1993) and subsequently studied by other researchers, has opened up an alternative research direction for speech recognition. In PSM, speech frames within a segment are jointly modeled such that any change in the boundaries of a segment would require the re-computation of the likelihood of all the frames within the segment. While estimation of the best segment boundaries are possible, the computation consideration typically constrains the PSM model to limit the search to center around some pre-segmentation typically obtained by using another model such as an HMM, in effect limiting the possibility of using PSM itself. In this paper we introduce a new approach to evaluate the likelihood of a PSM segment by efficiently "accumulating" segment likelihood incrementally, i.e. one frame at a time. Based on this incremental likelihood evaluation, an efficient PSM search and training algorithm are also introduced. We show the effectiveness of the incremental likelihood evaluation by building a PSM-based TIMIT recognition system (both training and test) without the need of using another model for pre-segmentation.