Incorporating Background Distribution
Instead of using log-likelihood values in the PWM, as described in the previous paragraph, several methods uses log-odds scores in the PWMs. An element in a PWM is then calculated as, where is the probability of observing symbol i at position j of the motif, and is the probability of observing the symbol i in a background model. The PWM score then corresponds to the log-odds of the substring being generated by the motif versus being generated by the background, in a generative model of the sequence.
Read more about this topic: Position-specific Scoring Matrix
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