Basic PWM With Log-likelihoods
A PWM assumes independence between positions in the pattern, as it calculates scores at each position independently from the symbols at other positions. The score of a substring aligned with a PWM can be interpreted as the log-likelihood of the substring under a product multinomial distribution. Since each column defines log-likelihoods for each of the different symbols, where the sum of likelihoods in a column equals one, the PWM corresponds to a Multinomial distribution. A PWM's score is the sum of log-likelihoods, which corresponds to the product of likelihoods, meaning that the score of a PWM is then a product-multinomial distribution. The PWM scores can also be interpreted in a physical framework as the sum of binding energies for all nucleotides (symbols of the substring) aligned with the PWM.
Read more about this topic: Position-specific Scoring Matrix
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