Position-specific Scoring Matrix - Basic PWM With Log-likelihoods

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.