Position weight matrix - Wikipedia

Abstraction: Matrix representation of biological sequence motifs using position-specific log-odds scores

Key points:

• Built from aligned sequences: count occurrences of each nucleotide/amino acid at each position (PFM), normalize to get probabilities (PPM), then convert to log-odds vs. background (PWM)
• PWM elements are log(p_ij / b_i) where b_i is background frequency; sequence score is sum of position log-odds, making log-likelihood calculation additive rather than multiplicative
• Pseudocounts (Laplace estimators) applied to avoid zero-probability entries when training data is small; equivalent to using a Dirichlet prior per position
• Assumes statistical independence between positions — each column is an independent multinomial distribution
• Information content (IC) of a PWM quantifies how different the motif is from background, using KL divergence; high IC columns are highly conserved positions
• Extensions: PSSM with insertion/deletion probabilities = profile hidden Markov model (approach used by Pfam)

Connections: Pfam · Position Weight Matrix · Bioinformatics · Sequence Motifs · Information Theory

Source: http://en.wikipedia.org/wiki/Position_weight_matrix