Position weight matrices (PWMs) are the standard model for DNA and RNA regulatory motifs. In PWMs nucleotide probabilities are independent of nucleotides at other positions. Models that account for dependencies need many parameters and are prone to overfitting. We have developed a Bayesian approach for motif discovery using Markov models in which conditional probabilities of order k − 1 act as priors for those of order k. This Bayesian Markov model (BaMM) training automatically adapts model complexity to the amount of available data. We also derive an EM algorithm for de-novo discovery of enriched motifs. For transcription factor binding, BaMMs achieve significantly (P = 1/16) higher cross-validated partial AUC than PWMs in 97% of 446 ChIP-seq ENCODE datasets and improve performance by 36% on average. BaMMs also learn complex multipartite motifs, improving predictions of transcription start sites, polyadenylation sites, bacterial pause sites, and RNA binding sites by 26–101%. BaMMs never performed worse than PWMs. These robust improvements argue in favour of generally replacing PWMs by BaMMs.
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