  Biological sequences may contain patterns that are signal important
biomolecular functions; a classical example is regulation of gene expression by
transcription factors that bind to specific patterns in genomic promoter
regions. In motif discovery we are given a set of sequences that share a common
motif and aim to identify not only the motif composition, but also the binding
sites in each sequence of the set. We present a Bayesian model that is an
extended version of the model adopted by the Gibbs motif sampler, and propose a
new centroid estimator that arises from a refined and meaningful loss function
for binding site inference. We discuss the main advantages of centroid
estimation for motif discovery, including computational convenience, and how
its principled derivation offers further insights about the posterior
distribution of binding site configurations. We also illustrate, using
simulated and real datasets, that the centroid estimator can differ from the
maximum a posteriori estimator.
