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One application of Gibbs sampling useful in computational molecular biology is the detection and alignment of locally conserved regions (motifs) in sequences of amino acids or nucleic acids assuming no prior information in the patterns or motifs
Gibbs sampling strategies claim to be fast and sensitive, avoiding the problem that EM algorithms fall into as far as getting trapped by local optima
Gibbs sampling uses Monte Carlo sampling from the various prior, model, and predictive distributions indicated previously. The sampling is dependent (not pseudorandom) because the sampling at any iteration depends on the values in the previous iteration; however, the sampling procedure is known to converge on the desired posterior distribution.
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