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For prokaryotic gene prediction much of the problem with obtaining high‐confidence training data can be circumvented by using a bootstrap gene‐prediction approach. This is possible in prokaryotes because of their simpler and more compact genomic structure: simpler in that long ORFs are usually long genes, and compact in that motif searches upstream usually range over hundreds of bases rather than thousands (as in human).

−1−2−3−4−4

TotalCounts(length5)/TotalCounts(length4)

Hash interpolated Markov model (hIMM) and gap/hash interpolated Markov model (ghIMM)1LL1L − 11L1L − 11L − 1L1L − 1

−1−2−3−4−5−5

−5−2−1−3−2−1

Or, in terms of Kullback–Leibler divergences, if

1 3.1 In ssss1, the Maximum Entropy Principle is introduced. Using the Lagrangian formalism, find a solution that maximizes on Shannon entropy subject to the constraint of the “probabilities” sum to one.

2 3.2 Repeat the Lagrangian optimization of (Exercise 3.1) subject to the added constraint that there is a mean value, E(X) = μ.