Evaluation with dynamic programming. The simple DP scheme computes all probability vectors Q0, Q1, Q2 completely within the green marked area, corresponding to score ranges of prefix PSSMs M
. In contrast to the simple scheme, the restricted probability computation method computes only the upper end of the probability distribution until the given p-value threshold is exceeded, omitting parts of the green area. In this example we show how to compute the score threshold (π, M) for PSSM M of length m = 3 and a score range of [4,11] corresponding to a given p-value threshold of π = . For simplicity we assume a uniform character distribution of f(A) = f(C) = f(G) = f(T) = . Cells of the matrix that are computed in the step actually under consideration are marked red. In step d = 0, see (A), the algorithm computes Q2(11) recursively for all paths through M that achieve a score of 11, i.e. Q2(11) = Q1(8)·f(G), Q1(8) = Q0(4)·f(G), Q0(4) = Q-1(0)·f(A) = 1·, since AGG is the only path achieving score 11. It follows Q2(11) = . In step d = 1 all paths achieving a score of 11 - d = 10 to determine Q2(10) are computed, see (B). We conclude Q2(10) = . In this step, DP allows to reuse value Q1(8) without recomputation. In step d = 2, see (C) values Q1(7) and Q0(3) can be reused to compute Q2(9) = . In step d = 2 the cumulated probability Q2(11) + Q2(10) + Q2(9) = exceeds the given p-value threshold of π = , and the restricted probability computation method skips the rest of the computation. We obtain a score threshold of th = 10 correponding to π.