Inhomogeneous PMM of order 2.

Figure a) shows the general dependency structure among the random variables (positions in the motif). Each nucleotide depends here on its two predecessors. At each position, the conditional probability table may be further reduced by a parsimonious context tree. Figure b) shows a minimal PCT of depth 2, which is locally equivalent to a PWM model, since all contexts are merged. Figure c) shows an intermediate PCT of depth 2. The PCT encodes five sets of context sequences: {AA}, {CA,GA}, {TA}, {AC,AG,AT,GC,GG,GT}, and {CC,CG,CT,TC,TG,TT}. If we assume that this tree is used at position 4 in the motif, the nodes are colored according to the random variables they correspond to in the backbone of Figure a). Figure d) shows a maximal PCT of depth 2, which is locally equivalent to an inhomogeneous Markov model of order 2, since none of the contexts are merged.