Table 4 Bayesian Wnt pathway from [1]

Bayesian Wnt pathway. Three static models have been developed based on particular gene set measured for human colorectal cancer cases [2]. Available epigenetic data for individual gene is also recorded. For sake of simplicity, the models are connoted as \(\mathcal {M}_{\text {PBK+EI}}\) (model with prior biological knowledge (PBK) and epigenetic information (EI)), \(\mathcal {M}_{\text {PBK}}\) (model with PBK only), and \(\mathcal {M}_{\text {NB+MPBK}}\) (model with naive Bayes (NB) formulation and minimal PBK). All models are simple directed acyclic graphs (DAG) with nodes and edges. Figure 2 shows a detailed influence diagram of \(\mathcal {M}_{\text {PBK+EI}}\) between the nodes and the edges. The nodes specify status of gene expression (D K K1, D K K2, D K K3-1, D K K3-2, D K K4, D A C T1, D A C T2, D A C T3, S F R P1, S F R P2, S F R P3, S F R P4, S F R P5, W I F1, MYC, C D44, C C N D1, and L E F1), methylation (M e D A C T1, M e D A C T2, M e S F R P1, M e S F R P2, M e S F R P4, M e S F R P5, M e D K K1, M e D K K4, and M e W I F1), histone marks for DACT3 (H3K27m e3 and H3K4m e3), transcription complex TRCMPLX, samples Sample and factors involved in formation of TRCMPLX like β-catenin, T C F4, and L E F1. Note that there were two recordings of gene expression D K K3 and thus were distinguished by D K K3−1 and D K K3−2. Some causal relations are based on prior biological knowledge and others are based on assumptions, elucidation of which follows in the next section.