Likelihood-based deviance information criterion (DIC) scores for 3 models compared in Experiment 1 are shown.

DIC has been computed from MCMC samples; preferred modelling hypotheses are characterized by lower DICs. The full causal model with confounders (M1) suggests causal relationship between 25-OHD and colorectal cancer and also models hidden confounding, causal model without confounders (M2) also proposes causal relationship, but hidden confounding is disregarded, and reverse model without confounders (M3) proposes that colorectal cancer leads to lower levels of 25-OHD, also ignoring hidden confounding. Digits after decimal point have been omitted from the table for clarity.Setting 1: precxt = 200, precx = 200, precy = 100; Setting 2: precxt = 1000, precx = 1000, precy = 0.1; Setting 3: precxt = 100, precx = 100, precy = 100. Sparsity parameter gamma is set to 0.025 in all models. In model with confounders (M1), precz = 1.**indicates the best model for each setting.