Table 2.

The results of running BayesMR on data generated from the model in Figure 14 for various degrees of nonlinearity, as parametrized by A (lower A corresponds to stronger nonlinearity).

	${\stackrel{\wedge }{\beta }}_{X\to Y}$
A	Q1	Median	Mean	Q3	$\stackrel{\wedge }{p}({\mathcal{M}}_{X\to Y}|\mathbf{D})$
0.5	0.260	0.289	0.276	0.309	$(0.744,0.880)$
1	0.494	0.511	0.500	0.530	$(0.817,0.919)$
2	0.739	0.758	0.737	0.786	$(0.821,0.921)$
4	0.906	0.921	0.927	0.940	$(0.780,0.900)$
8	0.970	0.985	0.992	1.003	$(0.815,0.918)$
16	0.990	1.006	1.011	1.025	$(0.776,0.899)$
32	0.991	1.009	0.996	1.028	$(0.827,0.924)$

Note: We report the 95% CI for the estimated probability that the direction of the causal link is $X\to Y$, as opposed to $Y\to X$. For the causal effect estimate ${\stackrel{\wedge }{\beta }}_{X\to Y}$, we report summary measures, including the first (Q1) and third quartiles (Q3).