Table 3.

The results of running BayesMR on data generated from the model in Figure 14 for various degrees of nonnormality, as parametrized by the number of degrees of freedom of the t-distributed noise (lower ν corresponds to stronger nonnormality).

	${\stackrel{\wedge }{\beta }}_{X\to Y}$
ν	Q1	Median	Mean	Q3	$\stackrel{\wedge }{p}({\mathcal{M}}_{X\to Y}|\mathbf{D})$
1	–1.541	0.001	0.294	1.998	$(0.635,0.823)$
2	$0.904$	1.010	0.915	1.066	$(0.743,0.876)$
4	$0.990$	1.019	0.990	1.044	$(0.879,0.948)$
8	$1.013$	1.032	1.021	1.053	$(0.809,0.914)$
16	$0.998$	1.015	1.017	1.033	$(0.828,0.924)$
32	$0.983$	0.999	0.980	1.017	$(0.852,0.936)$
64	$1.007$	1.024	1.025	1.043	$(0.800,0.913)$

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).