Introducing Causal Inference Using Bayesian Networks and do-Calculus

Figures & data

Fig. 1 The simplest DAG with two nodes and one edge.

Fig. 2 Two DAGs with three nodes.

Fig. 3 The DAG with one intervention node.

Fig. 4 The DAG of Example 1.

Fig. 5 Example 1 built in Netica.

Table 1 The contingency table of Sex and Pregnancy.

		Pregnancy
		Yes	No
Sex	Male	0	100
	Female	10	90

Table 2 The contingency table of Culture and Color.

		Color
		Black	Blue	Red
Culture	A	25	15	10
	B	5	10	35

Fig. 6 The DAG of Example 2.

Fig. 7 Example 2 built in Netica.

Table 3 Results of a clinical trial of medication treatment.

	Recovery
Treatment	Yes	No	Recovery Rate
Hospital A (40)
Medication	18	12	60%
Placebo	7	3	70%
Hospital B (40)
Medication	2	8	20%
Placebo	9	21	30%
Combined (80)
Medication	20	20	50%
Placebo	16	24	40%

Fig. 8 The DAG of Example 3.

Fig. 9 Example 3 built in Netica.

Table 4 The probability tables of Jen and Car.

Jen
Door 1	Door 2	Door 3
1/3	1/3	1/3
Car
Door 1	Door 2	Door 3
1/3	1/3	1/3

Fig. 10 The DAG of Example 4.

Fig. 11 Example 4 built in Netrica.

Table 5 The joint probability table of Jen, Car, and Host.

		Host
Jen	Car	Door 1	Door 2	Door 3
Door1	Door 1	0	1/2	1/2
Door 1	Door 2	0	0	1
Door 1	Door 3	0	1	0
Door 2	Door 1	0	0	1
Door 2	Door 2	1/2	0	1/2
Door 2	Door 3	1	0	0
Door 3	Door 1	0	1	0
Door 3	Door 2	1	0	0
Door 3	Door 3	1/2	1/2	0

Fig. 12 The DAG of Example 5.

Adapted from “Causal Inference in Introductory Statistics Courses,” by Cummiskey et al. 2020, Journal of Statistics Education, 28, p. 6 under the terms of the Creative Commons CC BY license.

Fig. 13 Example 5 built in Netica and intervention on Smoke only.

Fig. 14 The spurious relationship between Smoke and FEV in Example 5.

Fig. 15 Example 5 built in Netica and intervention on Smoke, Age, and Sex.

Fig. 16 The causal relationship between Smoke and FEV through Height in Example 5.

Fig. 17 The triangular substructures of the DAG of Example 5.

Cummiskey, K., Adams, B., Pleuss, J., Turner, D., Clark, N., and Watts, K. (2020), “Causal Inference in Introductory Statistics Courses,” Journal of Statistics Education, 28, 2–8. DOI: 10.1080/10691898.2020.1713936.

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