Table 2:

Summarizing exposure weights in BKMR and the MIM. For BKMR we report posterior inclusion probabilities (PIPs) for each exposure. For MIM, we report the PIP for the entire index via ρ; we also summarize the distribution of weights θ conditional on $\hat{\rho }\ne 0$ (otherwise it is not well defined). Est is the posterior mean standardized to satisfy the constraints; CI is 95% credible interval.

		QGC		BKMR	BSIM (M=1)				BMIM-3 (M=3)
		Weights		${\hat{r}}_p$	${\hat{\rho }}_1$	${\hat{\theta }}_{1l}\mid {\hat{\rho }}_1\ne 0$			${\hat{\rho }}_m$	${\hat{\theta }}_{ml}\mid {\hat{\rho }}_m\ne 0$
Group	Exposure	Pos	Neg	PIP	PIP	PIP	Est	CI	PIP	PIP	Est	CI
1	PCB074		0.10	0.11	1.00	0.17	0.04	(−0.22, 0.58)	0.60	0.37	0.39	(−0.49, 1.00)
	PCB099	0.14		0.18		0.16	0.06	(−0.06, 0.60)		0.39	0.60	(−0.38, 1.00)
	PCB138		0.02	0.12		0.15	0.02	(−0.21, 0.37)		0.33	0.29	(−0.46, 1.00)
	PCB153	0.11		0.13		0.17	0.01	(−0.35, 0.48)		0.40	0.38	(−0.60, 1.00)
	PCB170		0.16	0.13		0.15	−0.02	(−0.35, 0.13)		0.37	0.25	(−0.62, 1.00)
	PCB180		0.29	0.13		0.17	−0.04	(−0.45, 0.21)		0.41	0.28	(−0.62, 1.00)
	PCB187		0.02	0.11		0.15	0.02	(−0.21, 0.41)		0.34	0.21	(−0.5, 0.99)
	PCB194	0.08		0.09		0.14	−0.01	(−0.32, 0.20)		0.36	0.28	(−0.53, 1.00)
2	PCB126	0.09		0.09		0.16	0.07	(−0.03, 0.67)	0.44	0.51	0.46	(−0.18, 1.00)
	PCB169	0.10		0.18		0.25	0.13	(−0.07, 0.85)		0.79	0.89	(0.00, 1.00)
3	PCB118	0.10		0.11		0.30	0.24	(−0.02, 0.91)	0.97	0.25	0.15	(−0.11, 0.94)
	Dioxin1	0.05		0.10		0.13	0.01	(−0.20, 0.30)		0.19	−0.02	(−0.48, 0.37)
	Dioxin2		0.11	0.09		0.14	−0.03	(−0.37, 0.07)		0.23	−0.04	(−0.61, 0.49)
	Dioxin3		0.16	0.07		0.11	−0.02	(−0.28, 0.02)		0.17	0.00	(−0.36, 0.41)
	Furan1	0.18		0.88		0.81	0.95	(0.00, 1.00)		0.82	0.98	(−0.12, 1.00)
	Furan2	0.02		0.10		0.16	0.05	(−0.13, 0.47)		0.21	0.06	(−0.44, 0.76)
	Furan3		0.14	0.11		0.15	0.05	(−0.05, 0.46)		0.24	0.08	(−0.38, 0.87)
	Furan4	0.14		0.21		0.11	0.01	(−0.11, 0.25)		0.22	0.11	(−0.3, 0.94)