Bayesian Approach for Confidence Intervals of Variance on the Normal Distribution

Table 3

The coverage probability (CP) and average width (AW) via 95% confidence interval.

		ML		Bayesian approach with prior distribution						MCMC		Wald
				Gamma		Chi-squared		Exponential
		CP	AW	CP	AW	CP	AW	CP	AW	CP	AW	CP	AW
2	10	0.9506	5.714	0.9657	—	0.9832	—	0.9669	—	0.9628	—	0.8538	—
	50	0.9531	1.706	0.9517	1.628	0.9614	—	0.9554	—	0.9568	—	0.9256	—
	100	0.9480	1.155	0.9495	1.129	0.9537	1.147	0.9500	1.146	0.9511	1.159	0.9381	—
	300	0.9467	0.649	0.9470	0.644	0.9495	0.647	0.9475	0.647	0.9479	0.649	0.9404	—
	500	0.9510	0.500	0.9505	0.498	0.9505	0.499	0.9504	0.499	0.9505	0.500	0.9483	0.496
	1000	0.9504	0.352	0.9516	0.351	0.9519	0.351	0.9517	0.351	0.9506	0.352	0.9500	0.350
6	10	0.9506	17.14	0.8865	—	0.9307	—	0.9346	—	0.9617	—	0.8538	—
	50	0.9531	5.118	0.9297	—	0.9442	—	0.9466	4.965	0.9562	—	0.9256	—
	100	0.9480	3.467	0.9397	—	0.9457	3.395	0.9476	3.415	0.9511	3.477	0.9381	—
	300	0.9467	1.947	0.9415	—	0.9445	—	0.9454	—	0.9478	1.949	0.9404	—
	500	0.9510	1.500	0.9495	1.490	0.9496	1.494	0.9499	1.496	0.9509	1.501	0.9483	1.488
	1000	0.9504	1.056	0.9500	1.052	0.9511	1.054	0.9515	1.054	0.9507	1.056	0.9500	1.051
12	10	0.9506	34.28	0.8607	—	0.9081	—	0.9241	—	0.9627	—	0.8538	—
	50	0.9531	10.23	0.9246	—	0.9384	—	0.9438	—	0.9567	—	0.9256	—
	100	0.9480	6.934	0.9379	—	0.9434	—	0.9459	6.820	0.9511	6.957	0.9381	—
	300	0.9467	3.894	0.9401	—	0.9435	—	0.9444	—	0.9482	3.898	0.9404	—
	500	0.9510	3.001	0.9489	2.978	0.9496	2.987	0.9498	2.991	0.9511	3.003	0.9483	2.976
	1000	0.9504	2.112	0.9488	2.104	0.9508	2.107	0.9512	2.109	0.9515	2.113	0.9500	2.103

Note. The appearance in AW denotes CP in the range of the fixed confidence interval between 0.9457 and 0.9542 and italics minimum of AW.