Bayesian Approach for Confidence Intervals of Variance on the Normal Distribution

Table 2

The coverage probability (CP) and average width (AW) via 90% 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	0.9025	4.345	0.9456	—	0.9373	—	0.9512	—	0.9480	—	0.8196	—
	50	0.8994	1.407	0.9112	—	0.9220	—	0.9140	—	0.9151	—	0.8810	—
	100	0.8986	0.961	0.9084	—	0.9116	—	0.9097	—	0.9098	—	0.8924	—
	300	0.8930	—	0.8962	0.540	0.8981	0.543	0.8970	0.543	0.8958	0.545	0.8904	—
	500	0.8997	0.419	0.9019	0.417	0.9023	0.419	0.9021	0.419	0.9011	0.420	0.8990	0.416
	1000	0.9041	0.295	0.9052	0.294	0.9053	0.295	0.9052	0.295	0.9042	0.295	0.9028	0.294
6	10	0.9025	13.03	0.8522	—	0.9044	11.32	0.9094	—	0.9480	—	0.8196	—
	50	0.8994	4.222	0.8878	—	0.9021	4.117	0.9050	4.167	0.9151	—	0.8810	—
	100	0.8986	2.885	0.8958	2.807	0.9031	2.849	0.9049	2.866	0.9083	—	0.8924	—
	300	0.8930	—	0.8924	—	0.8942	1.623	0.8950	1.626	0.8952	1.635	0.8904	—
	500	0.8997	1.257	0.8995	1.250	0.9010	1.254	0.9011	1.255	0.9018	1.260	0.8990	1.248
	1000	0.9041	0.885	0.9027	0.883	0.9040	0.884	0.9045	0.885	0.9047	0.886	0.9028	0.882
12	10	0.9025	26.07	0.8229	—	0.8812	—	0.8982	24.05	0.9496	—	0.8196	—
	50	0.8994	8.446	0.8811	—	0.8974	—	0.9018	8.305	0.9157	—	0.8810	—
	100	0.8986	5.771	0.8915	—	0.9009	5.680	0.9031	5.723	0.9089	—	0.8924	—
	300	0.8930	—	0.8916	—	0.8932	—	0.8944	3.250	0.8955	3.171	0.8904	—
	500	0.8997	2.514	0.8988	2.499	0.9006	2.506	0.9010	2.510	0.9011	2.525	0.8990	2.497
	1000	0.9041	1.771	0.9023	1.766	0.9037	1.768	0.9039	1.770	0.9043	1.773	0.9028	1.765

Note. The appearance in AW denotes CP in the range of the fixed confidence interval between 0.8941 and 0.9058 and italics minimum of AW.