Bayesian Approach for Confidence Intervals of Variance on the Normal Distribution

Table 5

The interval width via 90%, 95%, and 99% confidence interval.

Confidence Interval Level (%)		Interval width of methods
		ML	Bayes’ with prior distribution			MCMC	Wald
			Gamma	Chi-squared	Exponential
90	10	30.486	31.334	37.219	41.268	54.133	47.741
	50	65.146	65.213	67.249	68.493	72.370	102.019
	100	62.380	62.402	63.356	63.931	65.351	97.686
	300	43.655	43.165	43.382	53.512	43.026	43.161
	500	33.652	33.425	33.526	33.585	34.607	33.423
	1000	26.154	26.066	26.105	26.128	26.065	26.002
95	10	36.326	37.337	44.350	49.173	64.503	59.260
	50	77.627	77.707	80.132	81.614	86.235	84.665
	100	74.330	74.356	75.494	76.178	77.871	77.579
	300	52.162	51.434	51.693	51.847	51.269	51.430
	500	40.165	39.828	39.948	40.020	41.237	39.826
	1000	31.190	31.059	31.106	31.134	30.984	30.059
99	10	47.741	49.069	58.286	64.625	84.772	99.590
	50	102.019	102.124	105.311	107.260	113.332	116.032
	100	97.686	97.721	99.215	100.116	102.340	104.075
	300	69.018	67.597	67.937	68.139	67.379	67.590
	500	53.001	52.344	52.501	52.595	54.194	52.341
	1000	41.074	40.819	40.880	40.917	40.720	40.018

Note. The shortest interval width is shown in bold font.