Table 4.

Ratio of MSEs for single Gibbs sampler (k = 4) to multiresolution sampler.

α MSE Ratio
	$\widehat{R}\pm \widehat{\text{sd}}(\widehat{R})$
Q0.05	120 ± 26
Q0.25	22 ± 5
Q0.5	8.8 ± 2.2
Q0.75	9.1 ± 2.3
Q0.95	87 ± 19

γ MSE Ratio
	$\widehat{R}\pm \widehat{\text{sd}}(\widehat{R})$
Q0.05	17 ± 4.4
Q0.25	5.8 ± 1.4
Q0.5	5.4 ± 1.2
Q0.75	6 ± 1.2
Q0.95	8.5 ± 1.6

β MSE Ratio
	$\widehat{R}\pm \widehat{\text{sd}}(\widehat{R})$
Q0.05	17 ± 4.6
Q0.25	4.2 ± 1.2
Q0.5	4.8 ± 1.2
Q0.75	7.2 ± 1.6
Q0.95	27 ± 4

σ MSE Ratio
	$\widehat{R}\pm \widehat{\text{sd}}(\widehat{R})$
Q0.05	26 ± 7
Q0.25	6.3 ± 1.3
Q0.5	3.2 ± 0.65
Q0.75	2.9 ± 0.55
Q0.95	3.3 ± 0.6

ρ MSE Ratio
	$\widehat{R}\pm \widehat{\text{sd}}(\widehat{R})$
Q0.05	60 ± 10
Q0.25	41 ± 8
Q0.5	21 ± 5
Q0.75	16 ± 3.8
Q0.95	14 ± 2.8