Table 1 True distributions and nonflat prior base measures for fixed-parameter experiments. In all cases, c ∗=c 0=0.5, and q ∗ and q 0 are obtained from p ∗ and p 0, respectively, by flipping left to right (see text.)
From: Bayesian estimation of the discrete coefficient of determination
True distribution | Base measure 1 | Base measure 2 | Base measure 3 | |
|---|---|---|---|---|
d=1 | p ∗ = (0.6,0.4) | \({\mathbf p}_{0}^{1} \,=\, (0.6,0.4)\) | \({\mathbf p}_{0}^{2} \,=\, (0.5,0.5)\) | \({\mathbf p}_{0}^{3} \,=\, (0.4,0.6)\) |
d=2 | p ∗ = (0.2,0.3,0.1,0.4) | \({\mathbf p}_{0}^{1} \,=\, (0.2,0.3,0.1,0.4)\) | \({\mathbf p}_{0}^{2} \,=\, (0.3,0.2,0.2,0.3)\) | \({\mathbf p}_{0}^{3} \,=\, (0.4,0.1,0.3,0.2)\) |
d=3 | p ∗ = (0.1,0.15,0.05,0.2, | \({\mathbf p}_{0}^{1} \,=\, (0.1,0.15,0.05,0.2,\) | \({\mathbf p}_{0}^{2} \,=\, (0.15, 0.1, 0.1, 0.15,\) | \({\mathbf p}_{0}^{3} \,=\, (0.2, 0.05, 0.15, 0.1,\) |
0.15,0.1,0.1,0.15) | 0.15,0.1,0.1,0.15) | 0.1,0.05,0.15,0.2) | 0.05,0.2,0.2,0.05) | |
Matched prior | Poorly matched prior | Mismatched prior |