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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