@article{oai:nagoya.repo.nii.ac.jp:00003880,
 author = {Ikeda, Mitsuru and 池田, 充 and Ishigaki, Takeo and 山内, 一信 and Yamauchi, Kazunobu},
 issue = {3},
 journal = {Computer Methods and Programs in Biomedicine},
 month = {Mar},
 note = {If we consider the Brier Score (B) in the context of the signal detection theory and assume that it makes sense to consider the existence of B as a parameter for the population (let B be this B), and if we assume that the calibration in the observer's probability estimate is perfect, we find that there is a theoretical relationship between B and the area under the binormal receiver operating characteristic (ROC) curve, AZ. We have derived this theoretical functional relationship between B and AZ, by using the parameter a and b in the binormal ROC model and the prior probability of signal events (α); here, the two underlying normal distributions are N(μs ,σs) and N(μn,σn); and, a = (μs - μn)/σs and b = σn/σs . We empirically found that, if parameters b and α are constant, B values in relation to given AZ values monotonically decrease as AZ values increase, and these relationship curves have monotonically decreasing slopes.},
 pages = {187--194},
 title = {Relationship between Brier score and area under the binormal ROC curve},
 volume = {67},
 year = {2002}
}