Can the calibration-discrimination decomposition of Brier score be viewed as the bias-variance decomposition of mean squared error?

Asked Nov 14 '23 at 18:35

Active Nov 28 '23 at 17:07

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The mean squared error has a famous decomposition into bias and variance.

$$ \text{MSE} = \text{bias}^2 + \text{var} $$

Brier score is also a mean squared error calculation, and Brier score has a decomposition into measure of how well the model is calibrated and how well the model can discriminate between categories.

Can these decompositions be related to each other?

edited Nov 28 '23 at 17:07

asked Nov 14 '23 at 18:35

Dave

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Consider this description https://rasbt.github.io/mlxtend/user_guide/evaluate/bias_variance_decomp/ – Ggjj11 Nov 28 '23 at 21:55
@Ggjj11 Could you please point to where that discusses calibration and discrimination? – Dave Nov 28 '23 at 22:01

Can the calibration-discrimination decomposition of Brier score be viewed as the bias-variance decomposition of mean squared error?

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