A power-prior posterior minimizing a weighted sum of Amari's alpha-divergences is exactly an alpha-geodesic between the no-borrowing and full-borrowing posteriors, with alpha controlling robustness.
(2004), The e-pca and m-pca: Dimension reduction of parameters by information geometry, in ‘2004 IEEE International Joint Conference on Neural Networks (IEEE Cat
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Generalized Power Priors for Improved Bayesian Inference with Historical Data
A power-prior posterior minimizing a weighted sum of Amari's alpha-divergences is exactly an alpha-geodesic between the no-borrowing and full-borrowing posteriors, with alpha controlling robustness.