I resume former discussions of the question whether a General Relativistic configuration with two aligned axisymmetric black holes in vacuum can be in equilibrium. To answer the question I formulate a boundary value problem for two separate (Killing-) horizons in axisymmetry and stationarity and apply th e inverse scattering method to solve it. Finally, I use a universal inequality for sub-extremal black holes and the positive mass theorem to show that two (sub-extremal or degenerate) black holes cannot be in equilibrium.

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For a normal model with a conjugate prior, we investigate the effects of the hyperparameters on the long-run frequentist properties of posterior point and interval estimates. Under an assumed sampling model for the data generating mechanism, we develop two types of hyperpararameter optimality. Mean squared error (MSE) optimal
hyperparameters minimize the MSE of posterior point estimates. Credible interval optimal hyperparameters result in credible intervals that have minimum length while still retaining nominal coverage. We give an example to demonstrate how to use our results to guide the selection of hyperparameters.

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