Established tests for proper calibration of multivariate density forecasts based on Rosenblatt probability integral transforms can be manipulated by changing the order of variables in the forecasting model. We derive order invariant tests. The new tests are applicable to densities of arbitrary...

We suggest to extend the stacking procedure for a combination of predictive densities, proposed by Yao et al in the journal Bayesian Analysis to a setting where dynamic learning occurs about features of predictive densities of possibly misspecified models. This improves the averaging process of...

We suggest to extend the stacking procedure for a combination of predictive densities, proposed by Yao, Vehtari, Simpson, and Gelman(2018), to a setting where dynamic learning occurs about features of predictive densities of possibly misspecified models. This improves the averaging process of...

Established tests for proper calibration of multivariate density forecasts based on Rosenblatt probability integral transforms can be manipulated by changing the order of variables in the forecasting model. We derive order invariant tests. The new tests are applicable to densities of arbitrary...