Predictively Oriented Posteriors

arXiv:2510.01915v3 Announce Type: replace-cross Abstract: We advocate for a new statistical principle that combines the most desirable aspects of both parameter inference and density estimation. This leads us to the predictively oriented (PrO) posterior, which expresses uncertainty as a consequence of predictive ability. We show that these posteriors converge to the predictively optimal model average and predictively dominate both classical and generalised Bayes posterior predictive distributions. Further, PrO posteriors adapt to the level of model misspecification: while they concentrate arou