On a prior based on the Wasserstein information matrix

TL;DR

This paper introduces a Wasserstein information matrix-based prior for univariate continuous distributions, invariant under reparameterisations, linking it to information geometry and demonstrating its good frequentist properties through simulations.

Contribution

It proposes a novel prior based on the Wasserstein information matrix, connecting it with information geometry and analyzing posterior propriety.

Findings

Posterior distributions exhibit good frequentist properties

Conditions for posterior propriety are established

The prior is invariant under reparameterisations

Abstract

We introduce a prior for the parameters of univariate continuous distributions, based on the Wasserstein information matrix, which is invariant under reparameterisations. We discuss the links between the proposed prior with information geometry. We present sufficient conditions for the propriety of the posterior distribution for general classes of models. We present a simulation study that shows that the induced posteriors have good frequentist properties.