Before revision:  As the latter, our new wald space also involves disconnected forests, it does not contain certain singularities of the latter, though. The geometry of wald spaceis that of the Fisher information metric of character distributions , either from a discrete Bernoulli or from a continuous Gaussian model.
After revision:  As the latter, our new wald space also involves disconnected forests, it does not contain certain singularities of the EP space. We investigate two related geometries on wald space. The first is the geometry of the Fisher information metric of character distributions , either from a discrete Bernoulli or from a continuous Gaussian model.