Abstract

July 1 - 16.50-17.40
J.Takeuchi, S. Amari - Alpha-parallel prior and its properties

It is known that the Jeffreys prior plays an important role in statistical inference. In this paper, we generalize the Jeffreys prior from the point of view of information geometry introducing a one-parameter family of prior distributions, which we named alpha-parallel priors. The alpha-parallel prior is defined as the parallel volume element with respect to the alpha-connection and coincides with the Jeffreys prior when alpha=0. Further, we analyze asymptotic behaviors of the various estimators such as the projected Bayes estimator (the estimator obtained by projecting the Bayes predictive density onto the original class of distributions) and the MDL estimator, when the alpha-parallel prior is used. The correction term due to the alpha-prior is shown to be regulated by an invariant vector field of the statistical model. Although the Jeffreys prior always exists, the existence of alpha-parallel prior with non-zero alpha is not always guaranteed. Hence we consider conditions for the existence of the alpha-parallel prior, elucidating the conjugate symmetry in a statistical model. [an error occurred while processing this directive]