New Metric and Connections in Statistical Manifolds

Abstract: We define a metric and a family of $\alpha$-connections in statistical manifolds, based on $\varphi$-divergence, which emerges in the framework of $\varphi$-families of probability distributions. This metric and $\alpha$-connections generalize the Fisher information metric and Amari's $\alpha$-connections. We also investigate the parallel transport associated with the $\alpha$-connection for $\alpha=1$.