In this paper, we present a novel (empirical) observability Gramian for nonlinear stochastic systems in the light of Bayesian inference. First, we define our observability Gramian, which we refer to as the estimability Gramian, based on the relation to the so-called Bayesian Fisher Information Matrix for initial state estimation. Then, we study the fundamental properties of an empirical version of the estimability Gramian. The practical usefulness of the proposed framework is examined through its application to a parameter and initial state estimation in a natural gas engine cylinder.