Spline Interpolation on the Manifold of Probability Measures

In this chapter, we present an efficient and accurate algorithm for constructing a \(C^{2}\) Bézier spline that interpolates a given ordered set of data points on the space of probability measuresSpace of probability measures \(\mathcal {P}_{+}\) , equipped with the Fisher–Rao metric. The distinctive aspect of the proposed method lies in its exploration of the inherent Riemannian structure within the space of probability measures, making the solution computationally feasible.