  We prove the Bonnet theorem for statistical manifolds, which states that if a
statistical manifold admits tensors satisfying the Gauss--Codazzi--Ricci
equations, then it is locally embeddable to a flat statistical manifold (or a
Hessian manifold). The proof is based on the notion of statistical embedding to
the product of a vector space and its dual space introduced by Lauritzen. As
another application of Lauritzen's embedding, we show that a statistical
manifold admitting an affine embedding of codimension 1 or 2 is locally
embeddable to a flat statistical manifold of the same codimension.
