<p>The geometry of statistical manifolds has its origin in information geometry, it is the study of just a Riemannian manifold equipped with a torsion-free affine connection satisfying the Codazzi equation. In Riemannian geometry, harmonic maps, critical points of the energy functional, are considered as one of the most important research subjects derived from the variation principle. Finding the corresponding subjects in the geometry of statistical manifolds has been a crucial task. However, it is difficult to generalize the energy functional for the statistical manifold setting. Therefore, the bi-energy functional for mappings between Riemannian manifolds is the functional that can be generalized on the mappings between statistical ones. In this paper, we present statistical biharmonic maps, a new class of mappings between statistical manifolds naturally derived from a variation problem. We give the Euler-Lagrange equation of this functional in the statistical setting. We illustrate examples of statistical biharmonic maps including improper affine hyperspheres. In the original Riemannian setting, it is known that the biharmonicity implies the harmonicity under certain conditions. We also give corresponding properties for statistical biharmonic mappings.</p>