Bernstein-Type Bounds for Beta Distribution

This work obtains a sharp closed-form exponential concentration inequality of Bernstein type for the ubiquitous beta distribution, improving upon sub-gaussian and sub-gamma bounds previously studied in this context. The proof leverages the novel and handy recursion of order 2 for central moments of the beta distribution, obtained from hyper-geometric representations; this recursion is useful for obtaining explicit expressions for central moments, as well as for developing their various approximations.