Mixtures, Envelopes and Hierarchical Duality
混合表示、包络表示与层级对偶
Summary We develop a connection between mixture and envelope representations of objective functions that arise frequently in statistics. We refer to this connection by using the term ‘hierarchical duality’. Our results suggest an interesting and previously underexploited relationship between marginalization and profiling, or equivalently between the Fenchel–Moreau theorem for convex functions and the Bernstein–Widder theorem for Laplace transforms. We give several different…