Xi'an's Og

I recently read the nice 2015 Series B paper of Polson and Scott on hierarchical duality that exposes a link between mixture and (Moreau) envelope representations of objective functions. In relation with several earlier papers and with Bayesian connections. Replacing an optimum with an integral is definitely interesting (to me) since it allows a priori for simulation-based substitutes and avoid numerical optimisation. (Which does not appear to be the point of the paper, aiming at optimisation by MAP derivations.) While the most general result finds an envelope representation for any multivariate log-likelihood with a Lipschitz continuous gradient, the scope does not seem to extend to the (private) settings I am interested in, but this proved a pleasant read!

This entry was posted on October 25, 2026 at 12:26 am and is filed under Books, Statistics with tags Bayesian optimisation, EM, envelope representations, Journal of the Royal Statistical Society, JRSS B, map, Moreau regularisation, NIck Polson, profile likelihood, proximal optimisation. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.