Bayes solutions for i.i.d. sampling from a decreasing density on the half line and for i.i.d. sampling from a symmetric unimodal density with an unknown mode are given. Posterior quantities are obtained as finite sums; Monte Carlo methods based on sampling finite Markov chains are developed for their evaluation.
"Bayes Methods for a Symmetric Unimodal Density and its Mode." Ann. Statist. 17 (4) 1550 - 1566, December, 1989. https://doi.org/10.1214/aos/1176347381