A novel partial order of concentration about a position is introduced and explored. It is designed as a criterion for comparing degrees of belief on a fixed position between two prior densities in Bayesian models. This order relates to stochastic orders of dispersion and peakedness, and owes its theoretical background to the definition of unimodality through a convex set. Fundamental properties and various examples are given.

informative prior, non-informative prior, stochastic largerness, unimodal function.