Global optimization methods can be used to numerically determine optimal design parameters for an object. However, this does not by itself give a good appreciation of other parameter choices that may be almost as good and even preferable from other points of view. In the present paper, Markov-chain Monte Carlo methods are used to go beyond the optimal solution and create an ensemble of object models in parameter space that covers a set of favorable models uniformly. In direct analogy with applications to Bayesian inversion with determination of an unknown posterior probability density, projections of the model ensemble onto parameter axes and planes are used to exhibit parameter sensitivities and dependencies. Design of anechoic rubber coatings, with cylinder cavities having axes in a lateral direction, is considered as a particular application. The anechoic effect is evaluated by the efficient layer-multiple-scattering method, which is extended to handle cylinder scatterers of noncircular cross sections and mixed types. As anticipated by computed scattering and absorption cross sections for an isolated cavity, the favorable coatings have oblate cavity cross-section shapes, which is useful to achieve good low-frequency reflection reduction with a thin coating.