Concentration of Posterior Model Probabilities and Normalized L0 Criteria

We study frequentist properties of Bayesian and $L_0$ model selection, with a focus on (potentially non-linear) high-dimensional regression. propose construction to how posterior probabilities normalized criteria concentrate the (Kullback-Leibler) optimal other subsets space. When such concentration occurs, one also bounds selecting correct model, type I II errors. These results hold generally, help validate use control error associated selection hypothesis tests. Regarding regression, we understand effect sparsity imposed by prior or penalty, problem characteristics as sample size, signal-to-noise, dimension true sparsity. A particular finding is that may less sparse formulations than would be asymptotically optimal, but still attain consistency often significantly better finite-sample performance. prove new related misspecifying mean covariance structures, give tighter rates for certain non-local priors currently available.