Multivariate Density Estimation via Adaptive Partitioning (II): Posterior Concentration

Understand

In this paper, we study a class of non-parametric density estimators under Bayesian settings.

• The estimators are piecewise constant functions on binary partitions.
• We analyze the concentration rate of the posterior distribution under a suitable prior, and demonstrate that the rate does not directly depend on the dimension of the problem.
• This paper can be viewed as an extension of a parallel work where the convergence rate of a related sieve MLE was established.