B0983
Title: Posterior concentration rate of a class of multivariate density estimators based on adaptive partitioning
Authors: Linxi Liu - University of Pittsburgh (United States) [presenting]
Wing Hung Wong - Stanford University (United States)
Abstract: 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 is as an extension of a companion work where the convergence rate of a related sieve MLE was established. Compared to the sieve MLE, the main advantage of the Bayesian method is that it can adapt to the unknown complexity of the true density function, thus achieving the optimal convergence rate without artificial conditions on the density.
