We study a class of non-parametric density estimators under Bayesian settings. The estimators are obtained by adaptively partitioning the sample space. Under a suitable prior, we analyze the concentration rate of the posterior distribution, and demonstrate that the rate does not directly depend on the dimension of the problem in several special cases. Another advantage of this class of Bayesian density estimators is that it can adapt to the unknown smoothness of the true density function, thus achieving the optimal convergence rate without artificial conditions on the density. We also validate the theoretical results on a variety of simulated data sets.
Linxi Liu (Columbia University)
Dangna Li (Stanford University)
Wing Hung Wong (Stanford university)
Wing Hung Wong is currently Professor of Statistics and Professor of Biomedical Data Science at Stanford University. He had held teaching positions at the University of Chicago (1980-1994), The Chinese University of Hong Kong (1994-1997), UCLA (1997-2000) and Harvard University (2000-2004), before joining Stanford University in 2004. His research contributions include 1) mathematical statistics, where he clarified the large sample properties of sieve maximum likelihood estimates in general spaces; 2) Bayesian statistics, where he introduced sampling-based algorithms into Bayesian computational inference; and 3) computational biology, where he developed basic models and methods for the analysis of microarrays gene expression data and RNA sequencing data. He is a member of the US National Academy of Sciences, the Academia Sinica, and the Academy of Sciences of Hong Kong.
More from the Same Authors
2016 Poster: Density Estimation via Discrepancy Based Adaptive Sequential Partition »
Dangna Li · Kun Yang · Wing Hung Wong