Activity Number:
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198
- SPEED: Nonparametric Statistics: Estimation, Testing, and Modeling
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Type:
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Contributed
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Date/Time:
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Monday, July 30, 2018 : 11:35 AM to 12:20 PM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract #332806
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Title:
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Convergence Rates of a Partition Based Bayesian Multivariate Density Estimation Method
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Author(s):
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Linxi Liu* and Dangna Li and Wing Hung Wong
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Companies:
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Columbia University and Stanford University and Stanford University
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Keywords:
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density estimation;
posterior concentration rate;
adaptive partitioning
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Abstract:
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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.
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Authors who are presenting talks have a * after their name.