# (Un)Conditional Sample Generation Based on Distribution Element Trees

@article{Meyer2018UnConditionalSG, title={(Un)Conditional Sample Generation Based on Distribution Element Trees}, author={Daniel W. Meyer}, journal={Journal of Computational and Graphical Statistics}, year={2018}, volume={27}, pages={940 - 946} }

ABSTRACT Recently, distribution element trees (DETs) were introduced as an accurate and computationally efficient method for density estimation. In this work, we demonstrate that the DET formulation promotes an easy and inexpensive way to generate random samples similar to a smooth bootstrap. These samples can be generated unconditionally, but also, without further complications, conditionally using available information about certain probability-space components. This article is accompanied by…

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## References

SHOWING 1-10 OF 22 REFERENCES

Density estimation with distribution element trees

- Computer ScienceStat. Comput.
- 2018

A new method that is based on a decomposition of the unknown distribution in terms of so-called distribution elements (DEs) that enable an adaptive and hierarchical discretization of the sample space with small or large elements in regions with smoothly or highly variable densities, respectively.

Optional P\'{o}lya tree and Bayesian inference

- Mathematics, Computer Science
- 2010

This work introduces an extension of the Polya tree approach for constructing distributions on the space of probability measures that gives rise to random measures that are absolutely continuous with piecewise smooth density on partitions that can adapt to fit the data.

Computational Aspects of Optional Pólya Tree

- Computer ScienceJournal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
- 2016

The first improvement, named limited-lookahead optional Pólya tree (LL-OPT), aims at accelerating the computation for OPT inference and the second improvement modifies the output of OPT or LL-opT and produces a continuous piecewise linear density estimate.

Density estimation trees

- Computer Science, MathematicsKDD
- 2011

DETs empirically exhibit the interpretability, adaptability and feature selection properties of supervised decision trees while incurring slight loss in accuracy over other nonparametric density estimators, suggesting they might be able to avoid the curse of dimensionality if the true density is sparse in dimensions.

Markov Chain Sampling Methods for Dirichlet Process Mixture Models

- Mathematics
- 2000

Abstract This article reviews Markov chain methods for sampling from the posterior distribution of a Dirichlet process mixture model and presents two new classes of methods. One new approach is to…

Bootstrap technology and applications

- Computer Science
- 1992

Some bootstrap resampling methods are reviewed, emphasizing applications through illustrations with some real data, and special attention is given to regression, problems with dependentData, and choosing tuning parameters for optimal performance.

Bootstrap choice of the smoothing parameter in kernel density estimation

- Business
- 1989

SUMMARY Cross-validation based on integrated squared error has already been applied to the choice of smoothing parameter in the kernel method of density estimation. In this paper, an alternative…

Nonparametric multivariate density estimation using mixtures

- MathematicsStat. Comput.
- 2015

A new method is proposed for nonparametric multivariate density estimation, which extends a general framework that has been recently developed in the univariate case based onNonparametric and semiparametric mixture distributions, and performs remarkably better than kernel-based density estimators.

A Bayesian Analysis of Some Nonparametric Problems

- Mathematics
- 1973

Bayesian approach remained rather unsuccessful in treating nonparametric problems. This is primarily due to the difficulty in finding workable prior distribution on the parameter space , which in…

Bootstrap Methods: Another Look at the Jackknife

- Mathematics
- 1979

We discuss the following problem given a random sample X = (X 1, X 2,…, X n) from an unknown probability distribution F, estimate the sampling distribution of some prespecified random variable R(X,…