Optional P\'{o}lya tree and Bayesian inference
Statistics Theory
2010-10-05 v1 Statistics Theory
Abstract
We introduce an extension of the P\'olya tree approach for constructing distributions on the space of probability measures. By using optional stopping and optional choice of splitting variables, the construction gives rise to random measures that are absolutely continuous with piecewise smooth densities on partitions that can adapt to fit the data. The resulting "optional P\'{o}lya tree" distribution has large support in total variation topology and yields posterior distributions that are also optional P\'{o}lya trees with computable parameter values.
Cite
@article{arxiv.1010.0490,
title = {Optional P\'{o}lya tree and Bayesian inference},
author = {Wing H. Wong and Li Ma},
journal= {arXiv preprint arXiv:1010.0490},
year = {2010}
}
Comments
Published in at http://dx.doi.org/10.1214/09-AOS755 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)