6,839 research outputs found
Computational Aspects of Optional P\'{o}lya Tree
Optional P\'{o}lya Tree (OPT) is a flexible non-parametric Bayesian model for
density estimation. Despite its merits, the computation for OPT inference is
challenging. In this paper we present time complexity analysis for OPT
inference and propose two algorithmic improvements. The first improvement,
named Limited-Lookahead Optional P\'{o}lya Tree (LL-OPT), aims at greatly
accelerate the computation for OPT inference. The second improvement modifies
the output of OPT or LL-OPT and produces a continuous piecewise linear density
estimate. We demonstrate the performance of these two improvements using
simulations
Regression tree models for designed experiments
Although regression trees were originally designed for large datasets, they
can profitably be used on small datasets as well, including those from
replicated or unreplicated complete factorial experiments. We show that in the
latter situations, regression tree models can provide simpler and more
intuitive interpretations of interaction effects as differences between
conditional main effects. We present simulation results to verify that the
models can yield lower prediction mean squared errors than the traditional
techniques. The tree models span a wide range of sophistication, from piecewise
constant to piecewise simple and multiple linear, and from least squares to
Poisson and logistic regression.Comment: Published at http://dx.doi.org/10.1214/074921706000000464 in the IMS
Lecture Notes--Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
- …