Computational Aspects of Optional Pólya Tree

Abstract

Optional Pólya tree (OPT) is a flexible nonparametric Bayesian prior for density estimation. Despite its merits, the computation for OPT inference is challenging. In this article, we present time complexity analysis for OPT inference and propose two algorithmic improvements. The first improvement, named limited-lookahead optional Pólya tree (LL-OPT), aims at accelerating 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 simulated and real date examples.