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