Automatic generation of non-uniform random variates for arbitrary pointwise computable probability densities by tiling

TL;DR

This paper introduces a fast, automatic rejection sampling method for generating non-uniform random variates from any pointwise computable probability density, including discontinuous ones, using recursive tiling and piecewise constant bounds.

Contribution

It presents a novel recursive tiling approach that efficiently generates random variates for arbitrary densities with minimal setup time and high independence from density computation.

Findings

Method is fast and unattended for densities with jumps and poles.

Setup time is short and scales linearly with table size.

Benchmarks show superior performance over similar rejection and transformation methods.

Abstract

We present a rejection method based on recursive covering of the probability density function with equal tiles. The concept works for any probability density function that is pointwise computable or representable by tabular data. By the implicit construction of piecewise constant majorizing and minorizing functions that are arbitrarily close to the density function the production of random variates is arbitrarily independent of the computation of the density function and extremely fast. The method works unattended for probability densities with discontinuities (jumps and poles). The setup time is short, marginally independent of the shape of the probability density and linear in table size. Recently formulated requirements to a general and automatic non-uniform random number generator are topped. We give benchmarks together with a similar rejection method and with a transformation method.