Scalable random number generation for truncated log-concave distributions

TL;DR

This paper advocates for using Devroye's rejection sampling method for stable and efficient generation of random numbers from truncated log-concave distributions, especially in regression contexts.

Contribution

It demonstrates the advantages of Devroye's rejection sampling over inverse transform, promoting its use as a standard for log-concave distributions.

Findings

Rejection sampling with Devroye's method guarantees at least 20% acceptance rate.

The method is more stable than inverse transform sampling for truncated distributions.

Simulations with Tweedie distributions illustrate practical effectiveness.

Abstract

Inverse transform sampling is an exceptionally general method to generate non-uniform-distributed random numbers, but can be rather unstable when simulating extremely truncated distributions. Many famous probability models share a property called log-concavity, which is not affected by truncation, so they can all be simulated via rejection sampling using Devroye's approach. This sampler is based on rejection and thus more stable than inverse transform, and uses a very simple envelope whose acceptance rate is guaranteed to be at least 20\%. The aim of this paper is threefold: firstly, to warn against the risk of wrongly simulating from truncated distributions; secondly, to motivate a more extensive use of rejection sampling to mitigate the issues; lastly, to motivate Devroye's automatic method as a practical standard in the case of log-concave distributions. We illustrate the proposal by means of simulations based on some Tweedie distributions, for their relevance in regression analysis.