qreject

qreject is a term used in statistics and computer science to denote a family of rejection-sampling techniques and the accompanying open-source software framework designed to improve efficiency when drawing samples from complex probability distributions. The core idea of qreject is to construct quantile-based envelopes around a target distribution, enabling proposals to be accepted with higher probability and reducing the number of discarded samples compared with classical rejection sampling. The approach is applicable to both continuous and discrete distributions and is intended to integrate with existing probabilistic programming workflows.

The qreject project typically provides a reference implementation and documentation across multiple programming languages, along with examples and diagnostics. Key features often include an API for specifying the target density, generating proposals, and performing adaptive envelope updates as more samples are drawn. Additional utilities commonly present in implementations are acceptance-rate tracking, effective sample size estimates, and mechanisms to assess the quality of the sampling process. The design aims to be modular so that qreject can function as a standalone sampler or be embedded within larger inference pipelines.

In practice, qreject is used in Bayesian inference and other simulation-heavy contexts where efficient sampling from complex posteriors is important. It serves as a complementary option to methods such as importance sampling and Markov chain Monte Carlo, offering fast standalone sampling when a suitable envelope around the target distribution can be constructed. Related topics include rejection sampling, adaptive rejection sampling, and probabilistic programming.