Adaptive Rejection Sampling with fixed number of nodes

TL;DR

This paper introduces CARS, a novel adaptive rejection sampling method that maintains constant computational effort per sample, making it more efficient than traditional ARS for large sample sizes.

Contribution

The paper proposes CARS, an ARS variant with fixed computational cost per sample, improving efficiency for large-scale sampling tasks.

Findings

CARS achieves faster sampling than ARS for large sample sizes.

CARS maintains constant computational effort per sample.

CARS provides high acceptance rates similar to ARS.

Abstract

The adaptive rejection sampling (ARS) algorithm is a universal random generator for drawing samples efficiently from a univariate log-concave target probability density function (pdf). ARS generates independent samples from the target via rejection sampling with high acceptance rates. Indeed, ARS yields a sequence of proposal functions that converge toward the target pdf, so that the probability of accepting a sample approaches one. However, sampling from the proposal pdf becomes more computational demanding each time it is updated. In this work, we propose a novel ARS scheme, called Cheap Adaptive Rejection Sampling (CARS), where the computational effort for drawing from the proposal remains constant, decided in advance by the user. For generating a large number of desired samples, CARS is faster than ARS.