Fast inverse transform sampling in one and two dimensions

TL;DR

This paper introduces a fast, robust inverse transform sampling algorithm for 1D and 2D smooth distributions using Chebyshev polynomial approximations, outperforming existing methods.

Contribution

The paper presents a novel polynomial approximation-based inverse transform sampling algorithm optimized for efficiency and robustness in low-dimensional spaces.

Findings

Outperforms existing sampling methods in speed and accuracy

Effective for a broad class of smooth probability distributions

Demonstrated robustness through numerical experiments

Abstract

We develop a computationally efficient and robust algorithm for generating pseudo-random samples from a broad class of smooth probability distributions in one and two dimensions. The algorithm is based on inverse transform sampling with a polynomial approximation scheme using Chebyshev polynomials, Chebyshev grids, and low rank function approximation. Numerical experiments demonstrate that our algorithm outperforms existing approaches.