A General Purpose Approximation to the Ferguson-Klass Algorithm for Sampling from L\'evy Processes Without Gaussian Components

TL;DR

This paper introduces a fast, general-purpose approximation to the Ferguson-Klass algorithm for sampling from non-Gaussian Levy processes, enabling scalable Bayesian nonparametric modeling.

Contribution

It presents a novel approximation method that significantly speeds up Levy process sampling without sacrificing accuracy, expanding computational possibilities.

Findings

Over 1000 times faster than standard Ferguson-Klass algorithm

Maintains high precision in sampling

Facilitates scalable Bayesian nonparametric models

Abstract

We propose a general-purpose approximation to the Ferguson-Klass algorithm for generating samples from L\'evy processes without Gaussian components. We show that the proposed method is more than 1000 times faster than the standard Ferguson-Klass algorithm without a significant loss of precision. This method can open an avenue for computationally efficient and scalable Bayesian nonparametric models which go beyond conjugacy assumptions, as demonstrated in the examples section.