Nested Sampling with Constrained Hamiltonian Monte Carlo

TL;DR

This paper introduces a new implementation of nested sampling that leverages constrained Hamiltonian Monte Carlo to efficiently sample from complex, constrained probability distributions in Bayesian inference.

Contribution

It presents a novel integration of constrained Hamiltonian Monte Carlo into nested sampling, improving sampling efficiency for complex distributions.

Findings

Enhanced sampling efficiency in constrained spaces

Applicable to a wide range of Bayesian inference problems

Demonstrates improved computational performance

Abstract

Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian Monte Carlo is readily adapted to efficiently sample from any smooth, constrained distribution. Utilizing this constrained Hamiltonian Monte Carlo, I introduce a general implementation of the nested sampling algorithm.