Langevin Diffusion for Population Based Sampling with an Application in Bayesian Inference for Pharmacodynamics

TL;DR

This paper introduces a novel sampling algorithm that combines Langevin diffusion with population-based methods to efficiently explore complex Bayesian posteriors, demonstrated on pharmacodynamics models with clinical data.

Contribution

The paper presents a new algorithm integrating Langevin diffusion with TMCMC, improving sampling efficiency and robustness for Bayesian inference, especially in unidentifiable models.

Findings

Superior to other population algorithms in gradient-available scenarios

Effectively handles unidentifiable models

Successfully applied to pharmacodynamics data

Abstract

We propose an algorithm for the efficient and robust sampling of the posterior probability distribution in Bayesian inference problems. The algorithm combines the local search capabilities of the Manifold Metropolis Adjusted Langevin transition kernels with the advantages of global exploration by a population based sampling algorithm, the Transitional Markov Chain Monte Carlo (TMCMC). The Langevin diffusion process is determined by either the Hessian or the Fisher Information of the target distribution with appropriate modifications for non positive definiteness. The present methods is shown to be superior over other population based algorithms, in sampling probability distributions for which gradients are available and is shown to handle otherwise unidentifiable models. We demonstrate the capabilities and advantages of the method in computing the posterior distribution of the parameters in a Pharmacodynamics model, for glioma growth and its drug induced inhibition, using clinical data.