Langevin Diffusion for Population Based Sampling with an Application in Bayesian Inference for Pharmacodynamics
For practitioners of Bayesian inference in pharmacodynamics and other fields, this method improves sampling efficiency and handles unidentifiable models better than existing population-based algorithms.
The authors propose a hybrid MCMC algorithm combining Langevin diffusion with population-based TMCMC for efficient Bayesian posterior sampling, demonstrating superior performance on a pharmacodynamics model for glioma growth using clinical data.
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.