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

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.

Data-driven prediction and origin identification of epidemics in population networks

“…Numerical error In this section, we describe the application of TMCMC to a simple example (sampling from a known distribution) where the error can be easily characterized. Further details on this analysis can be found in [ 45 ]. We first consider a d -dimensional multivariate Gaussian distribution with mean μ = 0 and a random covariance matrix Σ .…”

“…In this section, we describe the application of TMCMC to a simple example (sampling from a known distribution) where the error can be easily characterized. Further details on this analysis can be found in [ 45 ].…”

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