Langevin Diffusion Transitional Markov Chain Monte Carlo with an Application to Pharmacodynamics

We propose an algorithm for the sampling of the posterior distribution in Bayesian inference problems. The algorithm builds on the Transitional Markov Chain Monte Carlo (TMCMC) method with independent MC chains following the manifold Metropolis Adjusted Langevin transition kernels (mMALA). The algorithm combines the advantages of population based sampling algorithms -- global exploration of the parameter space, parallelizability, reliable estimator of evidence -- with the advantages of Langevin diffusion based Metropolis-Hastings MCMC -- efficient exploration of local space. Here, we use a bias free version of the TMCMC algorithm, namely the BASIS algorithm. We show that the proposed sampling scheme outperforms the existing algorithm in a test case of multidimensional Gaussian mixtures and the posterior distribution of a Bayesian inference problem in an 8 dimensional pharmacodynamics model.