  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.
