Assessment of an MCMC algorithm convergence for Bayesian estimation of the particle size distribution from multiangle dynamic light scattering measurements

Recovering the particle size distribution (PSD) from dynamic light scattering (DLS) measurements is known to be a highly ill-posed inverse problem. In a former study, we proposed a new Bayesian inference method applied directly to the multiangle DLS measurements to improve the estimation of multimodal PSDs. The posterior probability density of interest is sampled using a MCMC Metropolis-within-Gibbs algorithm. In this work, we experimentally examined the convergence of the used MCMC strategy using the simulation method recently proposed by Chauveau and Vandekerkhove (2013). This method is based on the evolution in time (iterations) of the KullbackLeibler divergence between the target posterior density and the successive densities of the algorithm of interest. The convergence of the used MCMC algorithm was examined when processing simulated and experimental data.