Application of Multiple-Block MCMC to a Mixture Distribution with Multi-Modal Likelihood

DOI: 10.5176/2251-1911_CMCGS18.21

Authors: Ariane Würbach

Abstract: MCMC methods have widely proven their applicability in settings with non-standard likelihoods. In particular the random-walk Metropolis (RWM) algorithm is promising since it is capable to sufficiently explore the whole parameter space. By design, the RWM algorithm makes random steps at each iteration and is therefore less likely to stick at a certain mode. To gain efficiency, multiple-block (MB-RWM) schemes are recommended [4]. Further advantage is expected from using randomized multiple-block (RMB-RWM) schemes [5]. To verify these findings from the literature, four different RWM schemes are applied to a complex mixture model. In the general heaping model, the underlying zero-inflated log-normal distribution, which accounts for the true but unobserved values, and the supposed heaping mechanism, that describes the response behavior, form a multi-modal likelihood [37]. This model was applied to self-reported income data in the German National Educational Panel Study. All four RWM specifications are compared according to their accuracy and efficiency by graphical inspection and the inefficiency factor. Results from a simulation study show that in the considered case estimates are better and more efficiently approximated by either MB-RWM or RMB-RWM schemes.

Keywords: random-walk Metropolis algorithm; (randomized) multiple-block scheme; inefficiency factor; heaping