Free energy biased sampling and mixture modelling

It is a pleasure to present this discussion of Chopin and Jacob (2010), which has been influenced by reading in parallel the recent paper by Chopin, Lelièvre and Stoltz (2010). This gives more detail on free-energy biasing, and applies it in the context of Markov chain Monte Carlo, and is also illustrated by applications to mixture modelling. My discussion focuses on the general ideas of free energy biased sampling (FEBS), including estimation of the free energy, and on comparisons of the different impact of FEBS on sequential Monte Carlo and Markov chain Monte Carlo. Turning to the mixtures application, I will give my own views on the label switching issue. Finally, I will comment on the prospects for wider use of FEBS in Monte Carlo methods for Bayesian computation.