  In this paper, we show analytically that the duality of normal factor graphs
(NFG) can facilitate stochastic estimation of partition functions. In
particular, our analysis suggests that for the $q-$ary two-dimensional
nearest-neighbor Potts model, sampling from the primal NFG of the model and
sampling from its dual exhibit opposite behaviours with respect to the
temperature of the model. For high-temperature models, sampling from the primal
NFG gives rise to better estimators whereas for low-temperature models,
sampling from the dual gives rise to better estimators. This analysis is
validated by experiments.
