  Normal factor graph duality offers new possibilities for Monte Carlo
algorithms in graphical models. Specifically, we consider the problem of
estimating the partition function of the ferromagnetic Ising and Potts models
by Monte Carlo methods, which are known to work well at high temperatures, but
to fail at low temperatures. We propose Monte Carlo methods (uniform sampling
and importance sampling) in the dual normal factor graph, and demonstrate that
they behave differently: they work particularly well at low temperatures. By
comparing the relative error in estimating the partition function, we show that
the proposed importance sampling algorithm significantly outperforms the
state-of-the-art deterministic and Monte Carlo methods. For the ferromagnetic
Ising model in an external field, we show the equivalence between the valid
configurations in the dual normal factor graph and the terms that appear in the
high-temperature series expansion of the partition function. Following this
result, we discuss connections with Jerrum-Sinclair's polynomial randomized
approximation scheme (the subgraphs-world process) for evaluating the partition
function of ferromagnetic
