  Computing partition functions, the normalizing constants of probability
distributions, is often hard. Variants of importance sampling give unbiased
estimates of a normalizer Z, however, unbiased estimates of the reciprocal 1/Z
are harder to obtain. Unbiased estimates of 1/Z allow Markov chain Monte Carlo
sampling of "doubly-intractable" distributions, such as the parameter posterior
for Markov Random Fields or Exponential Random Graphs. We demonstrate how to
construct unbiased estimates for 1/Z given access to black-box importance
sampling estimators for Z. We adapt recent work on random series truncation and
Markov chain coupling, producing estimators with lower variance and a higher
percentage of positive estimates than before. Our debiasing algorithms are
simple to implement, and have some theoretical and empirical advantages over
existing methods.
