We can directly sample from the conditional distribution of any log-affine model. The
algorithm is a Markov chain on a bounded integer lattice, and its transition
probability is the ratio of the UMVUE (uniformly minimum variance unbiased
estimator) of the expected counts to the total number of counts. The computation of
the UMVUE accounts for most of the computational cost, which makes the
implementation challenging. Here, we investigate an approximate algorithm that
replaces the UMVUE with the MLE (maximum likelihood estimator). Although it is
generally not exact, it is efficient and easy to implement; no prior study is required,
such as about the connection matrices of the holonomic ideal in the original
algorithm.
