  When an interval of integers between the lower bound $l_i$ and the upper
bound $u_i$ is the support of the marginal distribution $n_i|(n_{i-1},
...,n_1)$, Chen et al, 2005 noticed that sampling from the interval at each
step, for $n_i$ during a sequential importance sampling (SIS) procedure, always
produces a table which satisfies the marginal constraints. However, in general,
the interval may not be equal to the support of the marginal distribution. In
this case, the SIS procedure may produce tables which do not satisfy the
marginal constraints, leading to rejection Chen et al 2006. In this paper we
consider the uniform distribution as the target distribution. First we show
that if we fix the number of rows and columns of the design matrix of the model
for contingency tables then there exists a polynomial time algorithm in terms
of the input size to sample a table from the set of all tables satisfying all
marginals defined by the given model via the SIS procedure without rejection.
We then show experimentally that in general the SIS procedure may have large
rejection rates even with small tables. Further we show that in general the
classical SIS procedure in Chen et al, 2005 can have a large rejection rate
whose limit is one. When estimating the number of tables in our simulation
study, we used the univariate and bivariate logistic regression models since
under this model the SIS procedure seems to have higher rate of rejections even
with small tables.
