  For a Gaussian time series with long-memory behavior, we use the FEXP-model
for semi-parametric estimation of the long-memory parameter $d$. The true
spectral density $f_o$ is assumed to have long-memory parameter $d_o$ and a
FEXP-expansion of Sobolev-regularity $\be > 1$. We prove that when $k$ follows
a Poisson or geometric prior, or a sieve prior increasing at rate
$n^{\frac{1}{1+2\be}}$, $d$ converges to $d_o$ at a suboptimal rate. When the
sieve prior increases at rate $n^{\frac{1}{2\be}}$ however, the minimax rate is
almost obtained. Our results can be seen as a Bayesian equivalent of the result
which Moulines and Soulier obtained for some frequentist estimators.
