  Extended sources of the stochastic gravitational backgrounds have been
conventionally searched on the spherical harmonics bases. The analysis during
the previous observing runs by the ground-based gravitational wave detectors,
such LIGO and Virgo, have yielded the constraints on the angular power spectrum
$C_\ell$, yet it lacks the capability of estimating model parameters. In this
paper, we introduce an alternative Bayesian formalism to search for such
stochastic signals with a particular distribution of anisotropies on the sky.
This approach provides a Bayesian posterior of model parameters and also
enables selection tests among different signal models. While the conventional
analysis fixes the highest angular scale \textit{a priori}, here we show a more
systematic and quantitative way to determine the cut-off scale based on a Bayes
factor, which depends on the amplitude and the angular scale of observed
signals. Also, we analyze the third observing runs of LIGO and Virgo for the
population of milli-second pulsars and obtain the 95 % constrains of the signal
amplitude, $\epsilon < 2.7\times 10^{-8}$.
