  Motivated by the experimental accessibility of rare $B$ decays in the ongoing
and planned experiments, we propose to undertake a model-independent analysis
of the inclusive decay rates and distributions in the processes \bgamaxs~ and
\Bsell ~($B=B^\pm$ or $B^0_d$). We show how measurements of the decay rates and
distributions in these processes would allow us to extract the magnitude and
sign of the dominant Wilson coefficients of the magnetic moment operator $\mb
\bar{s}_L \sigma_{\mu \nu} b_R F^{\mu \nu }$ and the four-fermion operators
$(\bar{s}_L \gamma_\mu b_L)(\bar{\ell} \gamma^{\mu} \ell)$ and $(\bar{s}_L
\gamma_\mu b_L)(\bar{\ell} \gamma^{\mu}\gamma^5 \ell)$. Non-standard-model
effects could thus manifest themselves at low energy in rare $B$ decays through
the Wilson coefficient having values distinctly different from their
standard-model counterparts. We illustrate this possibility using the examples
of the two-doublet Higgs models and the minimal supersymmetric models. The
dilepton invariant mass spectrum and the forward-backward asymmetry of $\ell^+$
in the centre-of-mass system of the dilepton pair in the decay \Bsell ~are also
worked out for the standard model and some representative solutions for the
other two models.
