  In this paper, we introduce a new methodology for Bayesian variable selection
in linear regression that is independent of the traditional indicator method. A
diagonal matrix $\mathbf{G}$ is introduced to the prior of the coefficient
vector $\boldsymbol{\beta}$, with each of the $g_j$'s, bounded between $0$ and
$1$, on the diagonal serves as a stabilizer of the corresponding $\beta_j$.
Mathematically, a promising variable has a $g_j$ value that is close to $0$,
whereas the value of $g_j$ corresponding to an unpromising variable is close to
$1$. This property is proven in this paper under orthogonality together with
other asymptotic properties. Computationally, the sample path of each $g_j$ is
obtained through Metropolis-within-Gibbs sampling method. Also, in this paper
we give two simulations to verify the capability of this methodology in
variable selection.
