  In this work, we show that under specific choices of the copula, the lasso,
elastic net, and $g$-prior are particular cases of `copula prior,' for
regularization and variable selection method. We present `lasso with Gauss
copula prior' and `lasso with t-copula prior.' The simulation study and
real-world data for regression, classification, and large time-series data show
that the `copula prior' often outperforms the lasso and elastic net while
having a comparable sparsity of representation. Also, the copula prior
encourages a grouping effect. The strongly correlated predictors tend to be in
or out of the model collectively under the copula prior. The `copula prior' is
a generic method, which can be used to define the new prior distribution. The
application of copulas in modeling prior distribution for Bayesian methodology
has not been explored much. We present the resampling-based optimization
procedure to handle big data with copula prior.
