  We develop a framework to study posterior contraction rates in sparse high
dimensional generalized linear models (GLM). We introduce a new family of GLMs,
denoted by clipped GLM, which subsumes many standard GLMs and makes minor
modification of the rest. With a sparsity inducing prior on the regression
coefficients, we delineate sufficient conditions on true data generating
density that leads to minimax optimal rates of posterior contraction of the
coefficients in $\ell_1$ norm. Our key contribution is to develop sufficient
conditions commensurate with the geometry of the clipped GLM family, propose
prior distributions which do not require any knowledge of the true parameters
and avoid any assumption on the growth rate of the true coefficient vector.
