The paper addresses the problem of channel estimation in Impluse-Radio Ultra-Wideband (IR-UWB) communication system. The IEEE 802.15.4a channel model is used where the channel is assumed to be Linear Time Invariant (LTI) and thus the problem of channel estimation becomes the estimation of the sparse channel taps and their delays. Since, the bandwidth of the signal is very large, Nyquist rate sampling is impractical, therefore, we propose to estimate the channel taps from the sub-sampled versions of the received signal profile. We adopt the Bayesian framework to estimate the channel support by incorporating the a priori multipath arrival time statistics. In the first approach, we adopt a two-step method by employing Compressive Sensing to obtain coarse estimates and then refine them by applying Maximum A Posteriori (MAP) criterion. In the second approach, we develop a Low-Complexity MAP (LC-MAP) estimator. The computational complexity is reduced by identifying nearly orthogonal clusters in the received profile and by leveraging the structure of the sensing matrix.