Research concerned with underwater propagation in a shallow ocean environment is a growing area of study. In particular, the development of fast and accurate computational methods to estimate environmental parameters and source location is desired. In this work, only select features of the acoustic field are investigated, namely, the time delays and amplitudes of individual paths, the signal-to-noise ratio, and the number of multi-path arrivals. The amplitudes and delays contain pertinent information about the geometry associated with the environment of interest. Estimating the time delays and amplitudes of select paths in a manner that is both accurate and time efficient, however, is not a trivial task. A Gibbs Sampling Monte Carlo technique is proposed to recover these arrivals and their features. The method is tested on synthetic data as well as data from the Haro Straight experiment for the estimation of the number of arrivals, the amplitude and time delay associated with each arrival, and the variance of noise. Signals involved in shallow water propagation closely resemble signals obtained in other areas such as radar and communication problems. Therefore, the estimation techniques presented here may be useful in these, among several other, applications.