In this paper, we propose a Bayesian framework for parameter estimation in seismic site response analyses. The technique relies on acceleration records provided during excitation by vertical (downhole) arrays of accelerometers. The method uses finite elements simulations of site response to estimate the correlations between dynamic soil parameters and resulting response spectra. Actual acceleration records are incorporated into the analysis in order to estimate the optimal set of parameters that produces a close fit to the actual recorded signal. Experiments are performed making use of information retrieved from three earthquake acceleration records at the SGC station deposit in Bogota, Colombia.