Various versions of quantum transition state theory (QTST) for the calculation of chemical reaction rate coefficients have been developed. The Hansen-Andersen formulation of QTST approximates the reactive flux autocorrelation function of Miller, Schwartz, and Tromp for the problem of interest by the correlation function for a one-dimensional system with a suitably chosen parabolic reference potential. In this paper, we present a systematic method for correcting this approximation in order to obtain more accurate rate constants at low temperatures. Values of the correlation function for real or imaginary times, such as might be obtained from path integral Monte Carlo calculations, are used to construct an improved approximation for the flux autocorrelation function. Our method uses a Bayesian analysis that incorporates a modified form of the maximum entropy method. In contrast to other applications of the maximum entropy method to this problem, the improved approximation is consistent with the known analyticity properties of the correlation function. The method is applied to several test problems, including one based on the H-2 + Cl reaction. Our method yields significant corrections using a remarkably small amount of information. (C) 2003 American Institute of Physics.