Abstract
Assuming a homogeneous and isotropic universe and using both the 'Gold' Supernova Type Ia sample of Riess and co-workers and the results from the Supernova Legacy Survey, we carry out a critical investigation of how much the data reveal about the kinematics of the cosmic expansion history, based on the Bayesian marginal likelihood. We consider both spatially flat and curved models. Our results show that although there is strong evidence in the data for an accelerating universe, there is as yet no model-independent evidence for a deceleration parameter that varies with redshift.