  In this paper, using a significantly improved version of the
model-independent, cosmographic approach to cosmology (John, M. V. 2004, ApJ,
614, 1), we address an important question: Was there a decelerating past for
the universe? To answer this, the Bayes's probability theory is employed, which
is the most appropriate tool for quantifying our knowledge when it changes
through the acquisition of new data. The cosmographic approach helps to sort
out the models in which the universe was always accelerating from those in
which it decelerated for at least some time in the period of interest. Bayesian
model comparison technique is used to discriminate these rival hypotheses with
the aid of recent releases of supernova data. We also attempt to provide and
improve another example of Bayesian model comparison, performed between some
Friedmann models, using the same data. Our conclusion, which is consistent with
other approaches, is that the apparent magnitude-redshift data alone cannot
discriminate these competing hypotheses. We also argue that the lessons learnt
using Bayesian theory are extremely valuable to avoid frequent U-turns in
cosmology.
