Cosmography: Extracting the Hubble series from the supernova data

We perform a number of inter-related cosmographic fits to the legacy05 and gold06 supernova datasets. We pay particular attention to the influence of both statistical and systematic uncertainties, and also to the extent to which the choice of distance scale and manner of representing the redshift scale affect the cosmological parameters. While the "preponderance of evidence" certainly suggests an accelerating universe, we would argue that (based on the supernova data) this conclusion is not currently supported "beyond reasonable doubt". As part of the analysis we develop two particularly transparent graphical representations of the redshift-distance relation -- representations in which acceleration versus deceleration reduces to the question of whether the graph slopes up or down. Turning to the details of the cosmographic fits, three issues in particular concern us: First, the fitted value for the deceleration parameter changes significantly depending on whether one performs a chi^2 fit to the luminosity distance, proper motion distance, angular diameter distance, or other suitable distance surrogate. Second, the fitted value for the deceleration parameter changes significantly depending on whether one uses the traditional redshift variable z, or what we shall argue is on theoretical grounds an improved parameterization y=z/(1+z). Third, the published estimates for systematic uncertainties are sufficiently large that they certainly impact on, and to a large extent undermine, the usual purely statistical tests of significance. We conclude that the case for an accelerating universe is considerably less watertight than commonly believed