A Bayesian approach to trends in cometary magnitude data

A Pareto distribution was used by Donnison (1990) to model the brightness of long- and short-period comets. The data was subsequently analysed for trends using a classical approach, including the “pool adjacent violaters algorithm” and likelihood ratio tests. In this new investigation the problems of variation in the brightness indices of long-period comets for a number of parameter ranges, including perihelion distance and discovery date, are examined from a Bayesian viewpoint using Gibbs sampling. The data set analysed is greatly enhanced and includes all those comets observed up to 1988. It is found that there is no evidence that the brightness index shows any ordering with discovery date using data from 584 ad to 1988 ad for comets with H10 < 6.0 mag. This result differs from previous estimates both classical and Bayesian using data up to 1978. There is also no strong statistical evidence that the brightness distribution of long-period comets with H10 < 6.0 mag is ordered as far as perihelion is concerned. The advantages of the Gibbs sampling method as against the classical method are outlined.