A Bayesian h-index: How to measure research impact

The quality of academic research is difficult to measure and rather controversial. Hirsch has proposed the h index [1], a measure that has the advantage of summarizing in a single summary statistic the information that is contained in the citation counts of each scientist. Although the h index has received a great deal of interest, only a few papers have analyzed its statistical properties and implications. We claim that statistical modeling can give a lot of added value over a simple summary like the h index. To show this, in this paper we propose a negative binomial distribution to jointly model the two main components of the h index: the number of papers and their citations. We then propose a Bayesian model that allows to obtain posterior inferences on the parameters of the distribution and, in addition, a predictive distribution for the h index itself. Such a predictive distribution can be used to compare scientists on a fairer ground, and in terms of their future contribution, rather than on their past performance.