I am working on sampling a posterior distribution for parameters in my model using approximate Bayesian computation (ABC). I would like to come up with a summary statistic to compare the similarity/distance of ranked order between my simulated data and observed data. My observed data are a list of 10 species biomass. So I would like to compare the rank of species i between simulated and observed data, and summarize over 10 species.
My questions are:
Is there some metrics that can quantify the rank differences between 2 vectors? So far, what I did is to take the rank difference per species and calculate the sum of absolute difference across the 10 species.
Because the metric should provide a distance-like result: the more similar the 2 vector ranks, the smaller the value is. I am not sure if I can use the test statstics in Wilcoxon signed-rank test. Anyone has any comments?
Thanks very much