I lost my reply because the site went down! I'll give a brief one here. > integers Or a matrix. Or with some dimension but not others. A total ranking is impl

I lost my reply because the site went down! I'll give a brief one here. > integers Or a matrix. Or with some dimension but not others. A total ranking is implausible and lossy, but partial rankings for some traits is tractable: you just have to be careful. If motivated by a decision the use of probability becomes more clear, since you can declare what kinds of errors you can handle and what you can't, relative to the information that you specifically want from an event. > positive information This is a problem with statistics, not Bayes. Null hypothesis testing with its p-values and t-tests can only reject a known distribution, not telling you the real distribution without testing for all of them. At that point it can be as prone to GIGO as Bayesian methods are. There are some statisticians who dissolve the whole Bayes vs Not debate by focusing on the optimisation of loss functions. Although it lacks the philosophical pyrotechnics of subjective probability, in practice it's probably the most reasonable approach: do what works.