Bayesian inferences on uncertain ranks and orderings
share
It is common to be interested in rankings or order relationships among entities. In complex settings where one does not directly measure a univariate statistic upon which to base ranks, such inferences typically rely on statistical models having entity-specific parameters. These can be treated as random effects in hierarchical models characterizing variation among the entities. The current literature struggles to present summaries of order relationships which appropriately account for uncertainty. A single estimated ranking can be highly misleading, particularly as it is common that the entities do not vary widely in the trait being measured, leading to large uncertainty and instability in ranking a moderate to large number of them. We observed such problems in attempting to rank player abilities based on data from the National Basketball Association (NBA). Motivated by this, we propose a general strategy for characterizing uncertainty in inferences on order relationships among parameters. Our approach adapts to scenarios in which uncertainty in ordering is high by producing more conservative results that improve interpretability. This is achieved through a reward function within a decision-theoretic framework. We show that our method is theoretically sound and illustrate its utility using simulations and an application to NBA player ability data.
READ FULL TEXT