Advantages of Bayesian Structuring: Estimating Ranks and Histograms

Introduction

Methods developed using the Bayesian formalism can be very effective in addressing both Bayesian and frequentist goals. These advantages are conferred by full probability modeling are most apparent in the context of non-linear models or in addressing non-standard goals. Once the likelihood and the prior have been specified and data observed, Bayes’ Theorem maps the prior distribution into the posterior. Then, inferences are computed from the posterior, possibly guided by a loss function. This last step allows proper processing for complicated, non-intuitive goals. In this context, we show how the Bayesian approach is effective in estimating ranks and CDFs (histograms). We give the basic ideas; see Lin et al. (2006, 2008); Paddock et al. (2006) and the references thereof for full details and generalizations.

Importantly, as Carlin and Louis (2009) and many authors caution, the Bayesian approach is not a panacea. Indeed, the requirements for an effective procedure are more...