Modeling Variability Order: A Semiparametric Bayesian Approach

In comparing two populations, sometimes a model incorporating a certain probability order is desired. In this setting, Bayesian modeling is attractive since a probability order restriction imposed a priori on the population distributions is retained a posteriori. Extending the work in Gelfand and Kottas (2000) for stochastic order specifications, we formulate modeling for distributions ordered in variability. We work with Dirichlet process mixtures resulting in a fully Bayesian semiparametric approach. The details for simulation-based model fitting and prior specification are provided. An example, based on two small subsets of time intervals between eruptions of the Old Faithful geyser, illustrates the methodology.