Transformations and Bayesian density estimation

Dirichlet-process mixture models, favored for their large support and for the relative ease of their implementation, are popular choices for Bayesian density estimation. However, despite the models’ flexibility, the performance of density estimates suffers in certain situations, in particular when the true distribution is skewed or heavy tailed. We detail a method that improves performance in a variety of settings by initially transforming the sample, choosing the transformation to facilitate estimation of the density on the new scale. The effectiveness of the method is demonstrated under a variety of simulated scenarios, and in an application to body mass index (BMI) observations from a large survey of Ohio adults.