Applied Bayesian Non- and Semi-parametric Inference using DPpackage

Inmany practical situations, a parametric model cannot be expected to describe in an appropriate manner the chance mechanism generating an observed dataset, and unrealistic features of some common models could lead to unsatisfactory inferences. In these cases, we would like to relax parametric assumptions to allow greater modeling flexibility and robustness against misspecification of a parametric statistical model. In the Bayesian context such flexible inference is typically achieved by models with infinitely many parameters. These models are usually referred to as Bayesian Nonparametric (BNP) or Semiparametric (BSP)models depending onwhether all or at least one of the parameters is infinity dimensional (Müller & Quintana, 2004). While BSP and BNP methods are extremely powerful and have a wide range of applicability within several prominent domains of statistics, they are not as widely used as one might guess. At least part of the reason for this is the gap between the type of software that many applied users would like to have for fitting models and the software that is currently available. The most popular programs for Bayesian analysis, such as BUGS (Gilks et al., 1992), are generally unable to cope with nonparametric models. The variety of different BSP and BNP models is huge; thus, building for all of them a general software package which is easy to use, flexible, and efficient may be close to impossible in the near future. This article is intended to introduce an R package, DPpackage, designed to help bridge the previously mentioned gap. Although its name is motivated by the most widely used prior on the space of the probability distributions, the Dirichlet Process (DP) (Ferguson, 1973), the package considers and will consider in the future other priors on functional spaces. Currently, DPpackage (version 1.0-5) allows the user to perform Bayesian inference via simulation from the posterior distributions for models considering DP, Dirichlet ProcessMixtures (DPM), Polya Trees (PT), Mixtures of Triangular distributions, and Random Bernstein Polynomials priors. The package also includes generalized additive models considering penalized B-Splines. The rest of the article is organized as follows. We first discuss the general syntax and design philosophy of the package. Next, the main features of the package and some illustrative examples are presented. Comments on future developments conclude the article.