A Simultaneous Transformation and Rounding Approach for Modeling Integer-Valued Data

We propose a simple yet powerful framework for modeling integer-valued data. The integer-valued data are modeled by Simultaneously Transforming And Rounding (STAR) a continuous-valued process, where the transformation may be known or learned from the data. Implicitly, STAR formalizes the commonly-applied yet incoherent procedure of (i) transforming integer-valued data and subsequently (ii) modeling the transformed data using Gaussian models. Importantly, STAR is well-defined for integer-valued data, which is reflected in predictive accuracy, and is designed to account for zero-inflation, bounded or censored data, and over- or underdispersion. Efficient computation is available via an MCMC algorithm, which provides a mechanism for direct adaptation of successful Bayesian methods for continuous data to the integer-valued data setting. Using the STAR framework, we develop new linear regression models, additive models, and Bayesian Additive Regression Trees (BART) for integer-valued data, which demonstrate substantial improvements in performance relative to existing regression models for a variety of simulated and real datasets.