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We propose a simple yet powerful framework for modeling integer-valued data,such as counts, scores, and rounded data. The data-generating process isdefined by Simultaneously Transforming and Rounding (STAR) a continuous-valuedprocess, which produces a flexible family of integer-valued distributionscapable of modeling zero-inflation, bounded or censored data, and over- orunderdispersion. The transformation is modeled as unknown for greaterdistributional flexibility, while the rounding operation ensures a coherentinteger-valued data-generating process. An efficient MCMC algorithm isdeveloped for posterior inference and provides a mechanism for adaptation ofsuccessful Bayesian models and algorithms for continuous data to theinteger-valued data setting. Using the STAR framework, we design a new BayesianAdditive Regression Tree (BART) model for integer-valued data, whichdemonstrates impressive predictive distribution accuracy for both syntheticdata and a large healthcare utilization dataset. For interpretableregression-based inference, we develop a STAR additive model, which offersgreater flexibility and scalability than existing integer-valued models. TheSTAR additive model is applied to study the recent decline in Amazon riverdolphins.

Simultaneous Transformation and Rounding (STAR) Models for Integer-Valued Data