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

## TL;DR

The paper introduces the STAR framework, a flexible Bayesian modeling approach that transforms and rounds continuous data to effectively model various types of integer-valued data, including zero-inflation and overdispersion.

## Contribution

It develops a novel Bayesian framework for integer-valued data using simultaneous transformation and rounding, extending continuous data models to discrete settings.

## Key findings

- STAR models outperform existing methods in predictive accuracy.
- The Bayesian BART model effectively captures complex data distributions.
- Application to healthcare and ecological data demonstrates practical utility.

## Abstract

We propose a simple yet powerful framework for modeling integer-valued data, such as counts, scores, and rounded data. The data-generating process is defined by Simultaneously Transforming and Rounding (STAR) a continuous-valued process, which produces a flexible family of integer-valued distributions capable of modeling zero-inflation, bounded or censored data, and over- or underdispersion. The transformation is modeled as unknown for greater distributional flexibility, while the rounding operation ensures a coherent integer-valued data-generating process. An efficient MCMC algorithm is developed for posterior inference and provides a mechanism for adaptation of successful Bayesian models and algorithms for continuous data to the integer-valued data setting. Using the STAR framework, we design a new Bayesian Additive Regression Tree (BART) model for integer-valued data, which demonstrates impressive predictive distribution accuracy for both synthetic data and a large healthcare utilization dataset. For interpretable regression-based inference, we develop a STAR additive model, which offers greater flexibility and scalability than existing integer-valued models. The STAR additive model is applied to study the recent decline in Amazon river dolphins.