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

arXiv: https://arxiv.org/abs/1906.11653 · HTML: https://mlsanity.com/paper/1906.11653/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2019.

## Built on by (most cited first, 4 of 4)

- [Semiparametric count data regression for self-reported mental health](https://mlsanity.com/paper/2106.09114/) (2021)
- [Semiparametric discrete data regression with Monte Carlo inference and prediction](https://mlsanity.com/paper/2110.12316/) (2021)
- [Warped Dynamic Linear Models for Time Series of Counts](https://mlsanity.com/paper/2110.14790/) (2021)
- [Monte Carlo inference for semiparametric Bayesian regression](https://mlsanity.com/paper/2306.05498/) (2023)

## Abstract (arXiv)

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.