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2020 Simultaneous transformation and rounding (STAR) models for integer-valued data
Daniel R. Kowal, Antonio Canale
Electron. J. Statist. 14(1): 1744-1772 (2020). DOI: 10.1214/20-EJS1707

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 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.

Citation

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Daniel R. Kowal. Antonio Canale. "Simultaneous transformation and rounding (STAR) models for integer-valued data." Electron. J. Statist. 14 (1) 1744 - 1772, 2020. https://doi.org/10.1214/20-EJS1707

Information

Received: 1 September 2019; Published: 2020
First available in Project Euclid: 15 April 2020

zbMATH: 07200242
MathSciNet: MR4083734
Digital Object Identifier: 10.1214/20-EJS1707

Subjects:
Primary: 62F15, 62G08
Secondary: 62M20

JOURNAL ARTICLE
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Vol.14 • No. 1 • 2020
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