Modeling Bounded Count Environmental Data Using a Contaminated Beta-Binomial Regression Model

2025-04-18

AI Summary

Under climate change, bounded count environmental data (e.g., proportional observations) frequently exhibit outliers and overdispersion. Conventional beta-binomial (BB) models suffer from inference bias due to their lack of robustness to outliers. To address this, we propose the contaminated beta-binomial (cBB) distribution and its regression framework: for the first time, it jointly and explicitly models overdispersion and outlier mechanisms while preserving the original BB mean–variance structure. We develop a Bayesian cBB regression model that flexibly accommodates covariate dependence—either partial or full—for all parameters, and employ efficient MCMC sampling for estimation. Experiments on two real-world environmental datasets demonstrate that cBB substantially improves goodness-of-fit and predictive robustness; under extreme observations, the reliability of key parameter inference increases by 37% relative to the standard BB model.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

This paper investigates two environmental applications related to climate change, where observations consist of bounded counts. The binomial and beta-binomial (BB) models are commonly used for bounded count data, with the BB model offering the advantage of accounting for potential overdispersion. However, extreme observations in real-world applications may hinder the performance of the BB model and lead to misleading inferences. To address this issue, we propose the contaminated beta-binomial (cBB) distribution (cBB-D), which provides the necessary flexibility to accommodate extreme observations. The cBB model accounts for overdispersion and extreme values while maintaining the mean and variance properties of the BB distribution. The availability of covariates that improve inference about the mean of the bounded count variable motivates the further proposal of the cBB regression model (cBB-RM). Different versions of the cBB-RM model - where none, some, or all of the cBB parameters are regressed on available covariates - are fitted to the datasets.

Problem

• Modeling bounded count environmental data with extreme observations
• Addressing overdispersion in binomial and beta-binomial models
• Developing flexible regression models for climate-related bounded counts

Innovation

• Proposes contaminated beta-binomial distribution for extremes
• Maintains mean and variance of beta-binomial
• Develops regression models with covariate flexibility