Multinomial count data, such as microbial composition profiles derived from sequencing studies, frequently contain anomalous observations that distort parameter estimates. The Dirichlet-multinomial (DM) distribution is widely used in this setting but remains sensitive to such contamination. We propose the contaminated Dirichlet-multinomial (CDM) distribution, a two-component mixture in which the regular data come from a DM component with a lower dispersion and the irregular data come from a DM component with an inflated dispersion parameter. This construction accommodates anomalies without requiring their removal, and yields a natural rule for anomaly detection via posterior probabilities. Through sensitivity analyses involving both single-point anomalies and background noise, we demonstrate that the CDM distribution effectively downweights the influence of anomalous observations on the parameter estimates. The model is applied to gut microbiome data from a colorectal carcinogenesis study, where it consistently outperforms the DM distribution across all information criteria and identifies biologically plausible anomaly proportions in both the healthy and carcinoma subsets.

翻译：多项计数数据（如测序研究中获得的微生物组成谱）常包含异常观测值，这些值会扭曲参数估计。狄利克雷-多项（DM）分布在此类场景中被广泛使用，但对该类污染仍然敏感。我们提出污染狄利克雷-多项（CDM）分布，这是一种双组分混合模型：常规数据来自低离散度的DM组分，而异常数据则来自具有膨胀离散参数的DM组分。该结构无需移除异常值即可处理异常情况，并通过后验概率形成自然的异常检测规则。通过对单点异常和背景噪声的敏感性分析，我们证明CDM分布能有效降低异常观测值对参数估计的影响。该模型应用于结直肠癌发生研究的肠道微生物组数据，在所有信息准则下均显著优于DM分布，并在健康与癌变子集中识别出具有生物学合理性的异常比例。