arXiv subjects

Andriëtte Bekker

Publications and source records attributed to Andriëtte Bekker.

6 recordsLinked to original sources

arXiv2026

Handling mild outliers and unobserved values in compositional datasets using finite mixtures of mean-parametrised Dirichlet models

Heterogeneous compositional data may be simultaneously affected by missing values and atypical points, posing challenges for both clustering and outlier detection. We develop a mixture model for incomplete compositional data under Huber's contamination model, with contamination defined directly on the simplex and on observations that may be missing at random. The model provides a principled representation of outliers and allows the distribution of missing parts to be derived while accounting for contamination. We establish that maximisation of the observed log-likelihood constructed from contaminated, mean-parametrised Dirichlet densities is a convex optimisation problem. We then develop a tailored expectation-maximisation. The E-step incorporates the moments from the distribution of the missing parts of the data. Although the resulting parameter estimates are not available in closed form, the maximisation step admits tractable element-wise iterative updates. Numerical experiments demonstrate the performance of the proposed approach under varying percentage of missingness and contamination, and different sample size. An application to the American Time Use Survey identifies two interpretable clusters corresponding to work-intensive and sociable recreational days, while revealing atypical time-use compositions. In contrast, a conventional Dirichlet mixture model identifies four clusters, reflecting the influence of outliers and an artificial splitting of one cluster.

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arXiv2026

Modelling and detecting mild and gross anomalies in circular data via double-contaminated models

In this paper, we propose a model-based framework to robustify inference for circular data in the presence of anomalous observations, distinguishing between mild and gross anomalies. Starting from a unimodal and symmetric reference model on $[0,2π)$, parametrized by a mean direction and concentration, we construct a family of finite mixtures: a gross-anomaly model obtained by adding a circular uniform component; a mild-anomaly (contaminated) model obtained by mixing the reference distribution with a less concentrated version sharing the same mean direction; and a general three-component specification combining both models, the double-contaminated model. Posterior component probabilities provide an automatic classification of observations without ad hoc thresholds, while the mixing weights yield interpretable measures of anomaly prevalence and dispersion inflation. For illustration, we consider two classical circular reference distributions, the wrapped normal and von Mises. The methodology is evaluated through an extensive simulation study and three real-data applications involving animal movement directions and wind directions. The results indicate that jointly modelling mild and gross departures improves model fit and yields an informative decomposition of the directional data, demonstrating that mixture-based robustness is valuable not only for anomaly detection but also for the interpretation and the identification of latent structure in directional data.

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arXiv2026

A Contaminated Model for Overdispersed Multinomial Microbiome Count Data

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.

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arXiv2026

Mean regression for (0,1) responses via beta scale mixtures

To achieve a greater general flexibility for modeling heavy-tailed bounded responses, a beta scale mixture model is proposed. Each member of the family is obtained by multiplying the scale parameter of the conditional beta distribution by a mixing random variable taking values on all or part of the positive real line and whose distribution depends on a single parameter governing the tail behavior of the resulting compound distribution. These family members allow for a wider range of values for skewness and kurtosis. To validate the effectiveness of the proposed model, we conduct experiments on both simulated data and real datasets. The results indicate that the beta scale mixture model demonstrates superior performance relative to the classical beta regression model and alternative competing methods for modeling responses on the bounded unit domain.

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arXiv2025

Mixtures of multivariate linear asymmetric Laplace regressions with multiple asymmetric Laplace covariates

In response to the challenge of accommodating non-Gaussian behaviour in data, the shifted asymmetric Laplace (SAL) cluster-weighted model (SALCWM) is introduced as a model-based method for jointly clustering responses and random covariates that exhibit skewness. Within each cluster, the multivariate SAL distribution is assumed for both the covariates and the responses given the covariates. To mitigate the effect of possible atypical observations, a heavy-tailed extension, the contaminated SALCWM (cSALCWM), is also proposed. In addition to the SALCWM parameters, each mixture component has a parameter controlling the proportion of outliers, one controlling the proportion of leverage points, one specifying the degree of outlierness, and another specifying the degree of leverage. The cSALCWM has the added benefit that once the model parameters are estimated and the observations are assigned to components, a more refined intra-group classification in typical points, (mild) outliers, good leverage, and bad leverage points can be directly obtained. An expectation-conditional maximization algorithm is developed for efficient maximum likelihood parameter estimation under this framework. Theoretical identifiability conditions are established, and empirical results from simulation studies and validation via real-world applications demonstrate that the cSALCWM not only preserves the modelling strengths of the SALCWM but also significantly enhances outlier detection and overall inference reliability. The methodology proposed in this paper has been implemented in an \texttt{R} package, which is publicly available at https://github.com/arnootto/ALCWM.

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arXiv2025

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

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.

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