arXiv subjects

André F. B. Menezes

Publications and source records attributed to André F. B. Menezes.

4 recordsLinked to original sources

arXiv2026

Bayesian palaeoclimate reconstruction from zero-inflated count-compositional pollen data: A case study of Lago Grande di Monticchio in southern Italy

Bayesian palaeoclimate reconstruction from fossil pollen counts relies on a modern pollen-climate calibration data set to infer the pollen-climate relationships used to reconstruct past climates. While geographically large calibration data sets improve coverage of climate space and reduce unreliable extrapolation, they also introduce substantial heterogeneity, structural zeros, and complex pollen-climate relationships. We propose a Bayesian modular framework for palaeoclimate reconstruction from count-compositional pollen data that addresses these challenges, and provides coherent uncertainty quantification. The framework employs the zero-and-$N$-inflated multinomial logistic-normal distribution to describe the compositional pollen counts coupled with Bayesian additive regression tree priors to model the nonlinear effects and interactions among the climate covariates. Inference is formulated through a cut posterior distribution that modularises the analysis into forward and reconstruction modules. The forward module is fitted once using a large modern calibration data set and its posterior uncertainty is subsequently propagated to reconstruct climate variables from fossil pollen counts. For the reconstruction module, we develop and compare three inverse posterior sampling schemes. Simulation studies and empirical validation on the modern data set demonstrate that a combination of sampling importance resampling with a multiple imputation technique and a continuous uniform prior over the domain of the modern climate variables achieves the best predictive performance, with well-calibrated uncertainty quantification for the climate reconstruction. In our motivating case study, we further illustrate the proposed methodology by reconstructing a three-dimensional climate vector from fossil pollen records collected at Lago Grande di Monticchio in southern Italy.

stat.AP↗

arXiv2026

Bayesian nonparametric models for zero-inflated count-compositional data using ensembles of regression trees

Count-compositional data arise in many different fields, including high-throughput sequencing experiments, ecological surveys, and palaeoclimate studies, where a common, important goal is to understand how covariates relate to the observed compositions. Existing methods often fail to simultaneously address key challenges inherent in such data, namely: overdispersion, an excess of zeros, cross-sample heterogeneity, and complex covariate effects. To address these concerns, we propose two novel Bayesian models based on ensembles of regression trees. Specifically, we leverage the recently introduced zero-and-$N$-inflated multinomial distribution and assign independent nonparametric Bayesian additive regression tree (BART) priors to both the compositional and structural zero probability components of the model, to flexibly capture covariate effects. We further extend this by adding latent random effects to capture overdispersion and more general dependence structures among the categories. We develop an efficient inferential algorithm combining recent data augmentation schemes with established BART sampling routines. We evaluate our proposed models in simulation studies and illustrate their applicability through a case study of palaeoclimate modelling.

stat.ME↗

arXiv2026

Finite mixture representations of zero-and-$N$-inflated distributions for count-compositional data

We provide novel probabilistic portrayals of two multivariate models designed to handle zero-inflation in count-compositional data. We develop a new unifying framework that represents both as finite mixture distributions. One of these distributions, based on Dirichlet-multinomial components, has been studied before, but has not yet been properly characterised as a sampling distribution of the counts. The other, based on multinomial components, is a new contribution. Using our finite mixture representations enables us to derive key statistical properties, including moments, marginal distributions, and special cases for both distributions. We develop enhanced Bayesian inference schemes with efficient Gibbs sampling updates, wherever possible, for parameters and auxiliary variables, demonstrating improvements over existing methods in the literature. We conduct simulation studies to evaluate the efficiency of the Bayesian inference procedures and present applications to a human gut microbiome dataset to illustrate the practical utility of the proposed distributions.

stat.ME↗

arXiv2021

A Model for Bimodal Rates and Proportions

The beta model is the most important distribution for fitting data with the unit interval. However, the beta distribution is not suitable to model bimodal unit interval data. In this paper, we propose a bimodal beta distribution constructed by using an approach based on the alpha-skew-normal model. We discuss several properties of this distribution such as bimodality, real moments, entropy measures and identifiability. Furthermore, we propose a new regression model based on the proposed model and discuss residuals. Estimation is performed by maximum likelihood. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the results. An application is provided to show the modelling competence of the proposed distribution when the data sets show bimodality.

stat.ME↗