arXiv subjects

Keefe Murphy

Publications and source records attributed to Keefe Murphy.

12 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.

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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.

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arXiv2025

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.

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arXiv2024

Joint Models for Handling Non-Ignorable Missing Data using Bayesian Additive Regression Trees: Application to Leaf Photosynthetic Traits Data

Dealing with missing data poses significant challenges in predictive analysis, often leading to biased conclusions when oversimplified assumptions about the missing data process are made. In cases where the data are missing not at random (MNAR), jointly modeling the data and missing data indicators is essential. Motivated by a real data application with partially missing multivariate outcomes related to leaf photosynthetic traits and several environmental covariates, we propose two methods under a selection model framework for handling data with missingness in the response variables suitable for recovering various missingness mechanisms. Both approaches use a multivariate extension of Bayesian additive regression trees (BART) to flexibly model the outcomes. The first approach simultaneously uses a probit regression model to jointly model the missingness. In scenarios where the relationship between the missingness and the data is more complex or non-linear, we propose a second approach using a probit BART model to characterize the missing data process, thereby employing two BART models simultaneously. Both models also effectively handle ignorable covariate missingness. The efficacy of both models compared to existing missing data approaches is demonstrated through extensive simulations, in both univariate and multivariate settings, and through the aforementioned application to the leaf photosynthetic trait data.

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arXiv2024

Seemingly unrelated Bayesian additive regression trees for cost-effectiveness analyses in healthcare

In recent years, theoretical results and simulation evidence have shown Bayesian additive regression trees to be a highly-effective method for nonparametric regression. Motivated by cost-effectiveness analyses in health economics, where interest lies in jointly modelling the costs of healthcare treatments and the associated health-related quality of life experienced by a patient, we propose a multivariate extension of BART which is applicable in regression analyses with several dependent outcome variables. Our framework allows for continuous or binary outcomes and overcomes some key limitations of existing multivariate BART models by allowing each individual response to be associated with different ensembles of trees, while still handling dependencies between the outcomes. In the case of continuous outcomes, our model is essentially a nonparametric version of seemingly unrelated regression. Likewise, our proposal for binary outcomes is a nonparametric generalisation of the multivariate probit model. We give suggestions for easily interpretable prior distributions, which allow specification of both informative and uninformative priors. We provide detailed discussions of MCMC sampling methods to conduct posterior inference. Our methods are implemented in the R package "subart". We showcase their performance through extensive simulation experiments and an application to an empirical case study from health economics. By also accommodating propensity scores in a manner befitting a causal analysis, we find substantial evidence for a novel trauma care intervention's cost-effectiveness.

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arXiv2023

A modern approach to transition analysis and process mining with Markov models: A tutorial with R

This chapter presents an introduction to Markovian modeling for the analysis of sequence data. Contrary to the deterministic approach seen in the previous sequence analysis chapters, Markovian models are probabilistic models, focusing on the transitions between states instead of studying sequences as a whole. The chapter provides an introduction to this method and differentiates between its most common variations: first-order Markov models, hidden Markov models, mixture Markov models, and mixture hidden Markov models. In addition to a thorough explanation and contextualization within the existing literature, the chapter provides a step-by-step tutorial on how to implement each type of Markovian model using the R package seqHMM. The chaper also provides a complete guide to performing stochastic process mining with Markovian models as well as plotting, comparing and clustering different process models.

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arXiv2023

An introduction and tutorial to model-based clustering in education via Gaussian mixture modelling

Heterogeneity has been a hot topic in recent educational literature. Several calls have been voiced to adopt methods that capture different patterns or subgroups within students behavior or functioning. Assuming that there is an average pattern that represents the entirety of student populations requires the measured construct to have the same causal mechanism, same development pattern, and affect students in exactly the same way. Using a person-centered method (Finite Gaussian mixture model or latent profile analysis), the present tutorial shows how to uncover the heterogeneity within engagement data by identifying three latent or unobserved clusters. This chapter offers an introduction to the model-based clustering that includes the principles of the methods, a guide to choice of number of clusters, evaluation of clustering results and a detailed guide with code and a real-life dataset. The discussion elaborates on the interpretation of the results, the advantages of model-based clustering as well as how it compares with other methods.

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arXiv2022

GP-BART: a novel Bayesian additive regression trees approach using Gaussian processes

The Bayesian additive regression trees (BART) model is an ensemble method extensively and successfully used in regression tasks due to its consistently strong predictive performance and its ability to quantify uncertainty. BART combines "weak" tree models through a set of shrinkage priors, whereby each tree explains a small portion of the variability in the data. However, the lack of smoothness and the absence of an explicit covariance structure over the observations in standard BART can yield poor performance in cases where such assumptions would be necessary. The Gaussian processes Bayesian additive regression trees (GP-BART) model is an extension of BART which addresses this limitation by assuming Gaussian process (GP) priors for the predictions of each terminal node among all trees. The model's effectiveness is demonstrated through applications to simulated and real-world data, surpassing the performance of traditional modeling approaches in various scenarios.

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arXiv2021

Accounting for shared covariates in semi-parametric Bayesian additive regression trees

We propose some extensions to semi-parametric models based on Bayesian additive regression trees (BART). In the semi-parametric BART paradigm, the response variable is approximated by a linear predictor and a BART model, where the linear component is responsible for estimating the main effects and BART accounts for non-specified interactions and non-linearities. Previous semi-parametric models based on BART have assumed that the set of covariates in the linear predictor and the BART model are mutually exclusive in an attempt to avoid poor coverage properties and reduce bias in the estimates of the parameters in the linear predictor. The main novelty in our approach lies in the way we change the tree-generation moves in BART to deal with this bias and resolve non-identifiability issues between the parametric and non-parametric components, even when they have covariates in common. This allows us to model complex interactions involving the covariates of primary interest, both among themselves and with those in the BART component. Our novel method is developed with a view to analysing data from an international education assessment, where certain predictors of students' achievements in mathematics are of particular interpretational interest. Through additional simulation studies and another application to a well-known benchmark dataset, we also show competitive performance when compared to regression models, alternative formulations of semi-parametric BART, and other tree-based methods. The implementation of the proposed method is available at \url{https://github.com/ebprado/CSP-BART}.

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arXiv2019

Clustering Longitudinal Life-Course Sequences Using Mixtures of Exponential-Distance Models

Sequence analysis is an increasingly popular approach for analysing life courses represented by ordered collections of activities experienced by subjects over time. Here, we analyse a survey data set containing information on the career trajectories of a cohort of Northern Irish youths tracked between the ages of 16 and 22. We propose a novel, model-based clustering approach suited to the analysis of such data from a holistic perspective, with the aims of estimating the number of typical career trajectories, identifying the relevant features of these patterns, and assessing the extent to which such patterns are shaped by background characteristics. Several criteria exist for measuring pairwise dissimilarities among categorical sequences. Typically, dissimilarity matrices are employed as input to heuristic clustering algorithms. The family of methods we develop instead clusters sequences directly using mixtures of exponential-distance models. Basing the models on weighted variants of the Hamming distance metric permits closed-form expressions for parameter estimation. Simultaneously allowing the component membership probabilities to depend on fixed covariates and accommodating sampling weights in the clustering process yields new insights on the Northern Irish data. In particular, we find that school examination performance is the single most important predictor of cluster membership.

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arXiv2017

Gaussian Parsimonious Clustering Models with Covariates and a Noise Component

We consider model-based clustering methods for continuous, correlated data that account for external information available in the presence of mixed-type fixed covariates by proposing the MoEClust suite of models. These models allow different subsets of covariates to influence the component weights and/or component densities by modelling the parameters of the mixture as functions of the covariates. A familiar range of constrained eigen-decomposition parameterisations of the component covariance matrices are also accommodated. This paper thus addresses the equivalent aims of including covariates in Gaussian parsimonious clustering models and incorporating parsimonious covariance structures into all special cases of the Gaussian mixture of experts framework. The MoEClust models demonstrate significant improvement from both perspectives in applications to both univariate and multivariate data sets. Novel extensions to include a uniform noise component for capturing outliers and to address initialisation of the EM algorithm, model selection, and the visualisation of results are also proposed.

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arXiv2017

Infinite Mixtures of Infinite Factor Analysers

Factor-analytic Gaussian mixture models are often employed as a model-based approach to clustering high-dimensional data. Typically, the numbers of clusters and latent factors must be specified in advance of model fitting, and remain fixed. The pair which optimises some model selection criterion is then chosen. For computational reasons, models in which the number of latent factors differ across clusters are rarely considered. Here the infinite mixture of infinite factor analysers (IMIFA) model is introduced. IMIFA employs a Pitman-Yor process prior to facilitate automatic inference of the number of clusters using the stick-breaking construction and a slice sampler. Furthermore, IMIFA employs multiplicative gamma process shrinkage priors to allow cluster-specific numbers of factors, automatically inferred via an adaptive Gibbs sampler. IMIFA is presented as the flagship of a family of factor-analytic mixture models, providing flexible approaches to clustering high-dimensional data. Applications to a benchmark data set, metabolomic spectral data, and a manifold learning handwritten digit example illustrate the IMIFA model and its advantageous features. These include obviating the need for model selection criteria, reducing the computational burden associated with the search of the model space, improving clustering performance by allowing cluster-specific numbers of factors, and quantifying uncertainty in the numbers of clusters and cluster-specific factors.

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