arXiv subjects

David B. Dunson

Publications and source records attributed to David B. Dunson.

At least 37 records · Page 2Linked to original sources

arXiv2025

Bayesian Level Set Clustering

Classically, Bayesian clustering interprets each component of a mixture model as a cluster. The inferred clustering posterior is highly sensitive to any inaccuracies in the kernel within each component. As this kernel is made more flexible, problems arise in identifying the underlying clusters in the data. To address this pitfall, this article proposes a fundamentally different approach to Bayesian clustering that decouples the problems of clustering and flexible modeling of the data density $f$. Starting with an arbitrary Bayesian model for $f$ and a loss function for defining clusters based on $f$, we develop a Bayesian decision-theoretic framework for density-based clustering. Within this framework, we develop a Bayesian level set clustering method to cluster data into connected components of a level set of $f$. We provide theoretical support, including clustering consistency, and highlight performance in a variety of simulated examples. An application to astronomical data illustrates improvements over the popular DBSCAN algorithm in terms of accuracy, insensitivity to tuning parameters, and providing uncertainty quantification.

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arXiv2025

Marginally interpretable spatial logistic regression with bridge processes

In including random effects to account for dependent observations, the odds ratio interpretation of logistic regression coefficients is changed from population-averaged to subject-specific. This is unappealing in many applications, motivating a rich literature on methods that maintain the marginal logistic regression structure without random effects, such as generalized estimating equations. However, for spatial data, random effect approaches are appealing in providing a full probabilistic characterization of the data that can be used for prediction. We propose a new class of spatial logistic regression models that maintain both population-averaged and subject-specific interpretations through a novel class of bridge processes for spatial random effects. These processes are shown to have appealing computational and theoretical properties, including a scale mixture of normal representation. The new methodology is illustrated with simulations and an analysis of childhood malaria prevalence data in the Gambia.

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arXiv2025

Leveraging ontologies to predict biological activity of chemicals across genes

High-throughput screening (HTS) is useful for evaluating chemicals for potential human health risks. However, given the extraordinarily large number of genes, assay endpoints, and chemicals of interest, available data are sparse, with dose-response curves missing for the vast majority of chemical-gene pairs. Although gene ontologies characterize similarity among genes with respect to known cellular functions and biological pathways, the sensitivity of various pathways to environmental contaminants remains unclear. We propose a novel Dose-Activity Response Tracking (DART) approach to predict the biological activity of chemicals across genes using information on chemical structural properties and gene ontologies within a Bayesian factor model. Designed to provide toxicologists with a flexible tool applicable across diverse HTS assay platforms, DART reveals the latent processes driving dose-response behavior and predicts new activity profiles for chemical-gene pairs lacking experimental data. We demonstrate the performance of DART through simulation studies and an application to a vast new multi-experiment data set consisting of dose-response observations generated by the exposure of HepG2 cells to per- and polyfluoroalkyl substances (PFAS), where it provides actionable guidance for chemical prioritization and inference on the structural and functional mechanisms underlying assay activation.

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arXiv2025

Model-based indicators for co-clustered environments and species communities

Accurate biodiversity monitoring is essential for effective environmental policy, yet current practices often rely on arbitrarily defined ecosystems, communities, and ad-hoc indicator species, limiting cost-efficiency and reproducibility. We present a model-based framework that infers ecological sub-communities and corresponding indicators in terms of habitat and species from species survey data, such as large-scale arthropod abundance data used here as example. Environments and species are co-clustered using Bayesian decoupling for Poisson factorization. Latent, hierarchical regression relates observable habitat features to each subcommunity. Additionally, we propose a novel, model-based ranking of indicator species based on the learned subcommunities, generalizing classical approaches. This integrated approach motivates model-based ecosystem classification and indicator species selection, offering a scalable, reproducible pathway for biodiversity monitoring and informed conservation.

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arXiv2025

Uncertainty Quantification in Bayesian Clustering

Bayesian clustering methods have the widely touted advantage of providing a probabilistic characterization of uncertainty in clustering through the posterior distribution. An amazing variety of priors and likelihoods have been proposed for clustering in a broad array of settings. There is also a rich literature on Markov chain Monte Carlo (MCMC) algorithms for sampling from posterior clustering distributions. However, there is relatively little work on summarizing the posterior uncertainty. The complexity of the partition space corresponding to different clusterings makes this problem challenging. We propose a post-processing procedure for any Bayesian clustering model with posterior samples that generates a credible set that is easy to use, fast to compute, and intuitive to interpret. We also provide new measures of clustering uncertainty and show how to compute cluster-specific parameter estimates and credible regions that accumulate a desired posterior probability without having to condition on a partition estimate or employ label-switching techniques. We illustrate our procedure through several applications.

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arXiv2025

Link prediction in ecological networks under extreme taxonomic bias

Ecological networks offer powerful insights into community function, but without first characterizing these networks accurately, our ability to detect and interpret changes under environmental stress is limited. We develop an approach to reduce bias in link prediction in the common scenario in which data are derived from studies focused on a small number of species. Our Extended Covariate-Informed Link Prediction (COIL+) framework employs a latent factor model that flexibly borrows information across species, incorporates species traits and phylogeny, and leverages information from multiple studies to address uncertainty in species occurrence. We also propose a trait-matching procedure that allows heterogeneity in species-level trait-interaction associations. We illustrate the approach with a literature-based dataset of 268 sources reporting Afrotropical frugivory and compare performance with and without correction for occurrence uncertainty. COIL+ substantially improves link prediction and reduces sampling bias, revealing 5637 likely but unobserved frugivory interactions (a median of nine additional interactions per frugivore). Newly predicted interactions are concentrated among poorly sampled frugivores, such as the water chevrotain (Hyemoschus aquaticus, a small forest-dwelling ungulate) and the rufous-bellied helmetshrike (Prionops rufiventris, a passerine bird of East African tropical forests). Additionally, the method improves model discrimination compared to existing methods under strong taxonomic bias and narrow study focus. This framework generalizes to diverse network contexts and provides a useful tool for link prediction in the face of biased interaction data.

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arXiv2025

Nonparametric predictive inference for discrete data via Metropolis-adjusted Dirichlet sequences

This article is motivated by challenges in conducting Bayesian inferences on unknown discrete distributions, with a particular focus on count data. To avoid the computational disadvantages of traditional mixture models, we develop a novel Bayesian predictive approach. In particular, our Metropolis-adjusted Dirichlet (MAD) sequence model characterizes the predictive measure as a mixture of a base measure and Metropolis-Hastings kernels centered on previous data points. The resulting MAD sequence is asymptotically exchangeable and the posterior on the data generator takes the form of a martingale posterior. This structure leads to straightforward algorithms for inference on count distributions, with easy extensions to multivariate, regression, and binary data cases. We obtain a useful asymptotic Gaussian approximation and illustrate the methodology on a variety of applications.

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arXiv2025

Scalable and robust regression models for continuous proportional data

Beta regression is used routinely for continuous proportional data, but it often encounters practical issues such as a lack of robustness to misspecification of the beta distribution and sensitivity to outliers. We develop an improved class of generalized linear models starting with the continuous binomial (cobin) distribution and further extending to dispersion mixtures of cobin distributions (micobin). The proposed cobin regression and micobin regression models have attractive robustness, computation, and flexibility properties. A key innovation is the Kolmogorov-Gamma data augmentation scheme, which facilitates Gibbs sampling for Bayesian computation, including in hierarchical cases involving nested, longitudinal, or spatial data. We demonstrate robustness, ability to handle responses exactly at the boundary (0 or 1), and computational efficiency relative to beta regression in simulation experiments and through analysis of the benthic macroinvertebrate multimetric index of US lakes using lake watershed covariates.

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arXiv2025

Sequential Gibbs Posteriors with Applications to Principal Component Analysis

Gibbs posteriors are proportional to a prior distribution multiplied by an exponentiated loss function, with a key tuning parameter weighting information in the loss relative to the prior and providing a control of posterior uncertainty. Gibbs posteriors provide a principled framework for likelihood-free Bayesian inference, but in many situations, including a single tuning parameter inevitably leads to poor uncertainty quantification. In particular, regardless of the value of the parameter, credible regions have far from the nominal frequentist coverage even in large samples. We propose a sequential extension to Gibbs posteriors to address this problem. We prove the proposed sequential posterior exhibits concentration and a Bernstein-von Mises theorem, which holds under easy to verify conditions in Euclidean space and on manifolds. As a byproduct, we obtain the first Bernstein-von Mises theorem for traditional likelihood-based Bayesian posteriors on manifolds. All methods are illustrated with an application to principal component analysis.

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arXiv2025

Joint species distribution modeling of abundance data through latent variable barcodes

Accelerating global biodiversity loss has highlighted the role of complex relationships and shared patterns among species in determining their responses to environmental changes. The structure of an ecological community, represented by patterns of dependence among constituent species, signals its robustness more than individual species distributions. We focus on obtaining community-level insights based on underlying patterns in abundances of bird species in Finland. We propose \texttt{barcode}, a modeling framework to infer latent binary and continuous features of samples and species, expanding the class of concurrent ordinations. This approach introduces covariates and spatial autocorrelation hierarchically to facilitate ecological interpretations of the learned features. By analyzing 132 bird species counts, we infer the dominant environmental drivers of the community, species clusters and regions of common profile. Three of the learned drivers correspond to distinct climactic regions with different dominant forest types. Three further drivers are spatially heterogeneous and signal urban, agricultural, and wetland areas, respectively.

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arXiv2025

Nonparametric IPSS: Fast, flexible feature selection with false discovery control

Feature selection is a critical task in machine learning and statistics. However, existing feature selection methods either (i) rely on parametric methods such as linear or generalized linear models, (ii) lack theoretical false discovery control, or (iii) identify few true positives. Here, we introduce a general feature selection method with finite-sample false discovery control based on applying integrated path stability selection (IPSS) to arbitrary feature importance scores. The method is nonparametric whenever the importance scores are nonparametric, and it estimates q-values, which are better suited to high-dimensional data than p-values. We focus on two special cases using importance scores from gradient boosting (IPSSGB) and random forests (IPSSRF). Extensive nonlinear simulations with RNA sequencing data show that both methods accurately control the false discovery rate and detect more true positives than existing methods. Both methods are also efficient, running in under 20 seconds when there are 500 samples and 5000 features. We apply IPSSGB and IPSSRF to detect microRNAs and genes related to cancer, finding that they yield better predictions with fewer features than existing approaches.

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arXiv2025

On the Posterior Computation Under the Dirichlet-Laplace Prior

Modern applications routinely collect high-dimensional data, leading to statistical models having more parameters than there are samples available. A common solution is to impose sparsity in parameter estimation, often using penalized optimization methods. Bayesian approaches provide a probabilistic framework to formally quantify uncertainty through shrinkage priors. Among these, the Dirichlet-Laplace prior has attained recognition for its theoretical guarantees and wide applicability. This article identifies a critical yet overlooked issue in the implementation of Gibbs sampling algorithms for such priors. We demonstrate that ambiguities in the presentation of key algorithmic steps, while mathematically coherent, have led to widespread implementation inaccuracies that fail to target the intended posterior distribution -- a target endowed with rigorous asymptotic guarantees. Using the normal-means problem and high-dimensional linear regressions as canonical examples, we clarify these implementation pitfalls and their practical consequences and propose corrected and more efficient sampling procedures.

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arXiv2025

Infinite joint species distribution models

Joint species distribution models are popular in ecology for modeling covariate effects on species occurrence, while characterizing cross-species dependence. Data consist of multivariate binary indicators of the occurrences of different species in each sample, along with sample-specific covariates. A key problem is that current models implicitly assume that the list of species under consideration is predefined and finite, while for highly diverse groups of organisms, it is impossible to anticipate which species will be observed in a study and discovery of unknown species is common. This article proposes a new modeling paradigm for statistical ecology, which generalizes traditional multivariate probit models to accommodate large numbers of rare species and new species discovery. We discuss theoretical properties of the proposed modeling paradigm and implement efficient algorithms for posterior computation. Simulation studies and applications to fungal biodiversity data provide compelling support for the new modeling class.

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arXiv2025

Identifiable and interpretable nonparametric factor analysis

Factor models are widely used to reduce dimensionality in modeling high-dimensional data. However, there remains a need for models that can be reliably fit in modest sample sizes and are identifiable, interpretable, and flexible. To address this gap, we propose a NIFTY model that uses a linear factor structure with Gaussian residuals, but with a novel latent variable modeling structure. In particular, we model each latent variable as a one-dimensional nonlinear mapping of a uniform latent location. A key innovation is allowing different latent variables to be transformations of the same latent locations, accommodating intrinsic lower-dimensional nonlinear structures. Leveraging on pre-trained data obtained by diffusion maps and post-processing of MCMC samples, we obtain model identifiability. In addition, we softly constrain the empirical distribution of the latent locations to be close to uniform to address a latent posterior shift problem, which is common in factor models and can lead to substantial bias in parameter inferences, predictions, and generative modeling. We show good performance in density estimation and data visualization in simulations, and apply NIFTY to bird song data in an environmental monitoring application.

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arXiv2025

Targeted empirical Bayes for more supervised joint factor analysis

Joint Bayesian factor models are popular for characterizing relationships between multivariate correlated predictors and a response variable. Standard models assume that all variables, including both the predictors and the response, are conditionally independent given latent factors. In marginalizing out these factors, one obtains a low rank plus diagonal factorization for the joint covariance, which implies a linear regression for the response given the predictors. Although there are many desirable properties of such models, these methods can struggle to identify the signal when the response is not dependent on the dominant principal components in the predictors. To address this problem, we propose estimating the residual variance in the response model with an empirical Bayes procedure that targets predictive performance of the response given the predictors. We illustrate that this can lead to substantial improvements in simulation performance. We are particularly motivated by studies assessing the health effects of environmental exposures and provide an illustrative application to NHANES data.

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arXiv2025

Factor pre-training in Bayesian multivariate logistic models

This article focuses on inference in logistic regression for high-dimensional binary outcomes. A popular approach induces dependence across the outcomes by including latent factors in the linear predictor. Bayesian approaches are useful for characterizing uncertainty in inferring the regression coefficients, factors and loadings, while also incorporating hierarchical and shrinkage structure. However, Markov chain Monte Carlo algorithms for posterior computation face challenges in scaling to high-dimensional outcomes. Motivated by applications in ecology, we exploit a blessing of dimensionality to motivate pre-estimation of the latent factors. Conditionally on the factors, the outcomes are modeled via independent logistic regressions. We implement Gaussian approximations in parallel in inferring the posterior on the regression coefficients and loadings, including a simple adjustment to obtain credible intervals with valid frequentist coverage. We show posterior concentration properties and excellent empirical performance in simulations. The methods are applied to insect biodiversity data in Madagascar.

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arXiv2025

Product Centered Dirichlet Processes for Bayesian Multiview Clustering

While there is an immense literature on Bayesian methods for clustering, the multiview case has received little attention. This problem focuses on obtaining distinct but statistically dependent clusterings in a common set of entities for different data types. For example, clustering patients into subgroups with subgroup membership varying according to the domain of the patient variables. A challenge is how to model the across-view dependence between the partitions of patients into subgroups. The complexities of the partition space make standard methods to model dependence, such as correlation, infeasible. In this article, we propose CLustering with Independence Centering (CLIC), a clustering prior that uses a single parameter to explicitly model dependence between clusterings across views. CLIC is induced by the product centered Dirichlet process (PCDP), a novel hierarchical prior that bridges between independent and equivalent partitions. We show appealing theoretic properties, provide a finite approximation and prove its accuracy, present a marginal Gibbs sampler for posterior computation, and derive closed form expressions for the marginal and joint partition distributions for the CLIC model. On synthetic data and in an application to epidemiology, CLIC accurately characterizes view-specific partitions while providing inference on the dependence level.

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arXiv2025

Gridding and Parameter Expansion for Scalable Latent Gaussian Models of Spatial Multivariate Data

Scalable spatial GPs for massive datasets can be built via sparse Directed Acyclic Graphs (DAGs) where a small number of directed edges is sufficient to flexibly characterize spatial dependence. The DAG can be used to devise fast algorithms for posterior sampling of the latent process, but these may exhibit pathological behavior in estimating covariance parameters. In this article, we introduce gridding and parameter expansion methods to improve the practical performance of MCMC algorithms in terms of effective sample size per unit time (ESS/s). Gridding is a model-based strategy that reduces the number of expensive operations necessary during MCMC on irregularly spaced data. Parameter expansion reduces dependence in posterior samples in spatial regression for high resolution data. These two strategies lead to computational gains in the big data settings on which we focus. We consider popular constructions of univariate spatial processes based on Matérn covariance functions and multivariate coregionalization models for Gaussian outcomes in extensive analyses of synthetic datasets comparing with alternative methods. We demonstrate effectiveness of our proposed methods in a forestry application using remotely sensed data from NASA's Goddard LiDAR, Hyper-Spectral, and Thermal imager (G-LiHT).

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