arXiv subjects

Anton H. Westveld

Publications and source records attributed to Anton H. Westveld.

13 recordsLinked to original sources

arXiv2026

Bayesian nonparametric modeling of dynamic pollution clusters through an autoregressive logistic-beta Stirling-gamma process

Fine suspended particulates (FSP), commonly known as PM2.5, are among the most harmful air pollutants, posing serious risks to population health and environmental integrity. As such, accurately identifying clusters of air-quality monitoring stations exhibiting similar FSP levels is essential for guiding targeted interventions and localized public-health response measures. This task, however, is notably nontrivial as FSP levels may depend on various regional and temporal factors, which should be incorporated in the modeling process. Thus, we capitalize on Bayesian nonparametric dynamic clustering ideas, in which clustering structures may be influenced by complex dependencies. Existing implementations of dynamic clustering, however, rely on copula-based dependent Dirichlet processes (DPs), presenting considerable computational challenges for real-world deployment. With this in mind, we propose a more efficient alternative for dynamic clustering by incorporating the novel ideas of logistic-beta dependent DPs. We also adopt a Stirling-gamma prior--a novel distribution family--on the concentration parameter of our underlying DP, easing the process of incorporating prior knowledge into the model. Efficient computational strategies for posterior inference are also presented. We apply our proposed method to identify dynamic clusters of air-quality monitoring stations across Chile and demonstrate its superior performance over existing approaches.

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arXiv2026

Gradient Boosted Mixed Models: Flexible Estimation of Mean and Variance Components for Clustered Data

We introduce a novel way to combine gradient boosting with mixed effects models, whereby the mean and variance components are learned jointly as functions of covariates via likelihood-based gradients. Gradient Boosted Mixed Models (GBMixed) estimates a nonparametric fixed effects function characterizing the overall mean of the response, while also allowing the random effects covariance matrix along with the residual variance to depend on covariates in a flexible manner. We demonstrate how GBMixed facilitates covariate-dependent random effect predictions, and subsequently point predictions and prediction intervals for individual treatment effects, that can adapt between population-level and cluster-level information. Experiments and applications to two real-world datasets show that GBMixed can accurately recover complex nonlinear fixed effect functions and covariate-dependent covariances in a linear mixed model, while also improving point and probabilistic predictive performance compared with several existing approaches such as parametric linear mixed models, Natural Gradient Boosting, and Gaussian Process Boosting. In simulations where the variance components are designed to vary as a function of covariates, GBMixed reduces the mean squared error in recovering the random effects variance function by a factor of eight relative to linear mixed models and Gaussian Process Boosting.

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arXiv2026

Bayesian Gaussian Mixture Modeling for Symmetric Matrix Variate Data

Statistical inference on individual activity networks has been a historically difficult task due to the lack of available data at the appropriate granularity and the complexity of modeling individual mobility patterns. The recent availability of GPS data from individual devices, combined with highly detailed demographic information, suggests that one of these challenges can now be addressed. We introduce a new model which we call the Symmetric Matrix-Variate Normal Mixture Model (STRUCTURED) to estimate how demographic traits influence changes in human activity networks, using sociomatrices that capture the probabilistic spatial overlap between individuals over time. We exploit the commutativity constraint inherent in the symmetric matrix-variate normal distribution to parameterize the column precision matrix as a polynomial of the row precision matrix, reducing the effective parameter space by an order of magnitude. We develop two variants of STRUCTURED: STRUCTURED-FP, which estimates the full polynomial, and STRUCTURED-RJ, which uses reversible-jump MCMC to select a reduced-order parameterization. Simulation studies demonstrate that STRUCTURED-RJ outperforms existing methods in sparse-data regimes, whereas STRUCTURED-FP is preferred when sample sizes are large. We apply the model to GPS-derived sociomatrices of 293 individuals in King County, WA, finding that local crime environments and youth employment density are the dominant demographic factors explaining variation in weekly activity overlap patterns.

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arXiv2025

Model-based calibration of gear-specific fish abundance survey data as a change-of-support problem

For commercial and recreational fisheries of a wide-ranging species to be sustainable, abundance studies from neighboring regions should be unified. For the first time in the USA, a single research project to estimate the abundance of the Greater Amberjack {Seriola dumerili) is being undertaken at the continental scale. A major methodological challenge lies in 1) the difference in fish detection gears deployed by regional survey teams that produce gear-specific relative abundance indices, and 2) the unknown relationship between actual abundance and these indices. In this paper, we develop a conversion tool that is operationalized from a Bayesian hierarchical model in an inferential context akin to the change-of-support problem often encountered in large-scale spatial studies; though, the context here is to reconcile abundance data observed at various gear-specific scales. To this end, we consider a small calibration experiment in which 2 to 4 different underwater video camera types were simultaneously deployed on each of 21 boat trips. Alongside the suite of deployed cameras was also an acoustic echosounder that recorded fish signals along surrounding transects. Our modeling framework is used to derive calibration formulae for translating camera-specific relative indices to the actual abundance scale in surveys that deploy a single camera. Cross-validation is conducted using mark-recapture abundance estimates (only available for 10 trips, all observed at a single habitat type) and through a separate simulation study. We also briefly discuss the case when surveys pair one camera with the echosounder.

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arXiv2025

Modeling Human Spatial Mobility Patterns with the Lévy Flight Cluster Model

Despite the extensive collection of individual mobility data over the past decade, fueled by the widespread use of GPS-enabled personal devices, the existing statistical literature on estimating human spatial mobility patterns from temporally irregular location data remains limited. In this paper, we introduce the Lévy Flight Cluster Model (LFCM), a hierarchical Bayesian mixture model designed to analyze an individual's activity distribution. The LFCM can be utilized to determine probabilistic overlaps between individuals' activity patterns and serves as an anonymization tool to generate synthetic location data. We present our methodology using real-world human location data, demonstrating its ability to accurately capture the key characteristics of human movement.

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arXiv2024

Adaptive Shrinkage with a Nonparametric Bayesian Lasso

Modern approaches to perform Bayesian variable selection rely mostly on the use of shrinkage priors. That said, an ideal shrinkage prior should be adaptive to different signal levels, ensuring that small effects are ruled out, while keeping relatively intact the important ones. With this task in mind, we develop the nonparametric Bayesian Lasso, an adaptive and flexible shrinkage prior for Bayesian regression and variable selection, particularly useful when the number of predictors is comparable or larger than the number of available data points. We build on spike-and-slab Lasso ideas and extend them by placing a Dirichlet Process prior on the shrinkage parameters. The result is a prior on the regression coefficients that can be seen as an infinite mixture of Double Exponential densities, all offering different amounts of regularization, ensuring a more adaptive and flexible shrinkage. We also develop an efficient Markov chain Monte Carlo algorithm for posterior inference. Through various simulation exercises and real-world data analyses, we demonstrate that our proposed method leads to a better recovery of the true regression coefficients, a better variable selection, and better out-of-sample predictions, highlighting the benefits of the nonparametric Bayesian Lasso over existing shrinkage priors.

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arXiv2024

BOB: Bayesian Optimized Bootstrap for Uncertainty Quantification in Gaussian Mixture Models

A natural way to quantify uncertainties in Gaussian mixture models (GMMs) is through Bayesian methods. That said, sampling from the joint posterior distribution of GMMs via standard Markov chain Monte Carlo (MCMC) imposes several computational challenges, which have prevented a broader full Bayesian implementation of these models. A growing body of literature has introduced the Weighted Likelihood Bootstrap and the Weighted Bayesian Bootstrap as alternatives to MCMC sampling. The core idea of these methods is to repeatedly compute maximum a posteriori (MAP) estimates on many randomly weighted posterior densities. These MAP estimates then can be treated as approximate posterior draws. Nonetheless, a central question remains unanswered: How to select the random weights under arbitrary sample sizes. We, therefore, introduce the Bayesian Optimized Bootstrap (BOB), a computational method to automatically select these random weights by minimizing, through Bayesian Optimization, a black-box and noisy version of the reverse Kullback-Leibler (KL) divergence between the Bayesian posterior and an approximate posterior obtained via random weighting. Our proposed method outperforms competing approaches in recovering the Bayesian posterior, it provides a better uncertainty quantification, and it retains key asymptotic properties from existing methods. BOB's performance is demonstrated through extensive simulations, along with real-world data analyses.

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arXiv2023

Latent Causal Socioeconomic Health Index

This research develops a model-based LAtent Causal Socioeconomic Health (LACSH) index at the national level. Motivated by the need for a holistic national well-being index, we build upon the latent health factor index (LHFI) approach that has been used to assess the unobservable ecological/ecosystem health. LHFI integratively models the relationship between metrics, latent health, and covariates that drive the notion of health. In this paper, the LHFI structure is integrated with spatial modeling and statistical causal modeling. Our efforts are focused on developing the integrated framework to facilitate the understanding of how an observational continuous variable might have causally affected a latent trait that exhibits spatial correlation. A novel visualization technique to evaluate covariate balance is also introduced for the case of a continuous policy (treatment) variable. Our resulting LACSH framework and visualization tool are illustrated through two global case studies on national socioeconomic health (latent trait), each with various metrics and covariates pertaining to different aspects of societal health, and the treatment variable being mandatory maternity leave days and government expenditure on healthcare, respectively. We validate our model by two simulation studies. All approaches are structured in a Bayesian hierarchical framework and results are obtained by Markov chain Monte Carlo techniques.

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arXiv2019

Modeling National Latent Socioeconomic Health and Examination of Policy Effects via Causal Inference

This research develops a socioeconomic health index for nations through a model-based approach which incorporates spatial dependence and examines the impact of a policy through a causal modeling framework. As the gross domestic product (GDP) has been regarded as a dated measure and tool for benchmarking a nation's economic performance, there has been a growing consensus for an alternative measure---such as a composite `wellbeing' index---to holistically capture a country's socioeconomic health performance. Many conventional ways of constructing wellbeing/health indices involve combining different observable metrics, such as life expectancy and education level, to form an index. However, health is inherently latent with metrics actually being observable indicators of health. In contrast to the GDP or other conventional health indices, our approach provides a holistic quantification of the overall `health' of a nation. We build upon the latent health factor index (LHFI) approach that has been used to assess the unobservable ecological/ecosystem health. This framework integratively models the relationship between metrics, the latent health, and the covariates that drive the notion of health. In this paper, the LHFI structure is integrated with spatial modeling and statistical causal modeling, so as to evaluate the impact of a policy variable (mandatory maternity leave days) on a nation's socioeconomic health, while formally accounting for spatial dependency among the nations. We apply our model to countries around the world using data on various metrics and potential covariates pertaining to different aspects of societal health. The approach is structured in a Bayesian hierarchical framework and results are obtained by Markov chain Monte Carlo techniques.

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arXiv2017

A Copula-based Imputation Model for Missing Data of Mixed Type in Multilevel Data Sets

We propose a copula based method to handle missing values in multivariate data of mixed types in multilevel data sets. Building upon the extended rank likelihood of \cite{hoff2007extending} and the multinomial probit model, our model is a latent variable model which is able to capture the relationship among variables of different types as well as accounting for the clustering structure. We fit the model by approximating the posterior distribution of the parameters and the missing values through a Gibbs sampling scheme. We use the multiple imputation procedure to incorporate the uncertainty due to missing values in the analysis of the data. Our proposed method is evaluated through simulations to compare it with several conventional methods of handling missing data. We also apply our method to a data set from a cluster randomized controlled trial of a multidisciplinary intervention in acute stroke units. We conclude that our proposed copula based imputation model for mixed type variables achieves reasonably good imputation accuracy and recovery of parameters in some models of interest, and that adding random effects enhances performance when the clustering effect is strong.

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arXiv2013

A Statistical Social Network Model for Consumption Data in Food Webs

We adapt existing statistical modeling techniques for social networks to study consumption data observed in trophic food webs. These data describe the feeding volume (non-negative) among organisms grouped into nodes, called trophic species, that form the food web. Model complexity arises due to the extensive amount of zeros in the data, as each node in the web is predator/prey to only a small number of other trophic species. Many of the zeros are regarded as structural (non-random) in the context of feeding behavior. The presence of basal prey and top predator nodes (those who never consume and those who are never consumed, with probability 1) creates additional complexity to the statistical modeling. We develop a special statistical social network model to account for such network features. The model is applied to two empirical food webs; focus is on the web for which the population size of seals is of concern to various commercial fisheries.

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arXiv2011

A mixed effects model for longitudinal relational and network data, with applications to international trade and conflict

The focus of this paper is an approach to the modeling of longitudinal social network or relational data. Such data arise from measurements on pairs of objects or actors made at regular temporal intervals, resulting in a social network for each point in time. In this article we represent the network and temporal dependencies with a random effects model, resulting in a stochastic process defined by a set of stationary covariance matrices. Our approach builds upon the social relations models of Warner, Kenny and Stoto [Journal of Personality and Social Psychology 37 (1979) 1742--1757] and Gill and Swartz [Canad. J. Statist. 29 (2001) 321--331] and allows for an intra- and inter-temporal representation of network structures. We apply the methodology to two longitudinal data sets: international trade (continuous response) and militarized interstate disputes (binary response).

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arXiv2010

A Statistical View of Learning in the Centipede Game

In this article we evaluate the statistical evidence that a population of students learn about the sub-game perfect Nash equilibrium of the centipede game via repeated play of the game. This is done by formulating a model in which a player's error in assessing the utility of decisions changes as they gain experience with the game. We first estimate parameters in a statistical model where the probabilities of choices of the players are given by a Quantal Response Equilibrium (QRE) (McKelvey and Palfrey, 1995, 1996, 1998), but are allowed to change with repeated play. This model gives a better fit to the data than similar models previously considered. However, substantial correlation of outcomes of games having a common player suggests that a statistical model that captures within-subject correlation is more appropriate. Thus we then estimate parameters in a model which allows for within-player correlation of decisions and rates of learning. Through out the paper we also consider and compare the use of randomization tests and posterior predictive tests in the context of exploratory and confirmatory data analyses.

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