arXiv subjects

Alexandra M. Schmidt

Publications and source records attributed to Alexandra M. Schmidt.

At least 19 recordsLinked to original sources

arXiv2026

Heterogeneous behavioral mechanisms in epidemiological models

Traditional epidemic models frequently assume behavioral homogeneity. The susceptible-infected-recovered model provides a robust foundation for characterizing disease transmission, but it does so without accounting for how people actually respond to risk. In contrast, behavioral change models incorporate mechanisms that capture how individuals adjust their actions during an outbreak, recognizing that rising infection risk typically motivates protective behaviors. Yet both approaches share a key limitation: they overlook the inherent heterogeneity of a population. In reality, communities are a complex mixture of risk tolerances and behavioral tendencies. Ignoring this inherent heterogeneity can obscure important differences in how individuals perceive and respond to disease threats. This paper introduces a novel Bayesian mixture model designed to address this limitation by partitioning the population into two distinct behavioral patterns: risk-neutral individuals, who maintain baseline contact rates, and risk-averse individuals, who modulate their behavior in response to epidemic severity. By integrating these disparate dynamics into a unified transmission framework, the proposed model explicitly accounts for varying population behaviors often overlooked by aggregate approaches. Through simulation studies and empirical data applications, we demonstrate that this approach significantly outperforms traditional models in parameter recovery, epidemic trajectory estimation, and forecasting precision. The findings suggest that failing to account for behavioral diversity leads to biased peak estimates and artificially stretched epidemic curves. Consequently, this research provides a more nuanced computational toolkit for predicting outbreak trajectories in socially fragmented environments, ensuring that public health intervention strategies are informed by a foundation of behavioral realism.

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arXiv2026

Multivariable Behavioral Change Modeling of Epidemics in the Presence of Undetected Infections

Epidemic models are invaluable tools to understand and implement strategies to control the spread of infectious diseases, as well as to inform public health policies and resource allocation. However, current modeling approaches have limitations that reduce their practical utility, such as the exclusion of human behavioral change in response to the epidemic or ignoring the presence of undetected infectious individuals in the population. These limitations became particularly evident during the COVID-19 pandemic, underscoring the need for more accurate and informative models. To address these challenges, we develop a novel Bayesian epidemic modeling framework to better capture the complexities of disease spread by incorporating behavioral responses and undetected infections. In particular, our framework makes three contributions: 1) leveraging additional data on hospitalizations and deaths in modeling the disease dynamics, 2) accounting for data uncertainty arising from the large presence of asymptomatic and undetected infections, and 3) allowing the population behavioral change to be dynamically influenced by multiple data sources (cases and deaths). We thoroughly investigate the properties of the proposed model via simulation, and illustrate its utility on COVID-19 data from Montreal and Miami.

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arXiv2026

Hidden Markov Individual-level Models of Infectious Disease Transmission

Individual-level epidemic models are increasingly being used to help understand the transmission dynamics of various infectious diseases. However, fitting such models to individual-level epidemic data is challenging, as we often only know when an individual first showed symptoms of the disease and not when they were infected or removed. We propose an autoregressive coupled hidden Markov model to infer unknown infection and removal times, as well as other model parameters, given only the symptom-onset times. More traditional data augmentation methods used in epidemic modelling have either assumed that the infection or removal times are known or that all infected individuals showed symptoms. In contrast, we build an observation model where there is a chance that an infectious individual never shows symptoms during the study, allowing for undetected (e.g., asymptomatic) infections. Symptom onset is not assumed to correspond to infection or removal. Bayesian coupled hidden Markov models have been used previously for individual-level epidemic data consisting of laboratory diagnostic test results. However, these models are not appropriate for symptom-onset data, as they have a chance of generating multiple symptom-onset times for an individual. In contrast, we incorporate autoregression into the observation process, ensuring that at most one symptom-onset time is observed per individual. We illustrate the flexibility of our approach by fitting two examples: an experiment on the spread of tomato spot wilt virus in pepper plants and an outbreak of norovirus among nurses in a hospital.

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arXiv2026

On the PM2.5 -- Mortality Association: A Bayesian Model for Spatio-Temporal Confounding

In epidemiological studies of air pollution and public health, estimating the health impact of exposure to air pollution may be hindered by the unknown functional form of the exposure-outcome association and by unmeasured confounding factors that are linked to both exposure and outcome. These challenges are especially relevant in spatio-temporal analyses, where their joint exploration remains limited. To study the effects of fine particulate matter on mortality among elderly people in Italy, we propose a Bayesian spatial dynamic generalized linear model that captures the non-linear exposure-outcome association and decomposes the exposure effect across fine and coarse spatio-temporal scales of variation. Together, these features allow reducing the spatio-temporal confounding bias and recovering the shape of the association, as demonstrated through simulation studies. The real-data analysis reveals a clear temporal pattern in the exposure effect, with peaks during summer months. We argue that this finding may be due to interactions of particulate matter with air temperature and unmeasured confounders.

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arXiv2025

Markov switching zero-inflated space-time multinomial models for comparing multiple infectious diseases

Univariate zero-inflated models are increasingly being used to account for excess zeros in spatio-temporal infectious disease counts. However, the multivariate case is challenging due to the need to account for correlations across space, time and disease in both the count and zero-inflated components of the model. We are interested in comparing the transmission dynamics of several co-circulating infectious diseases across space and time, where some of the diseases can be absent for long periods. We first assume there is a baseline disease that is well-established and always present in the region. The other diseases switch between periods of presence and absence in each area through a series of coupled Markov chains, which account for long periods of disease absence, disease interactions and disease spread from neighboring areas. Since we are mainly interested in comparing the diseases, we assume the cases of the present diseases in an area jointly follow an autoregressive multinomial model. We use the multinomial model to investigate whether there are associations between certain factors, such as temperature, and differences in the transmission intensity of the diseases. Inference is performed using efficient Bayesian Markov chain Monte Carlo methods based on jointly sampling all unknown presence indicators. We apply the model to spatio-temporal counts of dengue, Zika, and chikungunya cases in Rio de Janeiro, during the first triple epidemic there.

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arXiv2025

Co-SIVI: A Correlated Semi-Implicit Variational Approach for Spatial Models

We propose correlated semi-implicit variational inference (Co-SIVI), a scalable approach for full posterior approximation in large spatial models with exponential-family likelihoods. Co-SIVI incorporates dependence directly into the conditional variational distribution of spatial random effects through an iterative weighted least squares algorithm that accommodates both Gaussian process and nearest-neighbor Gaussian process (NNGP) priors. For large samples, we further propose reparameterizing the variational family for the covariance parameters to better capture posterior dependence. Co-SIVI addresses an important limitation of semi-implicit variational inference (SIVI), for which dependence induced through the mixing distribution may be insufficient when spatial random effects are explicitly included in the variational family. In simulations with Gaussian, Poisson, Gamma, and Bernoulli outcomes, Co-SIVI closely reproduces Hamiltonian Monte Carlo (HMC) results at substantially lower computational cost, while SIVI performs similarly for marginalized Gaussian models. We apply SIVI and Co-SIVI, both with NNGP priors, to two large-scale datasets: temperature data modeled with a Gaussian likelihood and housing price data modeled with a Gamma likelihood. Overall, Co-SIVI provides a scalable and flexible alternative to HMC for full posterior approximation in large non-Gaussian spatial models.

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arXiv2025

Bayesian spatiotemporal modeling of passenger trip assignment in metro networks

Assigning passenger trips to specific network paths using automatic fare collection (AFC) data is a fundamental application in urban transit analysis. The task is a difficult inverse problem: the only available information consists of each passenger's total travel time and their origin and destination, while individual passenger path choices and dynamic network costs are unobservable, and behavior varies significantly across space and time. We propose a novel Bayesian hierarchical model to resolve this problem by jointly estimating dynamic network costs and passenger path choices while quantifying their uncertainty. Our model decomposes trip travel time into four components -- access, in-vehicle, transfer, and egress -- each modeled as a time-varying random walk. To capture heterogeneous passenger behavior, we introduce a multinomial logit model with spatiotemporally varying coefficients. We manage the high dimensionality of these coefficients using kernelized tensor factorization with Gaussian process priors to effectively model complex spatiotemporal correlations. We develop a tailored and efficient Markov chain Monte Carlo (MCMC) algorithm for model inference. A simulation study demonstrates the method's effectiveness in recovering the underlying model parameters. On a large-scale dataset from the Hong Kong Mass Transit Railway, our framework demonstrates superior estimation accuracy over established benchmarks. The results reveal significant spatiotemporal variations in passenger preferences and provide robust uncertainty quantification, offering transit operators a powerful tool for enhancing service planning and operational management.

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arXiv2025

A Comparison between Markov Switching Zero-inflated and Hurdle Models for Spatio-temporal Infectious Disease Counts

In epidemiological studies, zero-inflated and hurdle models are commonly used to handle excess zeros in reported infectious disease cases. However, they can not model the persistence (changing from presence to presence) and reemergence (changing from absence to presence) of a disease separately. Covariates can sometimes have different effects on the reemergence and persistence of a disease. Recently, a zero-inflated Markov switching negative binomial model was proposed to accommodate this issue. We introduce a Markov switching negative binomial hurdle model as a competitor of that approach, as hurdle models are often also used as alternatives to zero-inflated models for accommodating excess zeroes. We begin the comparison by inspecting the underlying assumptions made by both models. Hurdle models assume perfect detection of the disease cases while zero-inflated models implicitly assume the case counts can be under-reported, thus we investigate when a negative binomial distribution can approximate the true distribution of reported counts. A comparison of the fit of the two types of Markov switching models is undertaken on chikungunya cases across the neighborhoods of Rio de Janeiro. We find that, among the fitted models, the Markov switching negative binomial zero-inflated model produces the best predictions and both Markov switching models produce remarkably better predictions than more traditional negative binomial hurdle and zero-inflated models.

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arXiv2025

Scalable Spatiotemporal Modeling for Bicycle Count Prediction

We propose a novel sparse spatiotemporal dynamic generalized linear model for efficient inference and prediction of bicycle count data. Assuming Poisson distributed counts with spacetime-varying rates, we model the log-rate using spatiotemporal intercepts, dynamic temporal covariates, and site-specific effects additively. Spatiotemporal dependence is modeled using a spacetime-varying intercept that evolves smoothly over time with spatially correlated errors, and coefficients of some temporal covariates including seasonal harmonics also evolve dynamically over time. Inference is performed following the Bayesian paradigm, and uncertainty quantification is naturally accounted for when predicting bicycle counts for unobserved locations and future times of interest. To address the challenges of high-dimensional inference of spatiotemporal data in a Bayesian setting, we develop a customized hybrid Markov Chain Monte Carlo (MCMC) algorithm. To address the computational burden of dense covariance matrices, we extend our framework to high-dimensional spatial settings using the sparse SPDE approach of Lindgren et al. (2011), demonstrating its accuracy and scalability on both synthetic data and Montreal Island bicycle datasets. The proposed approach naturally provides missing value imputations, kriging, future forecasting, spatiotemporal predictions, and inference of model components. Moreover, it provides ways to predict average annual daily bicycles (AADB), a key metric often sought when designing bicycle networks.

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arXiv2025

Regularized Principal Spline Functions to Mitigate Spatial Confounding

This paper proposes a new approach to address the problem of unmeasured confounding in spatial designs. Spatial confounding occurs when some confounding variables are unobserved and not included in the model, leading to distorted inferential results about the effect of an exposure on an outcome. We show the relationship existing between the confounding bias of a non-spatial model and that of a semi-parametric model that includes a basis matrix to represent the unmeasured confounder conditional on the exposure. This relationship holds for any basis expansion, however it is shown that using the semi-parametric approach guarantees a reduction in the confounding bias only under certain circumstances, which are related to the spatial structures of the exposure and the unmeasured confounder, the type of basis expansion utilized, and the regularization mechanism. To adjust for spatial confounding, and therefore try to recover the effect of interest, we propose a Bayesian semi-parametric regression model, where an expansion matrix of principal spline basis functions is used to approximate the unobserved factor, and spike-and-slab priors are imposed on the respective expansion coefficients in order to select the most important bases. From the results of an extensive simulation study, we conclude that our proposal is able to reduce the confounding bias more than competing approaches, and it also seems more robust to bias amplification.

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arXiv2024

Bayesian Analysis of Sigmoidal Gaussian Cox Processes via Data Augmentation

Many models for point process data are defined through a thinning procedure where locations of a base process (often Poisson) are either kept (observed) or discarded (thinned). In this paper, we go back to the fundamentals of the distribution theory for point processes to establish a link between the base thinning mechanism and the joint density of thinned and observed locations in any of such models. In practice, the marginal model of observed points is often intractable, but thinned locations can be instantiated from their conditional distribution and typical data augmentation schemes can be employed to circumvent this problem. Such approaches have been employed in the recent literature, but some inconsistencies have been introduced across the different publications. We concentrate on an example: the so-called sigmoidal Gaussian Cox process. We apply our approach to resolve contradicting viewpoints in the data augmentation step of the inference procedures therein. We also provide a multitype extension to this process and conduct Bayesian inference on data consisting of positions of two different species of trees in Lansing Woods, Michigan. The emphasis is put on intertype dependence modeling with Bayesian uncertainty quantification.

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arXiv2024

Computational Considerations for the Linear Model of Coregionalization

In the last two decades, the linear model of coregionalization (LMC) has been widely used to model multivariate spatial processes. However, it can be a challenging task to conduct likelihood-based inference for such models because of the cubic cost associated with Gaussian likelihood evaluations. Starting from an analogy with matrix normal models, we propose a reformulation of the LMC likelihood that highlights the linear, rather than cubic, computational complexity as a function of the dimension of the response vector. We describe how those simplifications can be exploited in Gaussian hierarchical models. In addition, we propose a new sparsity-inducing approach to the LMC that introduces structural zeros in the coregionalization matrix in an attempt to reduce the number of parameters in a principled and data-driven way. Our reformulation of the LMC likelihood ensures that our sparse approach comes at virtually no additional cost when included in a Markov chain Monte Carlo (MCMC) algorithm. It is shown, on synthetic data, to significantly improve predictive performance. We also apply our methodology to a dataset comprised of air pollutant measurements from the state of California. We investigate the strength of the correlation among the measurements by providing new insights from our sparse method.

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arXiv2024

A three-state coupled Markov switching model for COVID-19 outbreaks across Quebec based on hospital admissions

Recurrent COVID-19 outbreaks have placed immense strain on the hospital system in Quebec. We develop a Bayesian three-state coupled Markov switching model to analyze COVID-19 outbreaks across Quebec based on admissions in the 30 largest hospitals. Within each catchment area, we assume the existence of three states for the disease: absence, a new state meant to account for many zeroes in some of the smaller areas, endemic and outbreak. Then we assume the disease switches between the three states in each area through a series of coupled nonhomogeneous hidden Markov chains. Unlike previous approaches, the transition probabilities may depend on covariates and the occurrence of outbreaks in neighboring areas, to account for geographical outbreak spread. Additionally, to prevent rapid switching between endemic and outbreak periods we introduce clone states into the model which enforce minimum endemic and outbreak durations. We make some interesting findings, such as that mobility in retail and recreation venues had a positive association with the development and persistence of new COVID-19 outbreaks in Quebec. Based on model comparison our contributions show promise in improving state estimation retrospectively and in real-time, especially when there are smaller areas and highly spatially synchronized outbreaks. Furthermore, our approach offers new and interesting epidemiological interpretations, such as being able to estimate the effect of covariates on disease extinction.

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arXiv2024

A spatio-temporal model to detect potential outliers in disease mapping

Spatio-temporal disease mapping models are commonly used to estimate the relative risk of a disease over time and across areas. For each area and time point, the disease count is modelled with a Poisson distribution whose mean is the product of an offset and the disease relative risk. This relative risk is commonly decomposed in the log scale as the sum of fixed and latent effects. The Rushworth model allows for spatio-temporal autocorrelation of the random effects. We build on the Rushworth model to accommodate and identify potentially outlying areas with respect to their disease relative risk evolution, after taking into account the fixed effects. An area may display outlying behaviour at some points in time but not all. At each time point, we assume the latent effects to be spatially structured and include scaling parameters in the precision matrix, to allow for heavy-tails. Two prior specifications are considered for the scaling parameters: one where they are independent across space and one with spatial autocorrelation. We investigate the performance of the different prior specifications of the proposed model through simulation studies and analyse the weekly evolution of the number of COVID-19 cases across the 33 boroughs of Montreal and the 96 French departments during the second wave. In Montreal, 6 boroughs are found to be potentially outlying. In France, the model with spatially structured scaling parameters identified 21 departments as potential outliers. We find that these departments tend to be close to each other and within common French regions.

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arXiv2024

A Bayesian hierarchical model for disease mapping that accounts for scaling and heavy-tailed latent effects

In disease mapping, the relative risk of a disease is commonly estimated across different areas within a region of interest. The number of cases in an area is often assumed to follow a Poisson distribution whose mean is decomposed as the product between an offset and the logarithm of the disease's relative risk. The log risk may be written as the sum of fixed effects and latent random effects. The BYM2 model decomposes each latent effect into a weighted sum of independent and spatial effects. We build on the BYM2 model to allow for heavy-tailed latent effects and accommodate potentially outlying risks, after accounting for the fixed effects. We assume a scale mixture structure wherein the variance of the latent process changes across areas and allows for outlier identification. We propose two prior specifications for this scale mixture parameter. These are compared through simulation studies and in the analysis of Zika cases from the first (2015-2016) epidemic in Rio de Janeiro city, Brazil. The simulation studies show that, in terms of the model assessment criterion WAIC and outlier detection, the two proposed parametrisations perform better than the model proposed by Congdon (2017) to capture outliers. In particular, the proposed parametrisations are more efficient, in terms of outlier detection, than Congdon's when outliers are neighbours. Our analysis of Zika cases finds 19 out of 160 districts of Rio as potential outliers, after accounting for the socio-development index. Our proposed model may help prioritise interventions and identify potential issues in the recording of cases.

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arXiv2024

Conditional forecasting of bus travel time and passenger occupancy with Bayesian Markov regime-switching vector autoregression

Accurately forecasting bus travel time and passenger occupancy with uncertainty is essential for both travelers and transit agencies/operators. However, existing approaches to forecasting bus travel time and passenger occupancy mainly rely on deterministic models, providing only point estimates. In this paper, we develop a Bayesian Markov regime-switching vector autoregressive model to jointly forecast both bus travel time and passenger occupancy with uncertainty. The proposed approach naturally captures the intricate interactions among adjacent buses and adapts to the multimodality and skewness of real-world bus travel time and passenger occupancy observations. We develop an efficient Markov chain Monte Carlo (MCMC) sampling algorithm to approximate the resultant joint posterior distribution of the parameter vector. With this framework, the estimation of downstream bus travel time and passenger occupancy is transformed into a multivariate time series forecasting problem conditional on partially observed outcomes. Experimental validation using real-world data demonstrates the superiority of our proposed model in terms of both predictive means and uncertainty quantification compared to the Bayesian Gaussian mixture model.

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arXiv2023

Small Area Estimation with Random Forests and the LASSO

We consider random forests and LASSO methods for model-based small area estimation when the number of areas with sampled data is a small fraction of the total areas for which estimates are required. Abundant auxiliary information is available for the sampled areas, from the survey, and for all areas, from an exterior source, and the goal is to use auxiliary variables to predict the outcome of interest. We compare areal-level random forests and LASSO approaches to a frequentist forward variable selection approach and a Bayesian shrinkage method. Further, to measure the uncertainty of estimates obtained from random forests and the LASSO, we propose a modification of the split conformal procedure that relaxes the assumption of identically distributed data. This work is motivated by Ghanaian data available from the sixth Living Standard Survey (GLSS) and the 2010 Population and Housing Census. We estimate the areal mean household log consumption using both datasets. The outcome variable is measured only in the GLSS for 3\% of all the areas (136 out of 5019) and more than 170 potential covariates are available from both datasets. Among the four modelling methods considered, the Bayesian shrinkage performed the best in terms of bias, MSE and prediction interval coverages and scores, as assessed through a cross-validation study. We find substantial between-area variation, the log consumption areal point estimates showing a 1.3-fold variation across the GAMA region. The western areas are the poorest while the Accra Metropolitan Area district gathers the richest areas.

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arXiv2023

Bayesian Modeling of Dynamic Behavioral Change During an Epidemic

For many infectious disease outbreaks, the at-risk population changes their behavior in response to the outbreak severity, causing the transmission dynamics to change in real-time. Behavioral change is often ignored in epidemic modeling efforts, making these models less useful than they could be. We address this by introducing a novel class of data-driven epidemic models which characterize and accurately estimate behavioral change. Our proposed model allows time-varying transmission to be captured by the level of "alarm" in the population, with alarm specified as a function of the past epidemic trajectory. We investigate the estimability of the population alarm across a wide range of scenarios, applying both parametric functions and non-parametric functions using splines and Gaussian processes. The model is set in the data-augmented Bayesian framework to allow estimation on partially observed epidemic data. The benefit and utility of the proposed approach is illustrated through applications to data from real epidemics.

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