contagion parameter estimation and inference

Distinguishing simple contagion (e.g., independent cascade) from complex contagion (e.g., threshold-based activation) solely from observed diffusion data remains challenging due to reliance on strong parametric assumptions and sensitivity to noise and partial observability. Method: We propose the first topological classification framework based on Extended Persistent Homology (EPH), which captures the multiscale evolution of loop structures throughout the diffusion process—without assuming specific activation mechanisms or functional forms. Our approach integrates Topological Data Analysis (TDA), graph neural network–based diffusion simulation, and supervised learning. Contribution/Results: Evaluated on three real-world networks, the framework achieves high-accuracy contagion-type classification (average accuracy >92%) and accurate regression of key parameters (e.g., threshold values). It significantly improves robustness against observational noise, parameter uncertainty, and incomplete observations compared to conventional methods, establishing a novel model-agnostic paradigm for inferring contagion mechanisms from empirical data.

This study addresses key challenges in infectious disease dynamics—including real-time estimation of the instantaneous reproduction number, short-term forecasting, assessment of elimination probability, and simulation of intervention effects—by proposing a unified Bayesian online inference and prediction framework grounded in renewal models. Methodologically, it integrates sequential Monte Carlo (particle filtering) with epidemiological renewal modeling to jointly estimate and prospectively project the reproduction number, intervention effects, and elimination probability in real time. Its novelty lies in the first systematic unification of multi-objective inference and forecasting, concurrently correcting for observation delays, reporting biases, and model misspecification—substantially enhancing robustness. The framework is accompanied by open-source R/Python implementations and a practical algorithmic guide, lowering the barrier to deploying high-dimensional nonlinear models. Empirical validation on real-world data demonstrates high accuracy in reproduction number estimation and stable 7–14-day forecasts.

This paper addresses two key challenges in dynamic modeling of infectious disease burden: (1) difficulty in modeling cross-population dependencies and (2) insufficient robustness in temporal forecasting. To this end, we propose a Bayesian nonparametric framework based on multi-task Gaussian processes (MTGPs). Methodologically, we design an exchangeable GP-driven hierarchical dynamical model: a biologically interpretable mean function captures population-level heterogeneity; a structured covariance kernel explicitly encodes inter-population cross-dependencies; and a time-shrinkage mechanism enhances temporal generalization. Full Bayesian inference is performed via Markov Chain Monte Carlo (MCMC). Empirical evaluation across multiple real-world epidemic datasets demonstrates that our framework significantly outperforms state-of-the-art baselines—achieving higher predictive accuracy, superior sparse modeling capability, and more efficient cross-population information sharing. The approach thus provides an interpretable, robust, and scalable statistical foundation for infectious disease burden assessment.

This study addresses the compounded challenges in inferring epidemic spread on partially observed dynamic contact networks—namely, unknown infection times, incomplete network evolution, measurement errors in contacts, and external sources of infection. The authors propose a unified continuous-time stochastic process framework that jointly models SEIR transmission dynamics, state-dependent network evolution, and a symptom-contact observation mechanism. They derive, for the first time, the complete-data event-history likelihood of the coupled epidemic-network process under partial observability, establishing a theoretical foundation for both likelihood-based and Bayesian inference, and demonstrating that existing models arise as special cases. By integrating data augmentation and probabilistic graphical modeling, the approach simultaneously accounts for latent incubation periods, intermittent observations, contact misreporting, and exogenous infection pressure, revealing how disease progression and contact dynamics jointly govern parameter identifiability.

This study addresses the challenge of jointly modeling calibration and control parameters in computer model calibration, where the distribution of calibration parameters is unknown while that of control parameters is known. To tackle this issue, the authors propose a nonparametric Bayesian calibration method based on measure decomposition. The approach preserves the known marginal distribution of the control parameters while employing stochastic process modeling and Bayesian inference to construct a posterior distribution over the input space that aligns with field observations. Notably, this work is the first within a nonparametric calibration framework to explicitly maintain the prior distributional properties of the control parameters, thereby substantially enhancing the physical consistency and scientific credibility of the calibration results.

This work addresses the challenge of conducting calibrated Bayesian inference for parametric models whose likelihood functions are intractable, numerically unstable, or computationally prohibitive. Existing approaches lack finite-sample calibration guarantees under such conditions. The authors propose a fully probabilistic inference framework that requires neither a prior nor a likelihood, relying solely on the model’s simulation capability. By leveraging permutation-invariant functions—such as depth functions—to rank parameters and introducing a closed-form rescaling procedure, the method achieves finite-sample frequentist calibration. To the best of the authors’ knowledge, this is the first approach to provide theoretical calibration guarantees in a setting devoid of both likelihood and prior specifications. Empirical evaluations across four benchmark tasks—including differential privacy and the Ising model—as well as a spatial analysis of the 2025 U.S. measles outbreak demonstrate the method’s strong practical utility and robustness.

This study addresses sensitivity analysis and intervention optimization for discrete-time stochastic epidemic models under parameter uncertainty. The authors propose an unbiased gradient estimator tailored to posterior parameter distributions obtained via Bayesian calibration, enabling quantification of how vaccination coverage and contact rates influence the total number of infections over a finite time horizon. By integrating stochastic simulation with gradient estimation, the method achieves low variance—particularly outperforming finite-difference approaches in estimating derivatives with respect to contact rates—and reveals substantial discrepancies in sensitivity between the stochastic model and its deterministic limit. The findings indicate that parameter uncertainty attenuates indirect effects such as herd immunity, leading to more conservative optimal intervention strategies and an overall reduction in sensitivity.

This study addresses the challenge of structural unidentifiability and inference difficulty in nonlinear dynamic systems operating on unknown interaction networks. The authors propose an identification framework based on an implicit dependence matrix, establishing necessary and sufficient conditions for network identifiability by revealing its reliance on the spectral heterogeneity of the interaction matrix. The framework characterizes observational equivalence classes and overcomes the limitation of conventional approaches that erroneously conflate network dependencies with common shocks. Methodologically, it integrates semiparametric estimation, spectral analysis, and asymptotic theory to construct estimators with desirable asymptotic properties and develops a test for network dependence whose power is governed by spectral characteristics. The proposed framework demonstrates broad applicability across economic systems, including production networks and contagion models.

This study addresses the long-standing identification challenge of distinguishing whether similarity in binary nodal outcomes across two time points arises from social contagion or latent homophily, given only a single observed static network. The authors reframe contagion identification as a selection bias problem and propose a nonparametric sensitivity analysis framework that does not require specifying a network formation model. By integrating Smith’s approach to selection bias with the Ding–VanderWeele risk ratio bounds, they derive nonparametric bounds on the controlled direct effect, thereby recasting the question of “whether contagion exists” into “how strong latent homophily must be to explain the observed association.” Simulations demonstrate favorable error control and statistical power, and an application to 2008 U.S. House TARP voting data quantifies the robustness of contagion effects under plausible homophily assumptions.

This study addresses the challenges of causal inference in the endogenous formation of social networks—specifically unobserved confounding, reverse causality, equilibrium dependence, and sampling bias—by proposing a design-based nonparametric identification framework. Leveraging random variation in initial ties and repeated observations in panel network data, the approach treats nodes and their potential outcomes as non-stochastic, thereby circumventing conventional assumptions of random sampling and asymptotic approximations. An application to professional service firm data reveals a significant positive causal effect of indirect connections on tie formation, whereas the influence of node degree and local density is weak and statistically unstable. These findings underscore the method’s strength in handling the endogeneity and equilibrium complexity inherent in network formation processes.