identifiability analysis

This study investigates the trade-off degradation between parameter identifiability and predictive falsifiability in Bayesian model extensions. We formally establish, for the first time, their intrinsic negative correlation—where increased model complexity simultaneously degrades both properties. To mitigate this tension, we propose a novel inference framework grounded in the posterior joint structure of parameters and predictions. Through theoretical analysis and two canonical extension examples, we demonstrate that our approach improves the synergistic balance: it enhances the uniqueness of parameter interpretation (identifiability) while preserving empirical testability of predictions (falsifiability). Our core contribution is the introduction of a unified identifiability–falsifiability diagnostic perspective, providing a new paradigm for Bayesian modeling that integrates statistical rigor with scientific testability.

This study addresses parameter identifiability—a critical challenge in systems biology modeling—encompassing structural and practical identifiability, parameter interdependence, and reliability of extrapolative predictions. We propose embedding identifiability analysis throughout the entire modeling workflow, integrating global sensitivity analysis, simulation-based computational assessments (e.g., profile likelihood, Monte Carlo sampling), and output observability diagnostics to systematically quantify parameter uncertainty. A key innovation lies in emphasizing the synergistic roles of optimal experimental design, incorporation of prior knowledge, and model reduction in enhancing identifiability. Results demonstrate that weakly identifiable parameters severely compromise extrapolative predictive performance; our framework effectively pinpoints bottleneck parameters and informs targeted data acquisition strategies, thereby enabling the construction of biologically predictive models with robust uncertainty quantification.

Hypothesis testing in singular statistical models is often deemed infeasible due to non-identifiable parameters and degenerate Fisher information. This work circumvents these issues by reframing hypotheses in terms of identifiable functionals of the observable distribution rather than unidentifiable parameter functions, thereby recasting the problem as a classical testing problem in the space of probability distributions. The study introduces the novel concept of an “overlap barrier,” which reveals that hypotheses involving non-identifiable quantities inevitably lead to testing impossibility. A Hellinger-distance-based criterion for testability is established, enabling a structural classification of hypotheses in singular models. By integrating distribution-space analysis, posterior contraction theory, and test-driven Bayesian arguments, the framework is validated in Gaussian mixture models and reduced-rank regression, rigorously delineating the boundary between testable and non-testable hypotheses and clarifying the limits of valid statistical inference in singular settings.

This study addresses the structural identifiability of model parameters in partially observed stochastic processes, focusing on parameter uniqueness from two data modalities: single-particle trajectories and population density measurements. For spatiotemporal stochastic dynamics, the authors employ individual-based stochastic models to analyze trajectory data and partial differential equation (PDE)-based density evolution models for population-level observations. They innovatively extend differential algebraic methods to PDE models of stochastic processes and introduce a novel framework based on characteristic equations to construct Taylor expansions that explicitly account for the influence of initial conditions on identifiability. Their results demonstrate that parameters are globally identifiable from trajectory data, whereas only local identifiability can be achieved using density data alone, thereby highlighting the critical role of initial condition information in structural identifiability analysis.

This work addresses the structural identifiability of parameters in stochastic differential equation (SDE) models under multiple interventions—i.e., whether SDE parameters can be uniquely recovered from samples of post-intervention stationary distributions. Theoretically, we establish the first uniqueness guarantee for SDE parameter recovery under multi-intervention settings; for linear SDEs, we derive a tight lower bound on the minimum number of required interventions; for weak-noise nonlinear SDEs, we obtain an upper bound on identifiability. Methodologically, we propose a parametric framework featuring learnable activation functions, integrating intervention modeling, stationary distribution analysis, and weak-noise asymptotic theory. Experiments on synthetic data demonstrate that our approach accurately recovers ground-truth parameters, and the theory-guided learnable architecture significantly improves both estimation accuracy and robustness.

This study addresses the challenge of practical identifiability in parameter estimation for ordinary differential equation models of dynamical systems, which often arises due to limited, noisy, and partially observable data. To this end, the authors propose a Practical Identifiability Index (PII) that quantifies marginal parameter uncertainty via the logarithmic span of positive-parameter confidence intervals, offering a concise measure of how strongly observational data constrain each parameter. The PII enables consistent, order-of-magnitude comparisons across parameters, models, and experimental designs and complements existing approaches such as coverage probability and profile likelihood. Validated through parametric bootstrapping, sensitivity analysis, and structural identifiability theory on growth and compartmental epidemic models, the framework demonstrates that parameter uncertainty diminishes with more informative calibration windows, lower noise levels, and weaker parameter coupling; early-dynamics observability accelerates convergence, and additional measurements substantially enhance identifiability of latent-variable-associated parameters.

This work exposes a critical privacy risk: Bayesian posterior distributions and trained model parameters may inadvertently leak original training data. Addressing the lack of systematic analysis on Bayesian model reconstruction attacks, we propose the first unified score-matching framework capable of reconstructing training data from both Bayesian and non-Bayesian models. We further introduce the first theoretical characterization of attack-vulnerable data—leveraging the equivalence between maximum mean discrepancy (MMD) and kernel Stein discrepancy—to derive a mathematical criterion for training data recoverability. Through rigorous theoretical modeling and adversarial experiments, we quantitatively delineate the privacy boundary between model parameters and training data, precisely identifying the dimensions of information that remain reconstructible. Our results establish a novel paradigm for understanding data leakage mechanisms in machine learning and provide foundational theory for designing privacy-preserving defenses, including differential privacy and secure model publishing.

This work addresses the structural identifiability of ordinary differential equation (ODE)-based mechanistic models—specifically, whether model parameters can be uniquely determined from ideal observational data—and proposes a unified symbolic analysis framework implemented in Julia. Built upon the StructuralIdentifiability.jl package, the framework integrates symbolic computation with parameter-output mapping analysis to support assessments of local and global identifiability, observability, and extraction of identifiable parameter combinations. As the first fully reproducible tutorial within the SciML ecosystem, it not only enables model reparameterization and informs experimental design but also demonstrates its efficacy across seven representative case studies spanning epidemiology, pharmacokinetics, and other domains, thereby offering both a practical workflow and theoretical foundation for modeling complex dynamical systems.

This study addresses the challenge of parameter inference in ordinary differential equation models arising from structural non-identifiability. It introduces, for the first time, an explicit integration of structural identifiability analysis into the design of Markov chain Monte Carlo (MCMC) algorithms, proposing two novel sampling strategies: one constructs efficient proposals both within and orthogonal to the non-identifiable manifold, while the other performs inference in a low-dimensional space of identifiable parameter combinations and subsequently reconstructs the full parameter vector. By combining geometric MCMC with pseudo-marginal MCMC techniques, the method establishes a Bayesian inference framework tailored to equivalence solution manifolds. This approach significantly enhances sampling efficiency and convergence speed compared to standard MCMC methods, while preserving posterior correctness and chain ergodicity.

To address the ill-posedness, low identifiability, and difficulty in quantifying uncertainty in mechanical parameter inversion under sparse structural health monitoring (SHM) data, this paper proposes a unified framework integrating Fisher information matrix (FIM) analysis with Bayesian inversion. The FIM quantitatively characterizes the coupled influence of sensor placement and loading paths on parameter identifiability, revealing practically unidentifiable regions and fundamental spatial resolution limits. This enables robust identification of distributed mechanical parameters—such as flexural stiffness—and full-probabilistic uncertainty quantification. The method is validated on real-world bridge measurement data from the Open Laboratory at Technische Universität Dresden, successfully reconstructing spatially varying stiffness distributions and delivering physically interpretable credible intervals. It is the first to quantify spatial heterogeneity of data-informed information content and experimental design boundaries. The framework provides both theoretical foundations and practical tools for optimal sensor deployment and reliability assessment in SHM diagnostics.