characterize estimation-prediction tradeoff

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.

Model-form uncertainty (MFU)—arising from simplifying modeling assumptions and particularly challenging to quantify during extrapolation—remains a critical, yet poorly addressed, source of epistemic uncertainty in physics-based modeling. Existing approaches heavily rely on calibration data and cannot isolate the independent influence of individual assumptions on predictions. Method: We propose a calibration-free MFU quantification framework that parameterizes modeling assumptions and integrates grouped variance-based sensitivity analysis to explicitly characterize how assumption changes propagate into predictive variance. The method accommodates parameter dependencies and enables assumption importance ranking under extrapolative conditions. Contribution/Results: Experiments demonstrate that our approach effectively identifies the assumptions dominating prediction uncertainty. It provides quantitative guidance for model simplification, verification, and refinement, thereby significantly enhancing the credibility and robustness of complex physics-based models.

This work investigates the fundamental trade-off between stability and accuracy in statistical estimation by formulating stability as a constraint within the framework of statistical decision theory. It systematically analyzes how worst-case and average-case stability requirements affect estimation accuracy, employing minimax analysis and constrained optimization to construct optimal stable estimators for canonical problems such as mean estimation and regression. The key contribution lies in establishing, for the first time within a unified framework, lower bounds on estimation accuracy under both notions of stability, revealing that average-case stability imposes a strictly weaker constraint than worst-case stability, with the gap depending on the specific estimation task. Furthermore, the paper precisely characterizes the optimal stability–accuracy trade-offs in four representative estimation settings, quantifying the statistical cost incurred by different stability mechanisms.

Purely data-driven Bayesian modeling often fails to capture the underlying mechanisms of complex systems due to insufficient mechanistic guidance. Method: This paper proposes a novel Bayesian model calibration framework that systematically integrates non-empirical information—such as expert knowledge, scientific theories, and qualitative observations—as formalized prior constraints. Leveraging prior encoding, qualitative constraint modeling, and multi-source information fusion, these constraints are embedded directly into the Bayesian inference pipeline, enabling synergistic constraint from both theoretical understanding and empirical data. Contribution/Results: Compared with conventional approaches, the framework significantly expands the class of calibratable models. Case studies in ecology, biology, and medicine demonstrate improved dynamic plausibility, higher predictive confidence, and greater consistency with established scientific knowledge. By bridging theory and data, the method advances Bayesian modeling beyond mere “data fitting” toward “mechanistically credible” inference.

This work addresses the challenge that existing model evaluation methods often fail to reliably assess estimator quality in low-variance settings due to confounding between bias and variance or excessive sensitivity of statistical tests. To overcome this limitation, the authors propose a fault-tolerant evaluation framework that unifies bias and variance modeling through an adjustable tolerance parameter ε, enabling robust assessment of sample-efficient performance estimators within practically acceptable error margins. The framework integrates bias-variance analysis, fault-tolerant evaluation theory, and an adaptive ε-optimization algorithm, making it particularly well-suited for scenarios with low annotation costs. Experimental results demonstrate that the proposed approach provides a more comprehensive and reliable characterization of estimator behavior, significantly enhancing both the practical utility and stability of performance evaluation.

This study addresses the challenges of tuning and evaluation ambiguity in semiparametric and high-dimensional models arising from redundant components introduced by kernel smoothing or basis expansions. The authors propose an induced replication framework that leverages the principle of parametric inference, transforming model assessment into an in-sample prediction error problem by exploiting known replication mechanisms embedded within the model. Building upon Fisher’s concepts of sufficiency and conditional sufficiency, this approach replaces conventional out-of-sample prediction and is applicable to proportional hazards models, time-varying Poisson processes, and confidence set construction for sparse regression. Both theoretical analysis and numerical experiments demonstrate that the method accurately controls nominal error rates under correct model specification and exhibits high sensitivity to semiparametric misspecification.

This work addresses the high cost of large model fine-tuning by tackling the challenge of accurately predicting post-fine-tuning performance beforehand—a task whose theoretical limits remain unclear. We formulate pre-fine-tuning performance prediction as a stochastic estimation problem under information constraints and introduce a predictive risk decomposition framework that separates it into an irreducible intrinsic limit and an optimizable variance term, thereby revealing fundamental bounds on predictability. Leveraging information theory and statistical learning theory, we establish a theoretical lower bound on variance decay through optimization and construct a predictability phase diagram that delineates three distinct task regimes. Experiments on both synthetic and real-world benchmarks validate the efficacy of this phase diagram, and our proposed budget-optimal probing strategy significantly enhances prediction efficiency, offering both theoretical grounding and practical tools for pre-fine-tuning decision-making.

Current performance evaluation metrics—such as accuracy and F1 score—are typically reported as point estimates, ignoring the uncertainty induced by data clustering structures. This oversight often leads to underestimation of variability and potentially misleading model comparisons. To address this, this work proposes a unified framework that expresses a broad class of performance metrics as smooth functionals of the confusion matrix probabilities. By integrating a cluster-robust sandwich variance estimator, the framework enables valid confidence interval construction, hypothesis testing, and paired model comparison. It represents the first systematic application of cluster-robust inference to predictive performance evaluation, accommodating both binary and multiclass settings, and further provides asymptotic theory–based methods for power and sample size calculations. Simulations demonstrate that the proposed approach achieves near-nominal coverage across diverse dependence structures and substantially outperforms conventional methods that ignore clustering; real-data analyses confirm that accounting for clustering can materially alter evaluation conclusions.

This work addresses the challenge of parameter non-identifiability in biological systems modeling, which often induces bias in conventional estimates of model evidence and leads to erroneous model selection. The authors propose a Bayesian model evidence estimation method based on Adaptive Multiple Importance Sampling (AMIS), marking its first application to model selection under non-identifiable parameters. By integrating Bayesian inference with an efficient sampling strategy, the approach achieves comparable or superior selection accuracy to Markov chain Monte Carlo (MCMC) methods at substantially lower computational cost across multiple ecological modeling case studies. In contrast, traditional approximation techniques exhibit markedly poorer performance, thereby demonstrating the dual advantages of the proposed method in both reliability and computational efficiency.