probabilistic modeling

This paper systematically examines the structural role and evolutionary trajectory of simulation methods across the statistical lifecycle. Addressing the current fragmentation and conceptual ambiguity in simulation practice, the study introduces, for the first time, a comprehensive functional taxonomy—spanning model specification, diagnostic checking, validation, and inference—and proposes a “simulation-driven” paradigm for statistical practice, prioritizing computational scalability. Methodologically, it integrates Monte Carlo simulation, approximate Bayesian computation (ABC), simulation-based calibration, and posterior predictive checking, implemented via high-performance computing frameworks to enable large-scale empirical analysis. Key contributions are: (1) establishing simulation as foundational statistical infrastructure; (2) providing an actionable roadmap for algorithm design, statistical software development, and pedagogical reform; and (3) advancing a paradigm shift in statistical practice—from model-centric to simulation-augmented inference.

This work proposes the first general framework to systematically quantify and apportion epistemic uncertainty arising from substituting true subprocesses with approximate or learned submodels in stochastic simulation and digital twin applications. The framework constructs confidence or credible intervals for performance metrics via bootstrapping and Bayesian model averaging, and employs a tree-based decomposition to allocate total output variability to individual submodels, yielding importance scores. It is compatible with both parametric and nonparametric models, supports frequentist and Bayesian paradigms, and accommodates dynamic initialization scenarios. Validation on synthetic data and a call center digital twin demonstrates that the method effectively reveals each submodel’s contribution to overall uncertainty, significantly enhancing the interpretability and reliability of simulation outcomes.

This work addresses the challenge that existing automatic code generation methods often produce structurally invalid or physically inconsistent models, which are unsuitable for engineering simulation. To ensure physical consistency and simulatability, the authors propose a procedural modeling framework that integrates domain knowledge injection, constraint-guided fine-tuning, and closed-loop simulation validation. Key contributions include CivilInstruct—the first instruction-following dataset tailored for structural engineering—along with a two-stage fine-tuning strategy and MBEval, a validation-driven evaluation benchmark. Experimental results demonstrate that the proposed approach significantly outperforms baseline methods across multiple rigorous metrics, effectively suppressing hallucinations and constraint violations, and enabling the direct use of generated models in structural dynamics simulations.

This paper addresses the challenge of modeling nonlinear and asymmetric dynamic relationships among macroeconomic and financial variables. We propose the first scenario-analysis-oriented, dynamic nonparametric multivariate Bayesian machine learning framework. Methodologically, we adapt classical econometric tools—including conditional forecasting and generalized impulse response analysis—to high-dimensional Bayesian nonparametric models, integrating dynamic factor extensions and Monte Carlo simulation to enable asymmetric shock response estimation and conditional scenario inference. Our key contribution is the first systematic integration of traditional scenario-analysis tools with nonlinear Bayesian machine learning, explicitly capturing structural asymmetry. The framework is validated across three empirical domains: financial stress testing, macroeconomic risk assessment, and cross-border spillover analysis. Results demonstrate substantial improvements in risk measurement accuracy and cross-jurisdictional early-warning capability, offering a novel paradigm for prudential regulation and policy evaluation.

This work addresses the semantic fragmentation and toolchain fragmentation in traditional model-driven engineering, which stem from the lack of a unified formal foundation among models, metamodels, templates, and transformations. To bridge this gap, the paper introduces Model Expression Algebra, treating models as values and expressions as terms, and unifying modeling operations through an evaluation homomorphism. By embedding a domain-specific language (DSL), the approach integrates metamodeling, model construction, and transformation within a single functional algebraic framework—unifying all four aspects for the first time. A type system ensures transformation safety, while free variables represent templates and computational operators encode functional logic, enabling type-preserving evaluation and built-in support for large-model expressions. Experimental results demonstrate that a single language can fulfill the full spectrum of modeling tasks while providing formal guarantees.

This study addresses the challenge of uncertainty quantification in aggregated time series forecasting, particularly for annual totals and year-over-year growth rates. It proposes a simulation-augmented multi-step split conformal prediction method (SA-MSCP), which generates future trajectories via block bootstrap resampling from cross-validated residuals and constructs calibrated prediction intervals using empirical quantiles. By innovatively integrating a simulation-augmentation mechanism into the multi-step split conformal prediction framework, the method significantly improves empirical coverage for both aggregate totals and their growth rates, yielding more reliable uncertainty estimates without compromising predictive accuracy.

This work addresses the challenges of real-world data scarcity, high acquisition costs, and privacy sensitivity in multimodal AI training by introducing Simula, a novel framework that pioneers inference-driven synthetic data generation without requiring any seed data. By integrating an agent-based architecture with a controllable generation pipeline, Simula enables fine-grained control over data characteristics and computational resource allocation, substantially enhancing the interpretability and scalability of synthetic data. Through a comprehensive multidimensional evaluation protocol, the framework simultaneously validates both the intrinsic quality of the generated data and its effectiveness in downstream tasks across multiple benchmarks, offering a practical pathway and design paradigm for AI development under data-constrained conditions.

This work addresses the limitation of existing safety-critical systems, which typically evaluate only predictive accuracy while lacking rigorous validation of the overall calibration of predicted probability distributions. To bridge this gap, the authors propose a modular calibration testing framework that decouples the calibration process into four interchangeable components: data model, scoring rule, hypothesis formulation, and statistical test procedure. Built upon formal statistical hypothesis testing, the framework provides a single accept/reject decision for the entire predictive distribution. Crucially, it rejects only overly confident predictions while tolerating reasonable deviations, thereby balancing practicality with flexibility. Empirical evaluations on weather forecasting and robotic pose estimation tasks demonstrate that the framework effectively supports reliable deployment in safety-critical applications.

This study addresses a critical limitation in traditional reproducible research, where sharing only code and results fails to expose the implicit assumptions, expectations, and premises underlying an analyst’s reasoning—thereby hindering thorough evaluation of analytical quality. To overcome this, the paper proposes a formal modeling framework that explicitly translates the analyst’s tacit reasoning process into structured logical representations, statically capturing the construction logic of the analysis. This approach enables systematic scrutiny of the analytical chain of reasoning, assumption sensitivity, and conclusion robustness—even in the absence of the original data. Empirical validation on representative data analysis tasks demonstrates the framework’s effectiveness, achieving both logical visualization and data-free static assessment of analytical integrity.