parameter distribution inference

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.

To address inadequate calibration of both local (e.g., group-level random effects) and global parameters in multilevel Bayesian models under complex survey designs, this paper proposes an improved survey-weighted pseudo-posterior framework with an automated post-processing pipeline—enabling, for the first time, consistent uncertainty calibration for both parameter types within hierarchical structures. The method integrates mixed-effects modeling, weighted likelihood construction, and posterior reweighting calibration, ensuring asymptotic consistency theoretically and seamless compatibility with mainstream Bayesian software computationally. Simulation studies and empirical analysis using the National Survey on Drug Use and Health (NSDUH) demonstrate that the proposed approach substantially improves estimation accuracy and reliability of uncertainty quantification, particularly reducing bias in random-effects inference. The corresponding algorithms are publicly available and integrated into the R package `csSampling`, offering a scalable, reproducible solution for hierarchical Bayesian analysis under complex sampling.

This study addresses the heterogeneity of treatment effects in clinical research, where conventional subgroup analyses lack individual-level predictive power and purely machine learning–based approaches often lack statistical guarantees. To bridge this gap, the authors propose a two-stage hybrid workflow: first, using formal statistical hypothesis testing to confirm the presence of heterogeneous treatment effects, then constructing an individualized treatment strategy evaluated via cross-fitted doubly robust estimation under a Neyman–Pearson risk constraint. This framework integrates the interpretability of statistical inference with the predictive strength of machine learning, yielding a transparent, auditable, and statistically principled approach to heterogeneity. The method demonstrates efficacy in both simulation studies and the ACTG 175 HIV trial, and is accompanied by a practical implementation checklist along with guidance for alignment with regulatory-oriented heterogeneous treatment effect (HTE) assessment protocols.

This paper addresses the lack of robust design foundations for sensitivity analysis in finite-population causal inference. Methodologically, it introduces a novel sensitivity analysis framework grounded in the experimental design distribution—first integrating design-based distributions with partial identification theory to construct model-free, non-asymptotic confidence intervals for the average treatment effect (ATE). It further reinterprets the role of randomization in sensitivity analysis and provides a new design-driven rationale for covariate balance checks. Key contributions include: (1) model-free, finite-population inference under heterogeneous treatment effects; (2) robust ATE confidence intervals with clear identification-theoretic interpretation; and (3) empirical validation across three real-world applications, demonstrating reliability and practicality in small-sample and highly heterogeneous settings.

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.

本文提出了一种贝叶斯框架，用于处理多层数据生成过程中的模型误设问题，通过半参数方法估计总体参数并考虑集群和单元级别变化。

为了解决贝叶斯模型校准中构建信息先验分布的难题，Distribird通过自动化文献搜索、提取和加权相关值来生成参数的先验分布。

This study addresses the scalability and statistical validity bottlenecks in likelihood approximation and inference for complex simulation models by proposing a novel framework based on aggregated normalizing flow chains. Methodologically, it integrates information-theoretic formalization with sequential decision-making paradigms to construct flexible probability distributions through the sequential optimization of bijective transformation parameters. Furthermore, an empirical likelihood estimator under moment constraints is employed to iteratively update and aggregate the global flow parameters. This research establishes a surrogate model that simultaneously ensures computational feasibility and statistical power, enabling efficient parameter exploration, hypothesis testing, and uncertainty quantification. Ultimately, the proposed approach provides a reliable Bayesian inference solution for complex systems.

Traditional hybrid experimental designs struggle to robustly control the frequentist operating characteristics of Bayesian decisions under model misspecification and lack efficient sample size determination methods applicable to generalized posteriors. This work proposes a computationally efficient experimental design framework that requires simulations at only two sample sizes and leverages extrapolation modeling of posterior summary functions to infer performance across the entire sample size space. This approach enables identification of the minimal sample size and decision rule satisfying desired operating characteristics. It represents the first general and scalable method for sample size planning under generalized posteriors, substantially reducing computational burden while enhancing robustness to model misspecification. The method’s validity and broad applicability within Bayesian M-estimation–type experiments are demonstrated through the redesign of an adaptive clinical trial with time-to-event outcomes.

This study addresses the instability of inference in traditional linear mixed models under small-sample settings, which arises from reliance on numerical integration. To overcome this limitation, the authors introduce—for the first time in balanced-design simple linear mixed models—a four-parameter generalized Beta distribution as a conjugate prior, thereby deriving a closed-form Bayesian solution that eliminates the need for numerical integration or simulation-based sampling. The proposed approach enables fully analytical Bayesian inference and incorporates an empirical Bayes strategy for hyperparameter specification, offering a scalable pathway toward more complex models. Experimental results demonstrate that the method achieves estimation accuracy comparable to classical frequentist approaches while yielding slightly lower mean squared error, confirming its effectiveness and numerical stability.