bayesian joint estimation

To address the high computational cost arising from joint propagation of aleatoric and epistemic uncertainties in Bayesian two-stage inference, this paper proposes an efficient uncertainty propagation framework. First, a representative subset is selected via Pareto-smoothed importance sampling to reduce sampling redundancy. Second, an importance-weighted moment-matching strategy is introduced for lightweight posterior approximation. Third, an iterative mixture-distribution expansion mechanism is developed to jointly model both uncertainty types within surrogate modeling and MICE-based multiple imputation. The method preserves posterior accuracy while significantly reducing the cost of multi-model fitting—achieving several-fold improvements in computational efficiency. It establishes a scalable paradigm for Bayesian inference under complex, heterogeneous uncertainty scenarios.

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.

Bayesian inference for finite-population surveys is challenging when sampling units exhibit complex dependencies (e.g., spatial, network, or structural) and nonresponse is nonignorable. Method: We propose a unified hierarchical modeling framework that integrates graphical models and spatial random fields to characterize multivariate dependence; formally adopts the “unapologetic Bayesian” paradigm, embedding design-based weights (e.g., Horvitz–Thompson) naturally into prior and likelihood specifications; incorporates causal ignorability analysis to ensure identifiability under missing-not-at-random (MNAR) mechanisms; and employs MCMC and variational inference for scalable computation. Contribution/Results: The framework achieves improved small-area estimation accuracy and more reliable uncertainty quantification in two empirical spatial finite-population analyses. It rigorously reconciles design-based consistency with model-based flexibility, providing theoretical guarantees for valid Bayesian inference under complex survey designs and nonignorable nonresponse.

This work addresses the slow MCMC convergence in Gibbs posterior sampling under stochastic loss functions, which stems from spurious dependence on the number of pseudo-observations. We propose the first pseudo-sample-size–independent corrected piecewise deterministic Markov process (PDMP) sampler. By designing a novel jump-rate function and direction mechanism, our method rigorously ensures that the invariant measure remains invariant to the pseudo-observation count—thereby overcoming the inherent trade-off between asymptotic bias and slow convergence in conventional stochastic-loss inference. We prove that the sampler converges exactly to the target Gibbs posterior measure with a uniform convergence rate independent of pseudo-sample size. Empirical validation across three canonical settings—likelihood-intractable models, misspecified models, and stochastic losses—demonstrates elimination of pseudo-sample-size bias in posterior sampling, alongside substantial improvements in robustness and estimation accuracy.

Conventional Monte Carlo simulation for evaluating operating characteristics (e.g., decision accuracy) and determining sample size in Bayesian clinical trials with clustered data and multiple endpoints is computationally expensive and inefficient. Method: We derive, for the first time, an analytical functional relationship between posterior probability and sample size within a Bayesian hierarchical framework that accommodates clustering and multiple endpoints. This enables full operating characteristic curve extrapolation from only two Monte Carlo simulations. We further quantify how simulation variability affects recommended sample sizes. Contribution/Results: By integrating Bayesian hierarchical modeling, cluster-aware inference, and theoretical derivation, our approach drastically reduces computational burden. It is validated on real-world cluster-randomized, adaptive, multi-endpoint Bayesian trials, demonstrating robustness and enabling rapid, reliable sample size determination without sacrificing statistical rigor.

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 challenge of simultaneous misspecification of marginal distributions and the copula function in copula modeling by proposing a multi-module semi-modular inference (SMI) approach. The method introduces independent modules for each marginal distribution, each governed by its own influence parameter, and employs continuous relaxation to circumvent discrete search over exponentially many cut configurations. Integrated with Bayesian optimization for automatic hyperparameter tuning, the framework adaptively accommodates varying degrees of misspecification across margins. Theoretical analysis and empirical evaluations demonstrate that the proposed method achieves notable robustness and superior performance on both synthetic data and real-world financial datasets—such as modeling the asymmetric dependence between equity volatility and bond yields using a skew-normal copula.

This paper addresses the limitations of strong modeling assumptions and insufficient robustness in Bayesian causal inference. We propose a general framework grounded in treatment randomization design, which bypasses explicit modeling of the marginal distribution of potential outcomes. Instead, it fixes the observed data and constructs the likelihood directly from the randomization distribution, enabling model-agnostic robust inference. Theoretical contributions include: (i) establishing an intrinsic connection between the posterior mean and classical estimators such as the Hodges–Lehmann estimator; (ii) proving a Bernstein–von Mises theorem and asymptotic consistency; and (iii) supporting posterior model checking as well as flexible extensions—including inverse probability weighting and Hájek estimation. Simulation studies and a nutritional experiment demonstrate that our method effectively uncovers causal heterogeneity undetected by conventional approaches, balancing theoretical rigor with practical interpretability.

This study addresses the challenge of conducting valid Bayesian inference for target parameters—such as causal effects—in the presence of finite-dimensional nuisance parameters. The authors propose a general framework that integrates Bayesian bootstrap with Dirichlet process priors within an estimating equation approach, explicitly accounting for uncertainty in propensity score estimation. The method is robust to model misspecification and remains valid under only single robustness conditions. It extends the "linked Bayesian bootstrap" to nonstandard Bayesian settings, yielding posterior inferences with favorable frequentist properties. Theoretical analysis demonstrates that the resulting posterior distribution exhibits desirable asymptotic behavior, with credible intervals achieving nominal coverage probabilities in large samples.

This study addresses the challenge of propagating uncertainty for cross-classified statistics under hierarchical Bayesian (HB) calibration by introducing a Posterior Inference Engine (PHIE). PHIE transforms Markov chain Monte Carlo (MCMC) posterior draws from an HB model into replicate survey weights via chi-square calibration and integrates them with design-based variance to construct Calibrated Bayesian Intervals (CBI). By innovatively combining HB posteriors with post-calibration weights, this approach enables reliable inference for arbitrary cross-tabulations—a capability not previously attainable. The proposed three-tier classification framework and CBI methodology maintain near-nominal coverage even under weak correlation conditions, revealing that dominant uncertainty stems from compositional sampling variation. Empirical results demonstrate that CBI substantially outperforms inference based solely on PHIE across diverse cross-tabulated cells, with coefficients of variation meeting standard publication criteria.