posterior diagnostics

Approximate Bayesian inference often underestimates true uncertainty due to posterior credible intervals that are excessively narrow. This work proposes two simulation-based calibration (SBC)-driven methods for recalibrating approximate posteriors, systematically leveraging the SBC framework to adjust the width of posterior uncertainty intervals and achieve marginal calibration. The approach is applicable to complex model structures, including hierarchical models, and demonstrates consistent efficacy across diverse experimental settings by meaningfully widening posterior intervals. As a result, the proposed recalibration substantially enhances the calibration accuracy and reliability of approximate Bayesian inference.

This work addresses the reliability of simulation-based Bayesian inference (SBI) under model misspecification by systematically analyzing the sources of posterior bias and proposing a unified robust framework. Methodologically, it identifies and unifies three classes of robust strategies—robust summary statistics, generalized Bayesian updates, and error modeling/adjustment parameters—and integrates generalized Bayesian theory, error-calibrated modeling, and robust statistical learning for theoretical development and simulation-based validation. Results demonstrate that standard SBI methods exhibit substantial posterior deviation from ground truth under misspecification, whereas the reviewed robust approaches significantly mitigate such bias, enhancing posterior accuracy, calibration, and generalizability. This study establishes a verifiable theoretical foundation and practical guidelines for deploying SBI in real-world complex systems where model fidelity cannot be guaranteed.

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 paper addresses the lack of directionality, statistical rigor, and computational efficiency in Bayesian model misspecification diagnostics. We propose a novel diagnostic framework based on Uniform Parameterization Checks (UPCs). Our core innovation is the first systematic exploitation of the theoretical property that posterior samples should follow the prior distribution under correct model specification; leveraging probability integral transforms, UPCs uniformly map all random components—across prior, likelihood, and data—into independent *u*-values. This enables interpretable, aggregable, statistically rigorous, and computationally efficient diagnostics (≈ cost of one posterior sample) for individual model components (prior, likelihood, data subsets). UPCs support targeted detection of specific misspecification types—including dependence structure violations, tail discrepancies, and missing correlations—and accurately localize sources of misspecification in both synthetic and real-world examples. Theoretical analysis establishes consistency of the proposed tests.

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.

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 clustering quantifies posterior uncertainty but lacks a general method to summarize uncertainty over the partition space. This paper proposes a generic post-processing framework for Markov chain Monte Carlo (MCMC) posterior samples: it constructs the first interpretable and computationally efficient posterior credible set of clusterings; introduces a novel uncertainty measure enabling cumulative posterior estimation and credible region construction for cluster-specific parameters; and operates entirely without point estimates of partitions or label alignment. By integrating statistical modeling on the partition space with optimization-based aggregation, the method enhances interpretability, robustness, and practical utility across multiple empirical studies. It establishes a reliable, off-the-shelf paradigm for uncertainty quantification in Bayesian clustering.

This work addresses the computational burden of prior sensitivity analysis in Bayesian model comparison, which is highly sensitive to prior choice yet traditionally requires repeated model refitting. We introduce, for the first time, the Learned Harmonic Mean Estimator (LHME) to this task, decoupling posterior sampling from marginal likelihood computation. This enables efficient evaluation of Bayesian evidence under multiple priors using a single set of posterior samples, eliminating the need for re-fitting and remaining agnostic to the underlying inference algorithm. In a cosmological case study, our approach achieves speedups of up to 6,000-fold compared to conventional methods while yielding results consistent with those obtained via MCMC and nested sampling.

This work addresses the ill-posed inverse problems arising from highly nonlinear forward models, the coexistence of additive and multiplicative noise, and censored observations. To tackle these challenges without approximating the likelihood function or neglecting any noise source, the authors propose a general hierarchical Bayesian modeling framework. Coupled with an efficient Markov chain Monte Carlo (MCMC) algorithm, the method directly samples from the complex posterior distribution, thereby avoiding biases introduced by model simplifications or ad hoc hyperparameter tuning in conventional approaches. Extensive experiments on synthetic astronomical data demonstrate that the proposed method consistently outperforms existing baselines and state-of-the-art techniques in terms of point estimation accuracy, predictive performance, and computational efficiency, achieving state-of-the-art uncertainty quantification and reliable inference.

Bayesian parameter inference for ordinary differential equation (ODE) models from observational data often neglects discretization error introduced by numerical solvers, leading to overconfident and biased posterior estimates. Method: We propose a joint uncertainty quantification framework that models discretization error as a time-evolving stochastic process. Leveraging an asymptotically justified Markov prior, we explicitly encode its variance structure; integrating a state-space model with randomized numerical solvers enables simultaneous Bayesian inference of both ODE parameters and discretization error. Contribution/Results: Experiments demonstrate that our approach significantly broadens the support of the parameter posterior distribution while accurately disentangling and quantifying uncertainties attributable to parameters versus discretization. This enhances robustness and interpretability of ODE models under sparse and noisy observations.