approximate bayesian computation

Approximate Bayesian computation (ABC) yields unreliable statistical inference under model misspecification and lacks diagnostic tools for incompatible summary statistics. To address these limitations, we propose the first robust ABC framework designed to withstand model misspecification. Our method introduces a reconstructed distance metric coupled with an uncertainty calibration mechanism, ensuring posterior consistency while enabling robust inference. Additionally, we embed a summary statistic compatibility diagnostic module that identifies and excludes statistics inconsistent with the true data-generating process. Extensive experiments—including both synthetic benchmarks and real-world applications—demonstrate substantial improvements in point estimation accuracy and uncertainty quantification quality over standard ABC and existing robust variants. The proposed framework establishes a new paradigm for trustworthy ABC inference under model misspecification.

In likelihood-free inference (LFI), selecting informative summary statistics is challenging when the likelihood is intractable, and individual LFI methods (e.g., ABC, SNPE, BOLFI) often suffer from bias and instability. To address these issues, this paper proposes a provably accurate pooled posterior framework that requires no hand-crafted summary statistics or method-specific assumptions. It integrates posterior estimates from multiple LFI algorithms via weighted Bayesian model averaging and kernel density estimation. Grounded in asymptotically optimal combination theory, the framework avoids high-dimensional posterior sampling while guaranteeing convergence and statistical consistency—thereby substantially improving robustness. Experiments on standard LFI benchmarks demonstrate significant gains in inference accuracy and a tenfold reduction in computational cost compared to state-of-the-art single-method approaches.

Traditional Approximate Bayesian Computation (ABC) methods rely on manually specified summary statistics, distance metrics, and tolerance thresholds, compromising the robustness and reproducibility of posterior inference. To address this, we propose ABCD-Conformal—the first fully automated, parameter-free ABC framework. It eliminates hand-crafted summary statistics and explicit distance computations by employing amortized neural likelihood-ratio estimation, augmented with Monte Carlo Dropout for principled uncertainty quantification. Crucially, we integrate conformal prediction to construct confidence sets for posterior moments—such as the posterior mean—with finite-sample, distribution-free frequentist coverage guarantees. Evaluated across four multivariate parameter inference tasks, ABCD-Conformal consistently outperforms state-of-the-art ABC methods in accuracy, calibration, and computational efficiency.

Traditional Monte Carlo methods struggle to efficiently approximate non-probabilistic credibility measures in possibility-based inference. Method: This paper proposes a novel inferential model (IM) framework that requires no prior specification and unifies frequentist reliability with Bayesian-like belief representation. It establishes, for the first time, a theoretical characterization of credible sets for possibility-based IMs and derives their optimal probabilistic approximation—a class of mixture distributions amenable to efficient sampling. A dedicated Monte Carlo algorithm is then designed to rapidly approximate possibility outputs with guaranteed calibration consistency and controllable error. Results: Numerical experiments demonstrate substantial improvements in both computational efficiency and accuracy: the method achieves small approximation error, fast convergence rates, and excellent frequentist calibration. It constitutes the first solution for possibility-based statistical inference that simultaneously ensures theoretical rigor and computational feasibility.

In likelihood-intractable scenarios, Approximate Bayesian Computation (ABC) faces key bottlenecks: difficulty in selecting informative summary statistics, complex tuning of distance metrics and tolerance thresholds, high computational cost, and substantial posterior uncertainty due to weak prior information. To address these challenges, this paper proposes ABC-SMC-(D)RF—a novel method integrating Distributed Random Forests (DRF) into the Sequential Monte Carlo (SMC) framework for the first time. It enables end-to-end learning of discriminative features, eliminating manual design of summary statistics and distance functions. Coupled with adaptive tolerance scheduling and a pre-acceptance shrinkage mechanism, it iteratively concentrates sampling on high-probability parameter regions. Experiments across diverse deterministic and stochastic models demonstrate significant improvements in posterior estimation accuracy and robustness; notably, stability under weak priors is markedly enhanced, and computational efficiency surpasses that of conventional ABC-RF.

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.

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 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.

本文提出一种通过概率积分变换和最大均值差异消除重采样噪声的方法，解决了混合不确定性下的模型更新问题，并采用TMCMC进行后验推断。

This study addresses the challenges of inefficient posterior estimation and difficult calibration in simulation-based inference (SBI) for models with intractable likelihoods but accessible forward simulators. We propose a sequential posterior estimation framework based on Gaussian mixture-of-experts surrogates. By leveraging localized conditional density approximations to construct proposal distributions, the method corrects the posterior via amortized ratio estimation and importance sampling. Furthermore, we introduce a localized simulation-based calibration (SBC) approach that efficiently reuses surrogates across broad neighborhoods at low computational cost. The effectiveness of this framework is validated through three case studies involving real-world epidemiological data, demonstrating substantial improvements in both the computational efficiency and inferential accuracy of SBI.