bayesian model selection and averaging

For model selection under intractable likelihoods, conventional approximate Bayesian computation (ABC) relying on hand-crafted summary statistics suffers from information loss and uncontrolled posterior approximation bias. This paper systematically develops and extends the full-data ABC framework: it directly compares observed and simulated datasets using statistical distances—including the Wasserstein distance and maximum mean discrepancy (MMD)—bypassing summary statistics and likelihood evaluation entirely. The framework integrates rejection sampling and sequential Monte Carlo for principled model comparison. Theoretically, it yields posterior approximations provably closer to the true posterior. Empirically, it achieves significantly higher model identification accuracy across multiple simulation studies and a real-world toad movement modeling task, demonstrating superior robustness, consistency, and generalizability over summary-statistic-based ABC methods.

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 work proposes a unified Bayesian calibration framework to address the lack of reliable and consistent calibration methods for computationally expensive and data-scarce scenarios. The framework uniquely supports both single-output and multi-output complex models within a coherent formulation and is accompanied by ACBICI, a modular open-source Python library. By integrating uncertainty quantification with Bayesian inference, the approach balances usability and extensibility, establishing a closed loop among theory, implementation, and practical application. The study delivers standardized calibration guidelines tailored to real-world engineering challenges and enhances reproducibility and deployment through its open-source toolkit, significantly improving the reliability and accessibility of calibrating complex scientific and engineering models.

This paper addresses key limitations of traditional Bayesian and frequentist inference frameworks—namely, their conceptual incompatibility, strong dependence on prior specification, and difficulty handling nuisance parameters. To resolve these issues, we propose a unified statistical inference framework grounded in the Bayes factor. Our core method treats the Bayes factor as a function of the null-hypothesis parameter value, enabling construction of a “support curve”; from this curve, we derive the maximum evidence estimator (a point estimate) and the support interval (an interval estimate), thereby integrating hypothesis testing and parameter inference. Key contributions include: (i) the first direct use of the Bayes factor for parameter estimation; (ii) introduction of novel concepts—support curve, maximum evidence estimator, and support interval; and (iii) elimination of prior specification and automatic resolution of nuisance-parameter issues, thus bridging the Bayesian–frequentist divide. Empirical applications in meta-analysis, replication studies, and logistic regression demonstrate improved interpretability, transparency, and reproducibility of statistical evidence.

This work addresses the challenge of parameter non-identifiability in biological systems modeling, which often induces bias in conventional estimates of model evidence and leads to erroneous model selection. The authors propose a Bayesian model evidence estimation method based on Adaptive Multiple Importance Sampling (AMIS), marking its first application to model selection under non-identifiable parameters. By integrating Bayesian inference with an efficient sampling strategy, the approach achieves comparable or superior selection accuracy to Markov chain Monte Carlo (MCMC) methods at substantially lower computational cost across multiple ecological modeling case studies. In contrast, traditional approximation techniques exhibit markedly poorer performance, thereby demonstrating the dual advantages of the proposed method in both reliability and computational efficiency.

This study addresses covariate selection and model uncertainty in stochastic frontier models under non-Gaussian errors by proposing an efficient inference framework based on Bayesian model averaging and selection. Leveraging parallelized exhaustive search, Monte Carlo simulation, and a normal-exponential stochastic frontier specification, the paper systematically evaluates the impact of asymmetric disturbances on posterior inference. The findings demonstrate that, in moderate-dimensional covariate settings, a well-designed exhaustive search strategy outperforms random search. Moreover, explicitly modeling the stochastic frontier structure significantly enhances the robustness and accuracy of model-averaged estimates across varying efficiency-to-noise ratios and signal strengths.

Traditional Bayesian modeling relies on model selection to balance complexity and generalization, yet this approach often compromises predictive performance in small-sample settings. This work proposes a “predictive consistency prior” that maintains stability in the prior predictive distribution as model complexity increases, thereby circumventing explicit model selection. By shifting the modeling focus from parameter sparsity to constructing reasonable and stable priors in predictive space, the method reveals that the perceived necessity of model selection fundamentally stems from inadequate prior specification. The authors implement this prior in Bayesian linear and logistic regression, forward variable selection, and nonlinear models, demonstrating through numerical experiments that flexible models equipped with the predictive consistency prior match or even outperform carefully selected simpler models in out-of-sample prediction across a range of tasks.

This work addresses the lack of explicit confidence modeling for various sources of uncertainty in Bayesian inference by proposing a general extension framework that, for the first time, explicitly incorporates confidence in key uncertainty components—such as the prior and likelihood—into Bayesian modeling. The framework not only introduces a novel regularization mechanism but also provides a unified approach to inducing model sparsity. Without compromising theoretical rigor, the method achieves controllable sparsity across diverse models, including linear regression, logistic regression, and Bayesian neural networks, thereby significantly enhancing both interpretability and generalization performance.

This work addresses the non-uniform distribution of posterior predictive p-values (ppp) under the Bayesian framework, which hinders reliable model diagnostics and cross-model comparisons. The authors propose a natural calibration method that transforms ppp values into calibrated posterior predictive p-values (cppp), which follow a standard uniform distribution under the true model. This calibration establishes, for the first time, a unified and comparable scale for ppp-based assessments. The approach is grounded in a double-simulation computational framework that seamlessly integrates Bayesian inference with posterior predictive checking, and it is applicable to both parametric and nonparametric models. Theoretical analysis demonstrates favorable statistical properties of cppp, while empirical studies illustrate its effectiveness in enabling fair comparisons among models and prior specifications on real-world data.