derive parameter priors

Gaussian processes (GPs) in surrogate modeling are highly sensitive to misspecification of covariance hyperparameters—particularly the length-scale parameter θ. While fully Bayesian hierarchical inference improves robustness and uncertainty quantification, its performance critically depends on the choice of prior distributions and Markov Chain Monte Carlo (MCMC) proposal mechanisms—a dependency lacking systematic evaluation in prior work. This paper conducts the first comprehensive study of how alternative priors for θ (uniform, Gamma, inverse-Gamma) and their corresponding MCMC proposals affect posterior sampling efficiency, convergence speed, and predictive performance. Leveraging both synthetic and real-world benchmarks under Bayesian GP inference, we demonstrate that principled alignment between prior and proposal distributions significantly enhances prediction accuracy, improves uncertainty calibration, and accelerates MCMC convergence. Our empirical findings provide actionable guidelines and practical design principles for hyperparameter prior selection in Bayesian GP modeling.

In Bayesian modeling, expert priors are often specified directly on observable or derived quantities (e.g., survival rates, R²), yet translating such domain knowledge into informative priors for latent model parameters remains a fundamental challenge. Method: We propose a hyperparameter optimization framework grounded in prior predictive distribution matching. It parameterizes a prior family and employs multi-stage Bayesian global optimization to minimize the discrepancy between the induced prior predictive distribution and the target expert-specified distribution—supporting mixed-type and nonstandard targets, as well as censored data, nonlinear structures, and complex derived statistics. Contribution/Results: Across three case studies—cure-rate survival models, R²-driven modeling, and nonlinear regression—the resulting informative priors substantially improve posterior stability and interpretability. Our approach provides the first systematic, computationally tractable, and empirically verifiable methodology for transforming marginal expert beliefs about observables into joint priors over latent parameters.

External data borrowing in Bayesian clinical trials is prone to bias, compromising statistical validity and estimation reliability. Method: This study systematically investigates the impact of four tuning parameters—mixture weight, location, scale, and distributional form—in robust mixture priors on operating characteristics under single-arm and hybrid control designs, via theoretical analysis and extensive simulation. Contribution/Results: We identify the location parameter as a key driver of Type I error inflation and estimation bias, and uncover strong coupling between weight and location/scale parameters. Building on sensitivity quantification and error trade-off analysis, we propose principled guidelines for parameter selection and introduce more robust alternative distributional forms. The results yield actionable, empirically validated parameter configurations that substantially enhance the statistical robustness and estimation accuracy of external data borrowing in Bayesian clinical trial design.

In simulation-based calibration (SBC) for Bayesian models, prior specification faces a fundamental trade-off: overly broad priors risk numerical instability, while overly narrow ones reduce sensitivity to inferential failures—yet ground-truth data are often unavailable for calibration. Method: We propose *primed priors*, an adaptive, data-free prior construction framework extending catalytic priors. It integrates parameter-space sensitivity analysis with SBC-specific objective-driven design to enhance detection of common inferential pathologies—such as posterior shrinkage miscalibration and marginal inconsistency—while ensuring numerical robustness. Contribution/Results: Three simulation studies demonstrate that primed priors significantly improve SBC’s failure detection rate over standard priors and completely avoid computational breakdowns induced by extreme parameter values. To our knowledge, this is the first SBC-tailored, interpretable, and data-agnostic prior generation method.

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 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.

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 Bayesian optimal experimental design under computationally expensive models with limited design evaluations. It proposes an adaptive sequential elimination algorithm that significantly reduces the variance and computational cost of nested Monte Carlo estimators by reusing parameter samples, employing common random numbers, and applying Rao–Blackwellization. A bootstrap-based probabilistic comparison mechanism is integrated to iteratively eliminate inferior designs. The method achieves high reliability while drastically reducing the number of model evaluations, making it well-suited for large-scale engineering applications where computational efficiency and decision accuracy must be carefully balanced.

This study addresses the lack of systematic guidance on the influence of prior hyperparameters in Bayesian Go/No-Go decision-making for early-phase clinical trials with dual endpoints. The authors propose a calibrated bivariate prior specification framework that constructs skeptical and optimistic priors by assigning target probabilities to predefined decision regions, requiring only the selection of a central location and a precision parameter κ. Theoretically, for any κ > 0, there exists a unique scaling parameter λ₀ that achieves calibration, and κ governs the prior’s discriminative power, supporting adaptive κ strategies. Under a normal–inverse-Wishart model (with default ν₀ = 2), simulations show that at κ = 10, the Go-rate difference between optimistic and skeptical priors reaches 0.56 while maintaining a false-positive rate below 0.01. In a real lupus dataset, optimistic priors with high κ yield Go rates up to three times those of skeptical priors, even with small sample sizes.