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Abstract Model calibration is crucial for optimizing the performance of complex computer models across various disciplines. In the era of Industry 4.0, symbolizing rapid technological advancement through the integration of advanced digital technologies into industrial processes, model calibration plays a key role in advancing digital twin technology, ensuring alignment between digital representations and real‐world systems. This comprehensive review focuses on the Kennedy and O'Hagan (KOH) framework (Kennedy and O'Hagan, Journal of the Royal Statistical Society: Series B 2001; 63(3):425–464). In particular, we explore recent advancements addressing the challenges of the unidentifiability issue while accommodating model inadequacy within the KOH framework. In addition, we explore recent advancements in adapting the KOH framework to complex scenarios, including those involving multivariate outputs and functional calibration parameters. We also delve into experimental design strategies tailored to the unique demands of model calibration. By offering a comprehensive analysis of the KOH approach and its diverse applications, this review serves as a valuable resource for researchers and practitioners aiming to enhance the accuracy and reliability of their computer models. This article is categorized under:Statistical Models > Semiparametric ModelsStatistical Models > Simulation ModelsStatistical Models > Bayesian Models 

Particle-based Bayesian inference methods by sampling from a partition-free target (posterior) distribution, e.g., Stein variational gradient descent (SVGD), have attracted significant attention. We propose a path-guided particle-based sampling (PGPS) method based on a novel Logweighted Shrinkage (LwS) density path linking an initial distribution to the target distribution. We propose to utilize a Neural network to learn a vector field motivated by the Fokker-Planck equation of the designed density path. Particles, initiated from the initial distribution, evolve according to the ordinary differential equation defined by the vector field. The distribution of these particles is guided along a density path from the initial distribution to the target distribution. The proposed LwS density path allows for an efficient search of modes of the target distribution while canonical methods fail. We theoretically analyze the Wasserstein distance of the distribution of the PGPS-generated samples and the target distribution due to approximation and discretization errors. Practically, the proposed PGPS-LwS method demonstrates higher Bayesian inference accuracy and better calibration ability in experiments conducted on both synthetic and real-world Bayesian learning tasks, compared to baselines, such as SVGD and Langevin dynamics, etc.