sequential bayesian calibration

Traditional Bayesian calibration struggles in dynamic systems to disentangle model parameters from discrepancy terms and is ill-equipped to handle both gradual drifts and abrupt shifts, often being confined to offline settings. This work proposes the Bayesian Recursive Projection Calibration (BRPC) framework, which extends projection-based calibration to online scenarios for the first time. BRPC ensures identifiability and tracks gradual changes by decoupling parameter updates from discrepancy modeling via Gaussian processes, while incorporating a theoretically grounded restart mechanism coupled with online change detection to respond to sudden shifts. Experimental results on synthetic data and industrial process simulations demonstrate that BRPC significantly outperforms sliding-window Bayesian calibration and data assimilation baselines, achieving higher accuracy under gradual drift and maintaining robustness during abrupt changes.

To address Bayesian calibration of complex systems under computationally expensive, data-sparse, or noisy conditions, this paper proposes a sequential surrogate modeling framework. It employs Gaussian process regression to progressively approximate the log-likelihood and its gradients, integrated with gradient-driven Metropolis-adjusted Langevin algorithm (MALA) sampling. We introduce an uncertainty-aware adaptive likelihood evaluation strategy that invokes the expensive true likelihood only in regions where the surrogate exhibits high predictive uncertainty and posterior sensitivity. This enables tight coupling between surrogate modeling and gradient-informed MCMC. Evaluated on synthetic benchmarks and a high-speed train parameter calibration case, the method scales to >20-dimensional parameter spaces, achieves significantly accelerated convergence, reduces computational cost by over 60%, and accurately recovers physically meaningful posterior distributions—even under missing-sensor conditions.

For real-time filtering in general-state-space hidden Markov models, this paper proposes the Online Rolling Controlled Sequential Monte Carlo (OR-CSMC) method. OR-CSMC employs a dual-particle system to jointly perform state filtering and sequential estimation of nonlinear distortion functions, while incorporating a fixed-length rolling window to ensure bounded computational complexity. It constitutes the first extension of controlled sequential Monte Carlo to strictly online settings, achieving both adaptivity and numerical stability. Experiments on high-dimensional linear-Gaussian, stochastic volatility, and neuroscience dynamical models demonstrate that OR-CSMC significantly outperforms standard particle filters in estimation accuracy and robustness—particularly in high-dimensional nonlinear scenarios—where it exhibits marked advantages in both convergence behavior and resilience to degeneracy.

This work addresses the limitations of conventional particle filtering approaches that rely on backward recursion for proposal distribution learning, which require access to the entire observation sequence and suffer from numerical instability, thereby hindering online deployment. To overcome these challenges, the authors propose a forward-only online learning mechanism that adaptively refines the proposal distribution by incrementally incorporating future observation information, achieving performance comparable to backward methods while relying solely on forward recursion. This framework constitutes the first fully online approach for proposal distribution learning, substantially improving numerical stability and algorithmic robustness. Experimental results on both synthetic and real-world data demonstrate that the method incurs only a marginal increase in the variance of marginal likelihood estimates while significantly enhancing the reliability of online inference.

This study addresses the limitation of traditional statistical process control, which emphasizes detecting historical shifts while neglecting the acceptability of the current process state. To overcome this, the authors propose a Bayesian sequential monitoring framework tailored for recoverable processes subject to parameter drift. By recursively computing the posterior probability that the process is in-control at the current time, the method shifts the monitoring focus toward real-time state assessment. The framework integrates time-to-failure modeling, Gaussian and binomial tracking, and multivariate data analysis within a unified Bayesian formulation. Demonstrated through simulation studies and an application to white wine quality data, the approach effectively identifies the current operational status of dynamic recoverable processes, significantly enhancing both monitoring accuracy and practical applicability.

本文通过提出p-CSMC算法，结合参数学习和祖先采样，解决了条件序列蒙特卡洛算法中静态参数和潜在状态联合估计的问题，提高了在强内部相关性情况下的探索效率。

This work addresses the long-standing bottleneck of the $O(T^{2/3})$ lower bound on calibration error in online binary sequence calibration. The authors propose an efficient randomized predictor that integrates the SPR-Calibration procedure with an outer Blackwell-style correction mechanism, supported by a novel analytical framework based on proxy sequences and residual decomposition. By leveraging quadratic potential function analysis and exploiting sparsity structures, the method achieves—while maintaining computational efficiency—the first improvement over the classical bound, reducing the expected calibration error to $O(T^{2/3-\varepsilon})$ for some $\varepsilon > 0$, thereby significantly outperforming the previous best-known results.

该研究提出了一种有限时间校准方法，通过最大似然估计和预测路径生成解决von Mises-Fisher模型中的参数估计问题，并使用终端线性校正来调整协方差。

This work addresses the inefficiency, high latency, and unbounded memory consumption associated with likelihood computation in Bayesian state estimation by introducing a novel Bayesian filtering approach grounded in native processor operations. For the first time, it integrates native uncertainty tracking into Bayesian inference and combines it with deterministic stratified importance resampling, enabling online inference for arbitrary procedural dynamic models. The proposed method achieves root mean square error (RMSE) accuracy comparable to particle filters while delivering up to an 805× average speedup over Monte Carlo methods. It further guarantees deterministic latency, bounded memory usage, and attains Pareto optimality in the trade-off between accuracy and latency.

This work addresses the problem of multiple hypothesis testing for edge distributions across multiple data streams. It proposes a sequential testing procedure that, for the first time, systematically incorporates arbitrary forms of prior information about the configuration of true and false hypotheses—such as known values or lower bounds on the number of active streams under each hypothesis, or mutual exclusivity constraints—while rigorously controlling the familywise error rate. By integrating sequential analysis with a search strategy over minimal alternative hypothesis configurations, the method achieves asymptotic optimality in terms of expected sample size among all valid procedures, without compromising reliability. Theoretical analysis establishes its computational efficiency and asymptotic optimality, and numerical experiments further demonstrate its substantial advantages in both testing efficiency and accuracy.