A natural assumption is that if each model is individually calibrated, the aggregate prediction will also be well calibrated. We show that this assumption fails in multi-agent settings: individually calibrated predictors can become collectively miscalibrated when their predictions interact strategically--where "strategically" refers to the game-theoretic sense of Brier-optimal local response, not deliberate gaming or collusion, and arises naturally whenever agents are independently trained on overlapping data. This phenomenon affects multiple independent agents in federated healthcare, multi-vendor intrusion detection, and crowdsourced forecasting, where agents optimize their own objectives. Specifically, we prove that under Brier-score-based aggregation with positively correlated beliefs each agent's individually optimal report systematically underestimates the positive-class probability, yielding a Price of Anarchy strictly greater than one whenever Cov(bi,bj) > 0. At our canonical setting (n=5 agents, pairwise correlation ρ=0.5, base rate µ=0.3, threshold τ=0.3) the empirically measured PoA in false-negative rate is 7.25 (mean aggregate bias 0.375). In contrast, VCG-based aggregation, which rewards each agent's marginal contribution to aggregate accuracy, achieves dominant-strategy incentive compatibility and the lowest empirical PoA among all mechanisms studied (PoA 1.0). On three real-world datasets (NSL-KDD, UNSW-NB15, Credit Card Fraud) with featurepartitioned agents, VCG provides the strongest robustness guarantees among the aggregation methods we evaluate, while maintaining comparable accuracy. In data-sparse regimes (n 500), VCG consistently outperforms stacking and majority voting; under adversarial agents, VCG maintains substantially lower false-negative rates than robust aggregation baselines. Adaptive weight updates further reduce false negatives by 20-22% under distribution shift, with O( T) online regret guarantees. These results establish that how probabilistic predictions are aggregated matters as much as how well individual models are calibrated.

Calibration is a conditional property that depends on the information retained by a predictor. We develop decomposition identities for arbitrary proper losses that make this dependence explicit. At any information level $\mathcal A$, the expected loss of an $\mathcal A$-measurable predictor splits into a proper-regret (reliability) term and a conditional entropy (residual uncertainty) term. For nested levels $\mathcal A\subseteq\mathcal B$, a chain decomposition quantifies the information gain from $\mathcal A$ to $\mathcal B$. Applied to classification with features $\boldsymbol{X}$ and score $S=s(\boldsymbol{X})$, this yields a three-term identity: miscalibration, a {\em grouping} term measuring information loss from $\boldsymbol{X}$ to $S$, and irreducible uncertainty at the feature level. We leverage the framework to analyze post-hoc recalibration, aggregation of calibrated models, and stagewise/boosting constructions, with explicit forms for Brier and log-loss.

Practitioners monitoring deployed probabilistic models face a fundamental trap: any fixed-sample test applied repeatedly over an unbounded stream will eventually raise a false alarm, even when the model remains perfectly stable. Existing methods typically lack formal error guarantees, conflate alarm time with changepoint location, and monitor indirect signals that do not fully characterize calibration. We present PITMonitor, an anytime-valid calibration-specific monitor that detects distributional shifts in probability integral transforms via a mixture e-process, providing Type I error control over an unbounded monitoring horizon as well as Bayesian changepoint estimation. On river's FriedmanDrift benchmark, PITMonitor achieves detection rates competitive with the strongest baselines across all three scenarios, although detection delay is substantially longer under local drift.

Reliable precipitation nowcasting is critical for weather-sensitive decision-making, yet neural weather models (NWMs) can produce poorly calibrated probabilistic forecasts. Standard calibration metrics such as the expected calibration error (ECE) fail to capture miscalibration across precipitation thresholds. We introduce the expected thresholded calibration error (ETCE), a new metric that better captures miscalibration in ordered classes like precipitation amounts. We extend post-processing techniques from computer vision to the forecasting domain. Our results show that selective scaling with lead time conditioning reduces model miscalibration without reducing the forecast quality.

Safety-critical assistive systems that directly decode user intent from neural signals require rigorous guarantees of reliability and trust. We present GUARDIAN (Gated Uncertainty-Aware Runtime Dual Invariants), a framework for real-time neuro-symbolic verification for neural signal-controlled robotics. GUARDIAN enforces both logical safety and physiological trust by coupling confidence-calibrated brain signal decoding with symbolic goal grounding and dual-layer runtime monitoring. On the BNCI2014 motor imagery electroencephalogram (EEG) dataset with 9 subjects and 5,184 trials, the system performs at a high safety rate of 94-97% even with lightweight decoder architectures with low test accuracies (27-46%) and high ECE confidence miscalibration (0.22-0.41). We demonstrate 1.7x correct interventions in simulated noise testing versus at baseline. The monitor operates at 100Hz and sub-millisecond decision latency, making it practically viable for closed-loop neural signal-based systems. Across 21 ablation results, GUARDIAN exhibits a graduated response to signal degradation, and produces auditable traces from intent, plan to action, helping to link neural evidence to verifiable robot action.

Randomized trials are widely considered as the gold standard for evaluating the effects of decision policies.

Despite the rapid expansion of Large Language Models (LLMs) in healthcare, robust and explainable evaluation of their ability to assess clinical trial reporting according to CONSORT standards remains an open challenge. In particular, uncertainty calibratio n and metacognitive reliability of LLM reasoning are poorly understood and underexplored in medical automation. This study applies a behavioral and metacognitive analytic approach using an expert - validated dataset, systematically comparing two representati ve LLMs -- one general and one domain - specialized -- across three prompt strategies. We analyze both cognitive adaptation and calibration error using metrics: Expected Calibration Error (ECE) and a baseline - normalized Relative Calibration Error (RCE) that enable s reliable cross - model comparison. Our results reveal pronounced miscalibration and overconfidence in both models, especially under clinical role - playing conditions, with calibration error persisting above clinically relevant thresholds. These findings und erscore the need for improved calibration, transparent code, and strategic prompt engineering for the development of reliable and explainable medical AI.

Probabilistic models must be well calibrated to support reliable decision-making. While calibration in single-output regression is well studied, defining and achieving multivariate calibration in multi-output regression remains considerably more challenging. The existing literature on multivariate calibration primarily focuses on diagnostic tools based on pre-rank functions, which are projections that reduce multivariate prediction-observation pairs to univariate summaries to detect specific types of miscalibration. In this work, we go beyond diagnostics and introduce a general regularization framework to enforce multivariate calibration during training for arbitrary pre-rank functions. This framework encompasses existing approaches such as highest density region calibration and copula calibration. Our method enforces calibration by penalizing deviations of the projected probability integral transforms (PITs) from the uniform distribution, and can be added as a regularization term to the loss function of any probabilistic predictor. Specifically, we propose a regularization loss that jointly enforces both marginal and multivariate pre-rank calibration. We also introduce a new PCA-based pre-rank that captures calibration along directions of maximal variance in the predictive distribution, while also enabling dimensionality reduction. Across 18 real-world multi-output regression datasets, we show that unregularized models are consistently miscalibrated, and that our methods significantly improve calibration across all pre-rank functions without sacrificing predictive accuracy.