## 1 Introduction  
High-stakes decision-making, especially in sectors such as healthcare, demands that predictive models be not only accurate but also robust, transparent, and trustworthy [1]. In these settings, the cost of erroneous predictions is exceptionally high, as misjudgments in risk assessment can lead to delayed treatments, misallocated resources, or even adverse patient outcomes [2]. As a result, ensuring that a model reliably quantifies uncertainty and provides clear, interpretable explanations is paramount [3]. Conformal Prediction (CP) has emerged as a powerful framework for uncertainty quantification (UQ) because it generates prediction regions with formal, distribution-free coverage guarantees under minimal assumptions, most notably exchangeability [4, 5, 6]. This characteristic is especially beneficial in high-stakes applications where traditional probabilistic assumptions may be violated or hard to verify [7; 8]. By constructing prediction sets that are statistically valid regardless of the underlying data distribution, CP offers a principled approach to ensure that the true outcome is captured with a pre-specified level of confidence [9]. However, the practical impact of CP is critically dependent on the quality of the underlying probability estimates [10; 11]. In many real-world scenarios, raw model outputs are miscalibrated--that is, the probabilities produced do not accurately reflect the true likelihood of events [12]. This miscalibration creates a disconnect between the statistical coverage guarantees provided by CP and the actual risk profile observed in practice. In high-stakes environments, such a gap can compromise both the interpretability of the prediction regions and the reliability of subsequent decision-making processes [13]. To address these challenges, researchers have developed a variety of post-hoc probability calibration techniques. Parametric methods, such as Platt scaling and beta calibration, impose a functional form to remap the raw outputs, while non-parametric approaches like isotonic regression and spline calibration offer the flexibility to capture more complex miscalibration patterns that often emerge in heterogeneous data [14]. Our work adopts a multilayer analytical framework that integrates these calibration techniques with CP to enhance the reliability and interpretability of predictive process monitoring (PPM) in high-stakes settings [15]. At the first layer, calibrated probability estimates serve as a more faithful representation of the true event likelihoods. When these refined probabilities are embedded within the CP framework, the resulting prediction regions are not only statistically valid but also more reflective of real-world risk. This integration is critical because tighter and more reliable prediction intervals directly translate into better-informed decision making. Moreover, a second layer of analysis is introduced through explainable artificial intelligence (XAI) techniques--specifically, methods such as SHAP (SHapley Additive exPlanations)--which explain the contributions of individual features to both high-confidence and ambiguous predictions. Such transparency is essential for building trust among domain experts and facilitating accountability in the deployment of AI systems. Preliminary analyses suggest that ensemble-based methods, particularly those relying on gradient boosting, may deliver superior performance on imbalanced and complex datasets. When combined with non-parametric calibration approaches, these models can more effectively capture subtle, non-linear patterns of miscalibration, thereby aligning predicted probabilities with observed outcomes more closely. Furthermore, integrating calibrated predictions into CP frameworks is expected to yield prediction regions with reduced coverage gaps and lower minority error contributions--a crucial advancement for applications where underestimating risk for a minority class can have significant repercussions.