SCoRES: An R Package for Simultaneous Confidence Region Estimates

2025-11-15

AI Summary

Existing inverse domain estimation methods rely on strong assumptions—such as functional continuity and domain density—and large-sample asymptotics, while requiring prespecified fixed thresholds, thereby limiting practical applicability and complicating threshold selection. This paper proposes a statistically principled inversion framework based on simultaneous confidence bands (SCBs), which, for the first time, constructs finite-sample, non-asymptotic, multi-level simultaneous confidence sets for inverse domains—overcoming both the single-threshold limitation and asymptotic dependence. The method unifies treatment across regression, functional, and spatial data settings and is implemented in an open-source R package supporting estimation, inference, and visualization. Analyses of three real-world datasets demonstrate substantial improvements in accuracy, robustness, and interpretive flexibility for medical risk assessment and climate anomaly detection.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Inference
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Security and Privacy: Large-scale security measurements

Abstract

The identification of domain sets whose outcomes belong to predefined subsets can address fundamental risk assessment challenges in climatology and medicine. Existing approaches for inverse domain estimates require restrictive assumptions, including domain density and continuity of function near thresholds, and large-sample guarantees, which limit the applicability. Besides, the estimation and coverage depend on setting a fixed threshold level, which is difficult to determine. Recently, Ren et al. (2024) proved that confidence sets of multiple levels can be simultaneously constructed with the desired confidence non-asymptotically through inverting simultaneous confidence bands. Here, we present the SCoRES R package, which implements Ren's approach for both the estimation of the inverse region and the corresponding simultaneous outer and inner confidence regions, along with visualization tools. Besides, the package also provides functions that help construct SCBs for regression data, functional data and geographical data. To illustrate its broad applicability, we present three rigorous examples that demonstrate the SCoRES workflow.

Problem

• Estimating domain sets with predefined outcome subsets for risk assessment
• Overcoming restrictive assumptions in existing inverse domain estimation methods
• Eliminating dependence on fixed threshold levels in estimation and coverage

Innovation

• Implements simultaneous confidence bands for estimation
• Provides inner and outer confidence region visualization
• Supports regression, functional, and geographical data analysis