Confidence distributions and related themes

2017-10-01

AI Summary

This work addresses the long-standing lack of a systematic theoretical foundation for confidence distributions (CDs) within the frequentist framework, which has hindered their broader adoption. By integrating and extending the theoretical underpinnings of CDs—drawing on Fisher’s concept of fiducial likelihood and modern frequentist inference techniques—the project establishes a unified framework for parametric inference. Through the systematic development of its methodology and promotion of interdisciplinary applications, the study not only strengthens the theoretical basis of CDs but also revitalizes their role in statistical practice. The findings synthesize cutting-edge research presented at the 2015 “Inference With Confidence” workshop in Oslo, significantly enhancing the influence and practical utility of confidence distributions in the statistical community.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Abstract This is the guest editors’ general introduction to a Special Issue of the Journal of Statistical Planning and Inference, dedicated to confidence distributions and related themes. Confidence distributions (CDs) are distributions for parameters of interest, constructed via a statistical model after analysing the data. As such they serve the same purpose for the frequentist statisticians as the posterior distributions for the Bayesians. There have been several attempts in the literature to put up a clear theory for such confidence distributions, from Fisher’s fiducial inference and onwards. There are certain obstacles and difficulties involved in these attempts, both conceptually and operationally, which have contributed to the CDs being slow in entering statistical mainstream. Recently there is a renewed surge of interest in CDs and various related themes, however, reflected in both series of new methodological research, advanced applications to substantive sciences, and dissemination and communication via workshops and conferences. The present special issue of the JSPI is a collection of papers emanating from the Inference With Confidence workshop in Oslo, May 2015. Several of the papers appearing here were first presented at that workshop. The present collection includes however also new research papers from other scholars in the field.

Problem

• confidence distributions
• frequentist inference
• fiducial inference
• statistical theory
• parameter uncertainty

Innovation

• Confidence Distributions
• Frequentist Inference
• Fiducial Inference
• Statistical Theory
• Bayesian Analogy