Large-scale signal detection: A unified perspective

Area of Science:

• Statistics
• Machine Learning
• Computational Science

Background:

• Extensive literature exists on large-scale inference problems using various modeling techniques.
• Current methods often stem from different theoretical backgrounds, leading to a fragmented understanding.

Purpose of the Study:

• To elucidate the connections between different simultaneous inference methods.
• To derive simpler, more intuitive formulas for these methods.
• To develop a unified algorithm for practical application in large-scale inference.

Main Methods:

• Review and synthesis of existing large-scale inference methodologies.
• Development of novel, intuitive derivations for key formulas.
• Construction of a unified algorithmic framework.

Main Results:

• Clarification of the relationships between disparate simultaneous inference techniques.
• Simplified mathematical expressions for core inferential procedures.
• A unified algorithm demonstrating practical utility on diverse datasets.

Conclusions:

• The presented unified approach simplifies and connects existing methods for large-scale inference.
• The derived formulas and algorithm offer practical advantages for researchers and practitioners.
• This work provides a foundation for future research in unified statistical inference.