Bayesianism from a philosophical perspective and its application to medicine

Area of Science:

• Philosophy of Science
• Statistics
• Systems Science

Background:

• Bayesian philosophy and statistics have diverged, with philosophers focusing on direct inference and statisticians on foundations.
• Standard Bayesian frameworks face challenges in coherently employing direct inference principles.

Purpose of the Study:

• To explain the divergence between Bayesian philosophy and statistics regarding direct inference.
• To propose a non-standard Bayesian framework capable of utilizing direct inference.
• To demonstrate the utility of this framework for data consolidation in systems science.

Main Methods:

• Analysis of the standard Bayesian framework's limitations regarding direct inference.
• Development of a non-standard Bayesian framework accommodating direct inference principles.
• Application of direct inference for data consolidation in systems medicine.

Main Results:

• The standard Bayesian framework is incompatible with direct inference principles.
• A non-standard Bayesian framework is proposed to enable coherent direct inference.
• Direct inference is essential for effective data consolidation in systems science.

Conclusions:

• The divergence between Bayesian philosophy and statistics necessitates a shift towards non-standard Bayesian approaches.
• The proposed non-standard Bayesian framework offers a viable solution for data consolidation challenges.
• Direct inference, enabled by this framework, is key for advancing systems science applications.