Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Fiducial inference then and now

Philip Dawid

Abstract

We conduct a review of the fiducial approach to statistical inference, following its journey from its initiation by R. A. Fisher, through various problems and criticisms, on to its general neglect, and then to its more recent resurgence. Emphasis is laid on the functional model formulation, which helps clarify the very limited conditions under which fiducial inference can be conducted in an unambiguous and self-consistent way.

Fiducial inference then and now

Abstract

We conduct a review of the fiducial approach to statistical inference, following its journey from its initiation by R. A. Fisher, through various problems and criticisms, on to its general neglect, and then to its more recent resurgence. Emphasis is laid on the functional model formulation, which helps clarify the very limited conditions under which fiducial inference can be conducted in an unambiguous and self-consistent way.

Paper Structure

This paper contains 26 sections, 23 equations.

Table of Contents

  1. Introduction
  2. Fisher's original fiducial argument
  3. Pivotal inference
  4. Validity
  5. Group-structured models
  6. Simple group model
  7. Structural models
  8. Functional models
  9. Simple functional model (SFM)
  10. Monotonic functional model
  11. Marginalization consistency
  12. Marginalization paradox
  13. Some difficulties
  14. Choice of group
  15. Marginalization inconsistency
  16. ...and 11 more sections

Theorems & Definitions (18)

  • Example 3.1
  • Example 3.2
  • Example 4.1
  • Example 4.2
  • Example 5.1
  • Example 6.1
  • Example 6.2
  • Example 7.1
  • Example 7.2
  • Example 7.3
  • ...and 8 more