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Statistical ThoughtA Perspective and History$
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Shoutir Kishore Chatterjee

Print publication date: 2003

Print ISBN-13: 9780198525318

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198525318.001.0001

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BEARING OF INTERPRETATIONS OF PROBABILITY ON STATISTICAL INDUCTION

BEARING OF INTERPRETATIONS OF PROBABILITY ON STATISTICAL INDUCTION

Chapter:
(p.61) 4 BEARING OF INTERPRETATIONS OF PROBABILITY ON STATISTICAL INDUCTION
Source:
Statistical Thought
Author(s):

Shoutir Kishore Chatterjee

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198525318.003.0004

Objective statistical induction may be behavioural, instantial, or pro-subjective (Bayesian), depending on the form of judging inferential uncertainty. In the behavioral case, the unknown parameters are fixed and uncertainty is judged by measures of procedural trustworthiness (like significance and confidence levels, power and risk functions), interpreted through repeated conceptual experimentation. Various principles are invoked for optimizing the procedure in different problems. The instantial approach (likelihood inference, P-value testing, and fiducial inference) remains pegged to the instance at hand without visualizing repetition, and weighs uncertainty in non-standard ways, although often like the behavioural approach, it also has to appeal to sampling theory. In the pro-subjective Bayesian approach, the unknown parameters are subjectively random with a known prior distribution, and inference is based on their posterior distribution. Various kinds of priors (improper/proper, impersonal/personal) fit in different tastes and situations. The subjective approach, based on a fully known subjective probability model, ‘previses’ about future observables, conditionally fixing the observations, often assuming exchangeability to simplify the process. Comparison of the different approaches shows that each has a natural setting in which it is advantageous.

Keywords:   objective behavioural, procedural trustworthiness, conceptual repetition, objective instantial, likelihood, P-value, fiducial, objective Bayesian, prior and posterior, subjective

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