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The Nature of Scientific EvidenceStatistical, Philosophical, and Empirical Considerations$
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Mark L. Taper and Subhash R. Lele

Print publication date: 2004

Print ISBN-13: 9780226789552

Published to Chicago Scholarship Online: February 2013

DOI: 10.7208/chicago/9780226789583.001.0001

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Taking the Prior Seriously: Bayesian Analysis without Subjective Probability

Taking the Prior Seriously: Bayesian Analysis without Subjective Probability

Chapter:
(p.379) 12 Taking the Prior Seriously: Bayesian Analysis without Subjective Probability
Source:
The Nature of Scientific Evidence
Author(s):

Daniel Goodman

Publisher:
University of Chicago Press
DOI:10.7208/chicago/9780226789583.003.0012

Decision theory requires the assignment of probabilities for the different possible states of nature. Bayesian inference provides such probabilities, but at the cost of requiring prior probabilities for the states of nature. In this century, the justification for prior probabilities has often rested on subjective theories of probability. Subjective probability can lead to internally consistent systems relating belief and action for a single individual; but severe difficulties emerge in trying to extend this model to justify public decisions. Objective probability represents probability as a literal frequency that can be communicated as a matter of fact and that can be verified by independent observers confronting the same information. This chapter argues that the Bayesian approach is best for making decisions and that one needs to put probabilities on various hypotheses. It proposes an interpretation of statistical inference for decision making, but disapproves of the subjective aspects of Bayesianism and suggests, as an alternative, using related data to create “objective” priors. The chapter also considers a compound sampling perspective and presents a concrete example of compound sampling.

Keywords:   Bayesian approach, subjective probability, objective probability, Bayesianism, statistical inference, decision making, compound sampling, objective priors

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