Chapter

Taking the Prior Seriously: Bayesian Analysis without Subjective Probability

Daniel Goodman

in The Nature of Scientific Evidence

Published by University of Chicago Press

Published in print October 2004 | ISBN: 9780226789552
Published online February 2013 | e-ISBN: 9780226789583 | DOI: http://dx.doi.org/10.7208/chicago/9780226789583.003.0012
Taking the Prior Seriously: Bayesian Analysis without Subjective Probability

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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

Chapter.  12412 words.  Illustrated.

Subjects: Animal Pathology and Diseases

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