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Bayesian analysis for proportions with an independent background effect
Author(s) -
Bi Jian
Publication year - 2007
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711005x86705
Subject(s) - posterior probability , bayesian probability , mathematics , statistics , bayesian linear regression , bayesian inference , beta distribution , prior probability , bayesian average , inverse chi squared distribution , bayesian hierarchical modeling , categorical distribution , distribution (mathematics) , econometrics , probability distribution , mathematical analysis , distribution fitting
Conventional Bayesian analysis for proportions is not appropriate for proportions with a background effect, for example, for the proportion of correct responses in a sensory difference test using a forced‐choice method with a guessing probability. The main difficulty is that it is not reasonable to assume that a proportion with a background effect has a beta prior distribution. A generalized posterior distribution for proportions is derived in this paper. It includes the standard beta posterior distribution for a proportion without background effect as a special case. Bayesian inference and Bayesian sample size determination for proportions based on the generalized posterior distribution are discussed.