Bayes Factors from Mixed Probabilities
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1978 · Volume 40 · Issue 1
DOI: 10.1111/j.2517-6161.1978.tb01645.x
Abstract
A new expression for a Bayes factor as a weighted average of conditional Bayes factors is given, resembling the familiar relation for a marginal probability as a weighted average of conditional probabilities. Interpretations are given for the three contexts of (i) the use of a non-sufficient statistic, (ii) inference for a simple hypothesis versus a vague alternative in terms of inference for a dichotomy and (iii) opinion pooling before sampling.
Keywords
bayesian inference, bayes factors, probability mixtures, insufficient statistics, group decision making
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