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The source of the prior distribution affects analysis and whether the Likelihood Principle (LP) is obeyed. If the prior is pure/subjective, LP applies. If the s
by clircle 6y ago
The source of the prior distribution affects analysis and whether the Likelihood Principle (LP) is obeyed. If the prior is pure/subjective, LP applies. If the source is not subjective LP does not apply, and with it goes some of the niceties of Bayesian analysis.
- RobertoG 6y agoNot sure what that means, a prior is always "subjective" because is the model of the world before the observation, but it comes from the observer experience of reality, where else could it come?, it just that those experiences change with the observer. Anyway, the prior is updated after every observation, so if it was a wrong prior, it should be less important in the result at every observation.
- clircle 6y agoData driven priors are more common now. Sometimes this is called empirical Bayes. Also priors can change after model checking. These are data driven priors, but not EB. The prior is only negligible in infinite sample sizes. It could still have a large effect given 100s or 1000s of observations. For example, if the prior variance is miss specified by an order of magnitude (not uncommon).
- kgwgk 6y agoThe likelihood principle (all of the information an experimental outcome provides about a parameter θ is expressed in the likelihood function) applies either way.