A discussion on learning and prior ignorance for sets of priors in the one-parameter exponential family
Alessio Benavoli, Marco Zaffalon · 2011
For a conjugate likelihood-prior model in the oneparameter exponential family of distributions, we show that, by letting the parametersof the conjugateexponential prior vary in suitable sets, it is possible to define a set of conjugate priors M that guarantees prior near-ignorance without producing vacuous inferences. This result is obtained followingboth a behaviouraland a sensitivity analysis interpretation of prior near-ignorance. We also discuss the problem of the incompatibility of learning and prior near-ignorance for sets of priors in the one-parameter exponential family of distributions in the case of imperfect observations. In particular, we prove that learning and priornear-ignoranceare compatibleunderan imperfectobservationmechanismifandonlyif the supportofthe priors in M is the whole real axis.