Given a regular Bayesian experiment we can consider the Lebesgue decomposition of the posterior distributions w.r.t. the prior. Then, by using the Lebesgue decomposition of each sampling distribution w.r.t. the predictive distribution, we show that the absolutely continuous parts of the posteriors are only determined by the absolutely continuous parts of the sampling distributions, while the singular parts of the posteriors are only determined by the singular parts.
Macci, C. (1996). On the Lebesgue decomposition of the posterior distribution with respect to the prior in regular Bayesian experiments. STATISTICS & PROBABILITY LETTERS, 26(2), 147-152 [10.1016/0167-7152(95)00004-6].
On the Lebesgue decomposition of the posterior distribution with respect to the prior in regular Bayesian experiments
MACCI, CLAUDIO
1996-01-01
Abstract
Given a regular Bayesian experiment we can consider the Lebesgue decomposition of the posterior distributions w.r.t. the prior. Then, by using the Lebesgue decomposition of each sampling distribution w.r.t. the predictive distribution, we show that the absolutely continuous parts of the posteriors are only determined by the absolutely continuous parts of the sampling distributions, while the singular parts of the posteriors are only determined by the singular parts.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
