For Bayesian Robustness Analysis, In The Prior Distribution Is Through Use Of ε-contamination Class

Class of distributions which have the formÏ€= (1 -ε)Ï€₀ +εq,Ï€₀ being the baseelicited prior, q being a "contamination". Andεreflecting the amount of error inÏ€₀that is deemed possible. D is the subset of distribution. This distributions class have special attraction in the Bayesian Robustness. The judgemental standard of Robustness isthe traditional Bayes risk rule, L(θ,a) is losing function,ρ(Ï€(θ|x),a)is the posterior expectation loss of a, then we use , judgingthe Robustness of a .Huber give a thesis in 1973,in this thesis, he discuss the Robustness of a on the base of D = {all distributions}.Some literature about Bayesian Robustness are all on base of this thesis. But in the actual apply, the range of D = [all distributions] is big that impact on the result of Robustness. So in this text,three issues in robust Bayesian analysis are studied. The first is that of determining the range of posterior probabilities of a set as D range over theε- contamination class. The second, if the D is in reason, a "good" prior distribution (the type-II maximum likelihood prior) from theΓis posterior robust. The third, using this prior in the subsequent analysis, discuss the Bayesian robust of the Normal distribution . In the last, whentheÏ€₀ is unimodal and the high point isθ₀. We give the robust class D and get the type-II maximum likelihood prior.