Selecting The Subset Of Distribution In The Prior Distribution Through Use Of ε-contamination Class

An important problem of Bayes statistic conclusion is Posterior Robustness.There are many method of Posterior Robustness analysis. The judgemental standard of Robustness is the traditional Bayes risk rule.Class of distributions which have the formÏ€=(1-ε)Ï€₀+εq,Ï€₀ being the base elicited prior,q being a "contamination".Andεreflecting the amount of error inÏ€₀ that is deemed possible.D is the subset of distribution.Bayes Risk rule is that,L(θ,α) is losing function,ρ[Ï€(θ|x),α) is theposterior expectation loss ofα,then we use ((?)ρ(Ï€(θ|x),α),(?)ρ(Ï€(θ|x),α))judging the Robustness ofα.Huber gives a thesis in 1973,in this thesis,he discusses the Robustness ofαon the base of D={all distributions}.But the paper [3] points out that the range of D={all distributions} is big that impact on the result of Robustness.D of the paper [3] is the set of uniform distributions,the result of Robustness is better than Huber's.Furthermore,the paper [3] discusses the posterior robust of the type-â…¡maximum likelihood prior within the reasonable D.However there are many methods of the selecting of the prior distribution in Bayes statistic,a usual one of them is the the conjugate distribution method. So in this text,we consider to select D using the conjugate distribution method,then we get a better Posterior Robustness.And the posterior robust of the type-â…¡likelihood prior is very good too.Therefore,selecting D using the conjugate distribution method is reasonable and feasible.