在貝式框架裡，損耗函數的穩健性亦被思考的。當損耗函數屬於某特定的種類時，探討其事後期望損耗( posterior expected loss) 的變量，事後期望損耗的範園、影響函數( influence function) 及大中取小的遺憾( minimax regret )原則
被採用，為了獲得穩健性與損耗函數的最佳選擇。在LINEX 損耗函數的種類下，因為使用連續型的指數家族( exponential family) 與離散型的幕級數分配(power series distributions ) ，得以完成廣泛的研究。這些方法被應用到典型例題，含常態、加碼與卡瓦松分配。 Robustness of the loss functions is considered in a Bayesian framework. Variations of the posterior expected loss are studied when the loss functions belong to a certain class. Ranges of the posterior expected loss, influence function and minimax regret principles are adopted to capture the robustness and optimum choice of the loss functions. Extensive studies are performed for the continuous exponential family and discrete power series distributions under the class of LINEX loss functions. Methods are applied to standard examples, including Normal, Gamma and Poisson distributions.
