This paper focuses on Bayesian inference for the parameters of the generalized exponential model under asymmetric and symmetric loss functions when the observations are described in terms of fuzzy numbers. First, a generalized likelihood function based on fuzzy data is derived. Then, considering general entropy, linear exponential and squared error loss functions, the Bayes estimates of the parameters are obtained. Since Bayes estimates could not be expressed in closed forms, Metropolis–Hasting samplers are used to compute the approximate Bayes estimates. For comparison purposes, the maximum likelihood estimates of the parameters are also computed. The proposed inferences are illustrated using three real-world examples. The numerical simulation results demonstrate the superiority of the Bayesian method over the maximum likelihood procedure.

中文翻译：

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基于模糊数据的广义指数模型的贝叶斯方法

当观测值用模糊数描述时，本文集中在非对称和对称损失函数下广义指数模型参数的贝叶斯推断。首先，推导基于模糊数据的广义似然函数。然后，考虑一般熵，线性指数和平方误差损失函数，获得参数的贝叶斯估计。由于无法以封闭形式表示贝叶斯估计，因此使用Metropolis-Hasting采样器来计算近似贝叶斯估计。为了比较，还计算了参数的最大似然估计。所提出的推论使用三个实际示例进行了说明。数值模拟结果证明了贝叶斯方法优于最大似然法的优越性。