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Bayesian Analysis of the Weibull Paired Comparison Model Using Numerical Approximation
Journal of Mathematics ( IF 1.3 ) Pub Date : 2020-12-15 , DOI: 10.1155/2020/6628379
Khalil Ullah 1, 2 , Muhammad Aslam 2
Affiliation  

The method of paired comparisons (PC) is widely used to rank items using sensory evaluations. The PC models are developed to provide basis for such comparisons. In this study, the Weibull PC model is analyzed under the Bayesian paradigm using noninformative priors and different loss functions, namely, Squared Error Loss Function (SELF), Quadratic Loss Function (QLF), DeGroot Loss Function (DLF), and Precautionary Loss Function (PLF). Numerical approximation is used to illustrate the entire estimation procedure. A real dataset showing usage preferences for different cellphone brands, Huawei (HW), Samsung (SS), Oppo (OP), QMobile (QM), and Nokia (NK), is used. Quadrature method is used to evaluate the Bayes estimates, their posterior risks, preference probabilities, predictive probabilities, and posterior probabilities to establish and verify ranking order of the competing cellphone brands under study. The results show that the paired comparison model under the study using Bayesian approach involving various loss functions can offer mathematical approach to evaluate cellphone brand preferences. The ranking provided by the model is justifiable according to the usage preference for these cellphone brands. The ranking given by the model indicates that cellphone brand Samsung is preferred the most and QMobile is the least preferred. The plausibility of the model is also assessed using the Chi square test of goodness of fit.

中文翻译:

基于数值近似的威布尔配对比较模型的贝叶斯分析

配对比较法(PC)被广泛用于使用感官评估对项目进行排名。开发PC模型可为此类比较提供基础。在这项研究中,使用非信息先验和不同的损失函数(即平方误差损失函数(SELF),二次损失函数(QLF),DeGroot损失函数(DLF)和预防损失函数)在贝叶斯范式下对Weibull PC模型进行了分析。 (PLF)。数值逼近用于说明整个估算过程。使用真实数据集显示不同手机品牌的使用偏好,这些品牌包括华为(HW),三星(SS),Oppo(OP),QMobile(QM)和诺基亚(NK)。正交方法用于评估贝叶斯估计,其后验风险,偏好概率,预测概率,以及建立和验证所研究的竞争手机品牌的排名顺序的后验概率。结果表明,采用贝叶斯方法的,涉及各种损失函数的配对比较模型可以为评估手机品牌偏好提供数学方法。根据这些手机品牌的使用偏好,该模型提供的排名是合理的。该模型给出的排名表明,手机品牌三星是最受青睐的,而QMobile是最不受欢迎的。还使用拟合优度的卡方检验来评估模型的合理性。结果表明,采用贝叶斯方法的,涉及各种损失函数的配对比较模型可以为评估手机品牌偏好提供数学方法。根据这些手机品牌的使用偏好,该模型提供的排名是合理的。该模型给出的排名表明,手机品牌三星是最受青睐的,而QMobile是最不受欢迎的。还使用拟合优度的卡方检验来评估模型的合理性。结果表明,采用贝叶斯方法的,涉及各种损失函数的配对比较模型可以为评估手机品牌偏好提供数学方法。根据这些手机品牌的使用偏好,该模型提供的排名是合理的。该模型给出的排名表明,手机品牌三星是最受青睐的,而QMobile是最不受欢迎的。还使用拟合优度的卡方检验来评估模型的合理性。
更新日期:2020-12-15
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