Bayesian Analysis of the Weibull Paired Comparison Model Using Numerical Approximation

Abstract

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.

Statistical Inferences of Burr XII Lifetime Models under Joint Type-1 Competing Risks Samples

“…In this section, we adopted Bayesian approach to estimate the model parameters under Type-I JCRS (see Ullah and Aslam [34]). So, we suppose that the prior information available about the parameters are independent Gamma prior distributions.…”

“…e point and interval estimate of model parameters under MCMC methods depend on the forms of full conditional distributions and the subclass of MCMC that can be applied. erefore, full conditional distribution given by ( 31) to (34) has shown that we can use the algorithms of Gibbs and generally Metropolis Hasting (MH) under Gibbs (for more details, see [35]) described in Algorithm 1.…”