Bayesian analysis of the Weibull paired comparison model using informative prior

Ullah, Khalil; Aslam, Muhammad; Sindhu, Tabassum Naz

doi:10.1016/j.aej.2020.02.032

Cited by 7 publications

(8 citation statements)

References 11 publications

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“…e basics for the development of the Weibull PC model is elaborated in Ullah et al [11]. According to the Weibull PC model, the probability of preferring treatment T j over treatment T k is denoted by θ j•jk and can be calculated as follows:…”

Section: E Weibull Paired Comparison Modelmentioning

confidence: 99%

“…is section presents the derivation of the Bayes Estimators and Posterior Risks (PRs) under loss functions using Uniform and Jeffreys priors. We used four different loss functions named as Squared Error Loss Function (SELF), Quadratic Loss Function (QLF), DeGroot Loss Function (DLF), and Precautionary Loss Function (PLF) [11]. e BEs and PRs, using various loss functions under Uniform and Jeffreys priors, are obtained and given in Tables 2 and 3.…”

Section: Graphical Analysis Of the Marginal Posteriormentioning

confidence: 99%

“…urstone [7], Bradley and Terry [8], Stern [9], and Abbas and Aslam [10] constructed different PC models. Ullah et al [11] suggested the Weibull PC model and analyzed it using Bayesian approach. Annis and Craig [12] and Cattelan [13] used PC technique to analyze sports-related problems.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Analysis of the Weibull Paired Comparison Model Using Numerical Approximation

Ullah

Aslam

2020

Journal of Mathematics

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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.

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Section: E Weibull Paired Comparison Modelmentioning

confidence: 99%

Section: Graphical Analysis Of the Marginal Posteriormentioning

confidence: 99%

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Bayesian Analysis of the Weibull Paired Comparison Model Using Numerical Approximation

Ullah

Aslam

2020

Journal of Mathematics

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“…Manual approaches include the ordinary least squares [15,16], unbiased good linear estimators [17], and weighted least squares [18]. Computational methods include maximum likelihood estimation [19], the moments estimation method [20], Bayesian approach [21], and least-squares estimation with particle swarm optimization [22].…”

Section: Introductionmentioning

confidence: 99%

Estimating Weibull Parameters Using Least Squares and Multilayer Perceptron vs. Bayes Estimation

Aydi¹,

Al-Duais²

2022

Computers, Materials &Amp; Continua

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The Weibull distribution is regarded as among the finest in the family of failure distributions. One of the most commonly used parameters of the Weibull distribution (WD) is the ordinary least squares (OLS) technique, which is useful in reliability and lifetime modeling. In this study, we propose an approach based on the ordinary least squares and the multilayer perceptron (MLP) neural network called the OLSMLP that is based on the resilience of the OLS method. The MLP solves the problem of heteroscedasticity that distorts the estimation of the parameters of the WD due to the presence of outliers, and eases the difficulty of determining weights in case of the weighted least square (WLS). Another method is proposed by incorporating a weight into the general entropy (GE) loss function to estimate the parameters of the WD to obtain a modified loss function (WGE). Furthermore, a Monte Carlo simulation is performed to examine the performance of the proposed OLSMLP method in comparison with approximate Bayesian estimation (BLWGE) by using a weighted GE loss function. The results of the simulation showed that the two proposed methods produced good estimates even for small sample sizes. In addition, the techniques proposed here are typically the preferred options when estimating parameters compared with other available methods, in terms of the mean squared error and requirements related to time.

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“…It has also been shown that Bradley-Terry model can be seen as a special case of a more general model. A very recent example of such treatment demonstrates a pairwise comparison model where the Weibull distribution is applied [ 10 ]. Another common generalization is to allow for the latent strengths to vary with time and it is the focus of our work.…”

Section: Introductionmentioning

confidence: 99%

A Bayesian approach to time-varying latent strengths in pairwise comparisons

Krese

Štrumbelj

2021

PLoS ONE

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The famous Bradley-Terry model for pairwise comparisons is widely used for ranking objects and is often applied to sports data. In this paper we extend the Bradley-Terry model by allowing time-varying latent strengths of compared objects. The time component is modelled with barycentric rational interpolation and Gaussian processes. We also allow for the inclusion of additional information in the form of outcome probabilities. Our models are evaluated and compared on toy data set and real sports data from ATP tennis matches and NBA games. We demonstrated that using Gaussian processes is advantageous compared to barycentric rational interpolation as they are more flexible to model discontinuities and are less sensitive to initial parameters settings. However, all investigated models proved to be robust to over-fitting and perform well with situations of volatile and of constant latent strengths. When using barycentric rational interpolation it has turned out that applying Bayesian approach gives better results than by using MLE. Performance of the models is further improved by incorporating the outcome probabilities.

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Bayesian analysis of the Weibull paired comparison model using informative prior

Cited by 7 publications

References 11 publications

Bayesian Analysis of the Weibull Paired Comparison Model Using Numerical Approximation

Bayesian Analysis of the Weibull Paired Comparison Model Using Numerical Approximation

Estimating Weibull Parameters Using Least Squares and Multilayer Perceptron vs. Bayes Estimation

A Bayesian approach to time-varying latent strengths in pairwise comparisons

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