A Comparison Analysis of Fuzzy and Bayesian Linear Model Parameter Estimates for Replicated Response Measures

Year 2021, , 251 - 270, 01.03.2021

Özlem Türkşen

https://doi.org/10.35378/gujs.660845

Abstract

It is possible to define functional relationship between replicated response measures and input variables by using fuzzy and Bayesian modeling approaches. The main aim of the study is to present the alternative usability of fuzzy modeling approach to Bayesian modeling approach with defining a proper alpha-cut level among the many alpha-cut levels. In this study, the uncertainty of estimated model parameters were compared by transforming the estimated parameter values to intervals. Interval valued parameter estimates were obtained through alpha-cut level presentation and credible intervals for fuzzy and Bayesian approaches, respectively. Thus, it was achieved to model the replicated response measured (RRM) data set without making any probabilistic modeling assumptions which were hard to satisfy for small sized RRM data set. To compare the interval valued model parameter estimates in the proposed study, midpoint, width, radius and Hausdorff metrics were used. And also, interval type residuals were calculated to see the performance of predicted fuzzy and Bayesian models for making clear comparison. Two data sets from the literature, which were called Roman Catapult and Printing Ink, were used and the obtained results were discussed in application part.

Keywords

Replicated response measures, Fuzzy modeling, Bayesian modeling, Interval arithmetic

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