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1

Bootstrapped tests for epistemic fuzzy data

Grzegorzewski Przemyslaw, Romaniuk Maciej

International Journal of Applied Mathematics and Computer Science

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2024

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Vol. 34, no. 2

277--289

EN

Epistemic bootstrap is a resampling algorithm that generates bootstrap real-valued samples based on some epistemic fuzzy data input. We apply this method as a universal basis for various statistical tests which can be then directly used for fuzzy random variables. Two classical goodness-of-fit tests are considered as an example to examine the suggested methodology for both synthetic and real data. The proposed approach is also compared with two other goodness-of-fit tests dedicated directly to fuzzy data.

2

Bootstrap estimation of sound power level determined by the survey method

Stępień Bartłomiej

Vibrations in Physical Systems

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2023

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Vol. 34, nr 2

art. no. 2023210

EN

The possibility of using the bootstrap method to determine the sound power level for the survey method was presented in this paper. Minimum values of the bootstrap algorithm input parameters have been determined for the estimation of sound power level. Two independent simulation experiments have been performed for that purpose. The first experiment served to determine the impact of the original random sample size, and the second to determine the impact of a number of the bootstrap replications on the accuracy of estimation of sound power level. The inference has been carried out based on the results of non-parametric statistical tests at significance level α = 0.05. The statistical analysis has shown that the minimum size of the original random sample n used to estimate the value of sound power level should be 4 elements for the survey method. The minimum number of bootstrap replications necessary for the estimation of sound power level should be B = 5100. The study on the usefulness and effectiveness of the bootstrap method in the determination of sound power level in real-life situation was carried out with the use of data representing actual results. The data used to illustrate the proposed solutions and carry out the analysis were the results of sound power levels of reference sound power source B&K 4205 were used.

3

Bootstrap methods for epistemic fuzzy data

Grzegorzewski Przemyslaw, Romaniuk Maciej

International Journal of Applied Mathematics and Computer Science

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2022

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Vol. 32, no. 2

285--297

EN

Fuzzy numbers are often used for modeling imprecise perceptions of the real-valued observations. Such epistemic fuzzy data may cause problems in statistical reasoning and data analysis. We propose a universal nonparametric technique, called the epistemic bootstrap, which could be helpful when the existing methods do not work or do not give satisfactory results. Besides the simple epistemic bootstrap, we develop its several refinements that aim to reduce the variance in statistical inference. We also perform an extended simulation study to examine statistical properties of the approaches considered. The discussion of the results is supplemented by some hints for practical use.

4

A fuzzy nonparametric Shewhart chart based on the bootstrap approach

Wang D., Hryniewicz O.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 2

389--401

EN

In this paper, we consider a nonparametric Shewhart chart for fuzzy data. We utilize the fuzzy data without transforming them into a real-valued scalar (a representative value). Usually fuzzy data (described by fuzzy random variables) do not have a distributional model available, and also the size of the fuzzy sample data is small. Based on the bootstrap methodology, we design a nonparametric Shewhart control chart in the space of fuzzy random variables equipped with some L2 metric, in which a novel approach for generating the control limits is proposed. The control limits are determined by the necessity index of strict dominance combined with the bootstrap quantile of the test statistic. An in-control bootstrap ARL of the proposed chart is also considered.

5

Bootstrap i inne metody oceny wiarygodności drzew filogenetycznych

Bartoszek K.

Zeszyty Naukowe Wydziału ETI Politechniki Gdańskiej. Technologie Informacyjne

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2007

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T. 12

103-108

PL

Ostatnim etapem analizy filogenetycznej jest ocena wiarygodności powstałego drzewa. Nie jest to łatwy problem, gdyż nie znamy pełnego modelu probabilistycznego ewolucji. Zaproponowano kilka metod, ale w literaturze jest szeroka dyskusja, co do ich stosowalności oraz interpretacji.

EN

The final step of phylogenetic analysis is the test of the generated tree. This is not a easy task for which there is an obvious methodology because we do not know the full probabilistic model of evolution. A number of methods have been proposed by they is a wide debate concerning the interpretations of the results they produce.