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Journal articles on the topic 'Test de permutation'

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Published: 4 June 2021

Last updated: 1 February 2022

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1

Anderson, Marti J. "Permutation tests for univariate or multivariate analysis of variance and regression." Canadian Journal of Fisheries and Aquatic Sciences 58, no. 3 (March 1, 2001): 626–39. http://dx.doi.org/10.1139/f01-004.

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The most appropriate strategy to be used to create a permutation distribution for tests of individual terms in complex experimental designs is currently unclear. There are often many possibilities, including restricted permutation or permutation of some form of residuals. This paper provides a summary of recent empirical and theoretical results concerning available methods and gives recommendations for their use in univariate and multivariate applications. The focus of the paper is on complex designs in analysis of variance and multiple regression (i.e., linear models). The assumption of exchangeability required for a permutation test is assured by random allocation of treatments to units in experimental work. For observational data, exchangeability is tantamount to the assumption of independent and identically distributed errors under a null hypothesis. For partial regression, the method of permutation of residuals under a reduced model has been shown to provide the best test. For analysis of variance, one must first identify exchangeable units by considering expected mean squares. Then, one may generally produce either (i) an exact test by restricting permutations or (ii) an approximate test by permuting raw data or some form of residuals. The latter can provide a more powerful test in many situations.

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2

Savchuk, M., and M. Burlaka. "Encoding and classification of permutations bу special conversion with estimates of class power." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 2 (2019): 36–43. http://dx.doi.org/10.17721/1812-5409.2019/2.3.

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Scientific articles investigating properties and estimates of the number of so-called complete permutations are surveyed and analyzed. The paper introduces a special S-transform on the set of permutations and determines the permutation properties according to this transform. Classification and coding of permutations by equivalence classes according to their properties with respect to S-transformation is proposed. This classification and permutation properties, in particular, generalize known results for complete permutations regarding determining certain cryptographic properties of substitutions that affect the cryptographic transformations security. The exact values of the number of permutations in equivalence classes for certain permutation sizes are calculated and the estimates of the cardinality of classes with various properties are constructed by statistical modeling. The complete list of permutation classes with the exact values of their sizes for permutations of order n = 11 is presented. The interval estimates for the size of classes with various characteristics for permutations of order n = 11, 26, 30, 31, 32, 33, 45, 55 are obtained. Monte Carlo estimates and bounds of confidence intervals used the approximation of the binomial distribution by the normal and Poisson distributions, as well as the Python programming language package Scipy. Statistical tables have been calculated that can be used for further conclusions and estimates. The classification of permutations by their properties with respect to the introduced transform can be used in constructing high-quality cryptographic transformations and transformations with special features. The classes of complete permutations with their properties are selected as the best for rotary cryptosystems applications. The obtained results can be used, in particular, to search for permutations with certain characteristics and properties, to find the probability that the characteristic of the generated permutation belongs to a collection of given characteristics, to estimate the complexity of finding permutations with certain properties. A statistical criterion of consent, which uses the characteristics of permutations by S-transformation to test the generators of random permutations and substitutions is proposed.

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3

Mielke, Paul W., Kenneth J. Berry, and Charles O. Neidt. "A Permutation Test for Multivariate Matched-Pair Analyses: Comparisons with Hotelling's Multivariate Matched-Pair T2 Test." Psychological Reports 78, no. 3 (June 1996): 1003–8. http://dx.doi.org/10.2466/pr0.1996.78.3.1003.

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A permutation alternative for Hotelling's multivariate matched-pair T2 test is introduced. The permutation test allows for analyses when the number of subjects is less than or equal to the number of measurements, which is not possible with Hotelling's multivariate matched-pair T2 test. For the data analyzed the permutation test is shown to provide improved discrimination over Hotelling's multivariate matched-pair T2 test.

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4

Sari, Resti Mustika, Yudiantri Asdi, and Ferra Yanuar. "PERBANDINGAN KUASA WILCOXON RANK SUM TEST DAN PERMUTATION TEST DALAM BERBAGAI DISTRIBUSI TIDAK NORMAL." Jurnal Matematika UNAND 3, no. 4 (December 1, 2014): 139. http://dx.doi.org/10.25077/jmu.3.4.139-146.2014.

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Kuasa dari suatu uji statistik adalah peluang menolak hipotesis nol kalauhipotesis nol tersebut salah. Simulasi dengan menggunakan software R dilakukan untukmembandingkan kuasa Wilcoxon Rank Sum Test dan Permutation Test untuk membandingkan dua nilai tengah populasi yang dibangkitkan dari distribusi Uniform, Eksponensial, Log Normal dan Weibull. Hasil simulasi data menunjukkan bahwa pada sebaranUniform uji yang lebih baik adalah Permutation Test. Untuk sampel menengah dansampel besar pada distribusi Eksponensial, Weibull dan Log-Normal uji yang lebih baikadalah Wilcoxon Rank Sum Test. Sedangkan untuk sampel berukuran kecil yang berasaldari distribusi Eksponensial, Weibull dan Log-Normal tidak bisa ditentukan mana uji yglebih baik diantara Wilcoxon Rank Sum Test dan Permutation Test.

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5

Collins, Mark F. "A Permutation Test for Planar Regression." Australian Journal of Statistics 29, no. 3 (September 1987): 303–8. http://dx.doi.org/10.1111/j.1467-842x.1987.tb00747.x.

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6

Cade, Brian S., and Jon D. Richards. "A permutation test for quantile regression." Journal of Agricultural, Biological, and Environmental Statistics 11, no. 1 (March 2006): 106–26. http://dx.doi.org/10.1198/108571106x96835.

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7

Basso, Dario, and Luigi Salmaso. "A permutation test for umbrella alternatives." Statistics and Computing 21, no. 1 (August 27, 2009): 45–54. http://dx.doi.org/10.1007/s11222-009-9145-8.

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8

Shparlinski, I. E. "A deterministic test for permutation polynomials." Computational Complexity 2, no. 2 (June 1992): 129–32. http://dx.doi.org/10.1007/bf01202000.

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9

Toth, Daniell. "A Permutation Test on Complex Sample Data." Journal of Survey Statistics and Methodology 8, no. 4 (August 13, 2019): 772–91. http://dx.doi.org/10.1093/jssam/smz018.

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Abstract Permutation tests are a distribution-free way of performing hypothesis tests. These tests rely on the condition that the observed data are exchangeable among the groups being tested under the null hypothesis. This assumption is easily satisfied for data obtained from a simple random sample or a controlled study after simple adjustments to the data, but there is no general method for adjusting survey data collected using a complex sample design to allow for permutation tests. In this article, we propose a general method for performing a pseudo-permutation test that accounts for the complex sample design. The proposed method is not a true permutation test in that the new values do not come from the set of observed values in general but of an expanded set of values satisfying a random-effects model on the clustered residuals of a design-consistent estimating equation. We provide a set of conditions under which this procedure leads to consistent test results. Tests using a simulated population and an application analyzing US Bureau of Labor Statistics consumer expenditure data comparing the performance of the proposed method to permutation tests that ignore the sample design demonstrate that it is necessary to account for the design features in order to obtain reasonable p value estimates.

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10

Berry, Kenneth J., and Paul W. Mielke. "Analysis of Multivariate Matched-Paired Data: A Fortran 77 Program." Perceptual and Motor Skills 83, no. 3 (December 1996): 788–90. http://dx.doi.org/10.2466/pms.1996.83.3.788.

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The FORTRAN program MVMPT is described which computes Hotelling's multivariate matched-pair T2 test and three permutation tests described by Miellte, et al. in 1996: an exact multivariate matched-pair permutation test, a non-asymptotic multivariate matched-pair permutation test, and the Hotelling multivariate matched-pair T2 permutation test.

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11

Kroehl, Miranda E., Sharon Lutz, and Brandie D. Wagner. "Permutation-based methods for mediation analysis in studies with small sample sizes." PeerJ 8 (January 22, 2020): e8246. http://dx.doi.org/10.7717/peerj.8246.

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Background Mediation analysis can be used to evaluate the effect of an exposure on an outcome acting through an intermediate variable or mediator. For studies with small sample sizes, permutation testing may be useful in evaluating the indirect effect (i.e., the effect of exposure on the outcome through the mediator) while maintaining the appropriate type I error rate. For mediation analysis in studies with small sample sizes, existing permutation testing methods permute the residuals under the full or alternative model, but have not been evaluated under situations where covariates are included. In this article, we consider and evaluate two additional permutation approaches for testing the indirect effect in mediation analysis based on permutating the residuals under the reduced or null model which allows for the inclusion of covariates. Methods Simulation studies were used to empirically evaluate the behavior of these two additional approaches: (1) the permutation test of the Indirect Effect under Reduced Models (IERM) and (2) the Permutation Supremum test under Reduced Models (PSRM). The performance of these methods was compared to the standard permutation approach for mediation analysis, the permutation test of the Indirect Effect under Full Models (IEFM). We evaluated the type 1 error rates and power of these methods in the presence of covariates since mediation analysis assumes no unmeasured confounders of the exposure–mediator–outcome relationships. Results The proposed PSRM approach maintained type I error rates below nominal levels under all conditions, while the proposed IERM approach exhibited grossly inflated type I rates in many conditions and the standard IEFM exhibited inflated type I error rates under a small number of conditions. Power did not differ substantially between the proposed PSRM approach and the standard IEFM approach. Conclusions The proposed PSRM approach is recommended over the existing IEFM approach for mediation analysis in studies with small sample sizes.

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12

Berry, Kenneth J., Paul W. Mielke, and Howard W. Mielke. "The Fisher-Pitman Permutation Test: An Attractive Alternative to the F Test." Psychological Reports 90, no. 2 (April 2002): 495–502. http://dx.doi.org/10.2466/pr0.2002.90.2.495.

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13

Aickin, Mikel. "Invalid Permutation Tests." International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–10. http://dx.doi.org/10.1155/2010/769780.

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Permutation tests are often presented in a rather casual manner, in both introductory and advanced statistics textbooks. The appeal of the cleverness of the procedure seems to replace the need for a rigorous argument that it produces valid hypothesis tests. The consequence of this educational failing has been a widespread belief in a “permutation principle”, which is supposed invariably to give tests that are valid by construction, under an absolute minimum of statistical assumptions. Several lines of argument are presented here to show that the permutation principle itself can be invalid, concentrating on the Fisher-Pitman permutation test for two means. A simple counterfactual example illustrates the general problem, and a slightly more elaborate counterfactual argument is used to explain why the main mathematical proof of the validity of permutation tests is mistaken. Two modifications of the permutation test are suggested to be valid in a very modest simulation. In instances where simulation software is readily available, investigating the validity of a specific permutation test can be done easily, requiring only a minimum understanding of statistical technicalities.

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14

Mewhort, D. J. K., Brendan T. Johns, and Matthew Kelly. "Applying the permutation test to factorial designs." Behavior Research Methods 42, no. 2 (May 2010): 366–72. http://dx.doi.org/10.3758/brm.42.2.366.

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15

Röhmel, Joachim. "The permutation distribution of the Friedman test." Computational Statistics & Data Analysis 26, no. 1 (November 1997): 83–99. http://dx.doi.org/10.1016/s0167-9473(97)00019-4.

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16

Lock, Robin H. "A sequential approximation to a permutation test." Communications in Statistics - Simulation and Computation 20, no. 1 (January 1991): 341–63. http://dx.doi.org/10.1080/03610919108812956.

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17

Hommola, K., J. E. Smith, Y. Qiu, and W. R. Gilks. "A Permutation Test of Host-Parasite Cospeciation." Molecular Biology and Evolution 26, no. 7 (March 27, 2009): 1457–68. http://dx.doi.org/10.1093/molbev/msp062.

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18

Smirnova, Ekaterina, Snehalata Huzurbazar, and Farhad Jafari. "PERFect: PERmutation Filtering test for microbiome data." Biostatistics 20, no. 4 (June 18, 2018): 615–31. http://dx.doi.org/10.1093/biostatistics/kxy020.

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Summary The human microbiota composition is associated with a number of diseases including obesity, inflammatory bowel disease, and bacterial vaginosis. Thus, microbiome research has the potential to reshape clinical and therapeutic approaches. However, raw microbiome count data require careful pre-processing steps that take into account both the sparsity of counts and the large number of taxa that are being measured. Filtering is defined as removing taxa that are present in a small number of samples and have small counts in the samples where they are observed. Despite progress in the number and quality of filtering approaches, there is no consensus on filtering standards and quality assessment. This can adversely affect downstream analyses and reproducibility of results across platforms and software. We introduce PERFect, a novel permutation filtering approach designed to address two unsolved problems in microbiome data processing: (i) define and quantify loss due to filtering by implementing thresholds and (ii) introduce and evaluate a permutation test for filtering loss to provide a measure of excessive filtering. Methods are assessed on three “mock experiment” data sets, where the true taxa compositions are known, and are applied to two publicly available real microbiome data sets. The method correctly removes contaminant taxa in “mock” data sets, quantifies and visualizes the corresponding filtering loss, providing a uniform data-driven filtering criteria for real microbiome data sets. In real data analyses PERFect tends to remove more taxa than existing approaches; this likely happens because the method is based on an explicit loss function, uses statistically principled testing, and takes into account correlation between taxa. The PERFect software is freely available at https://github.com/katiasmirn/PERFect.

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19

Al-Rawi, Mohammed S., Adelaide Freitas, João V. Duarte, Joao P. Cunha, and Miguel Castelo-Branco. "Permutations of functional magnetic resonance imaging classification may not be normally distributed." Statistical Methods in Medical Research 26, no. 6 (December 2017): 2567–85. http://dx.doi.org/10.1177/0962280215601707.

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A fundamental question that often occurs in statistical tests is the normality of distributions. Countless distributions exist in science and life, but one distribution that is obtained via permutations, usually referred to as permutation distribution, is interesting. Although a permutation distribution should behave in accord with the central limit theorem, if both the independence condition and the identical distribution condition are fulfilled, no studies have corroborated this concurrence in functional magnetic resonance imaging data. In this work, we used Anderson–Darling test to evaluate the accordance level of permutation distributions of classification accuracies to normality expected under central limit theorem. A simulation study has been carried out using functional magnetic resonance imaging data collected, while human subjects responded to visual stimulation paradigms. Two scrambling schemes are evaluated: the first based on permuting both the training and the testing sets and the second on permuting only the testing set. The results showed that, while a normal distribution does not adequately fit to permutation distributions most of the times, it tends to be quite well acceptable when mean classification accuracies averaged over a set of different classifiers is considered. The results also showed that permutation distributions can be probabilistically affected by performing motion correction to functional magnetic resonance imaging data, and thus may weaken the approximation of permutation distributions to a normal law. Such findings, however, have no relation to univariate/univoxel analysis of functional magnetic resonance imaging data. Overall, the results revealed a strong dependence across the folds of cross-validation and across functional magnetic resonance imaging runs and that may hinder the reliability of using cross-validation. The obtained p-values and the drawn confidence level intervals exhibited beyond doubt that different permutation schemes may beget different permutation distributions as well as different levels of accord with central limit theorem. We also found that different permutation schemes can lead to different permutation distributions and that may lead to different assessment of the statistical significance of classification accuracy.

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20

Hajung Jeon, 엄진섭, and Jin-Hun Sohn. "The Accuracy of Permutation Test in P300-based Concealed Information Test." Korean Journal of Cognitive and Biological Psychology 32, no. 1 (January 2020): 69–83. http://dx.doi.org/10.22172/cogbio.2020.32.1.005.

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21

Gondan, Matthias. "A permutation test for the race model inequality." Behavior Research Methods 42, no. 1 (February 2010): 23–28. http://dx.doi.org/10.3758/brm.42.1.23.

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22

Jung, Byoung Cheol, Myoungshic Jhun, and Seuck Heun Song. "A new random permutation test in ANOVA models." Statistical Papers 48, no. 1 (January 2007): 47–62. http://dx.doi.org/10.1007/s00362-006-0315-x.

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23

Maritz, J. S. "A PERMUTATION PAIRED TEST ALLOWING FOR MISSING VALUES." Australian Journal of Statistics 37, no. 2 (June 1995): 153–59. http://dx.doi.org/10.1111/j.1467-842x.1995.tb00649.x.

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24

Kang, Seung-Ho, Hyung W. Kim, and Chul W. Ahn. "A Permutation Test for Nonindependent Matched Pair Data." Drug Information Journal 35, no. 2 (April 2001): 407–11. http://dx.doi.org/10.1177/009286150103500209.

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25

Bero, Daniel, and Melissa Bingham. "A permutation test for three-dimensional rotation data." Involve, a Journal of Mathematics 8, no. 5 (September 28, 2015): 735–44. http://dx.doi.org/10.2140/involve.2015.8.735.

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26

Ganong, Peter, and Simon Jäger. "A Permutation Test for the Regression Kink Design." Journal of the American Statistical Association 113, no. 522 (April 3, 2018): 494–504. http://dx.doi.org/10.1080/01621459.2017.1328356.

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27

Yamada, Tomoya, and Takakazu Sugiyama. "On the permutation test in canonical correlation analysis." Computational Statistics & Data Analysis 50, no. 8 (April 2006): 2111–23. http://dx.doi.org/10.1016/j.csda.2005.03.006.

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28

Klebanov, L., A. Gordon, Y. Xiao, H. Land, and A. Yakovlev. "A permutation test motivated by microarray data analysis." Computational Statistics & Data Analysis 50, no. 12 (August 2006): 3619–28. http://dx.doi.org/10.1016/j.csda.2005.08.005.

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29

Huang, Hsiao-Yuan, Jui-Hsiang Lin, and Wen-Chung Lee. "A Permutation Test for Oligoset DNA Pooling Studies." PLOS ONE 10, no. 3 (March 12, 2015): e0119096. http://dx.doi.org/10.1371/journal.pone.0119096.

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30

Matilla-García, Mariano, and Manuel Ruiz Marín. "A non-parametric independence test using permutation entropy." Journal of Econometrics 144, no. 1 (May 2008): 139–55. http://dx.doi.org/10.1016/j.jeconom.2007.12.005.

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31

Stedman, Margaret R., David R. Gagnon, Robert A. Lew, Daniel H. Solomon, Elena Losina, and M. Alan Brookhart. "A SAS macro for a clustered permutation test." Computer Methods and Programs in Biomedicine 95, no. 1 (July 2009): 89–94. http://dx.doi.org/10.1016/j.cmpb.2009.02.005.

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32

Li, Shanshan. "A Permutation Test for High-Dimensional Covariance Matrix." Journal of Physics: Conference Series 1865, no. 4 (April 1, 2021): 042027. http://dx.doi.org/10.1088/1742-6596/1865/4/042027.

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33

Graves, Thomas S., and James L. Pazdan. "A permutation test analogue to tarone’s test for trend in survival analysis." Journal of Statistical Computation and Simulation 53, no. 1-2 (October 1995): 79–89. http://dx.doi.org/10.1080/00949659508811697.

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34

Swofford, David L., Jeffrey L. Thorne, Joseph Felsenstein, and Brian M. Wiegmann. "The Topology-Dependent Permutation Test for Monophyly Does Not Test for Monophyly." Systematic Biology 45, no. 4 (December 1, 1996): 575–79. http://dx.doi.org/10.1093/sysbio/45.4.575.

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35

Mielke, Paul W., and Kenneth J. Berry. "Two-Sample Multivariate Similarity Permutation Comparison." Psychological Reports 100, no. 1 (February 2007): 257–62. http://dx.doi.org/10.2466/pr0.100.1.257-262.

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A multivariate permutation test of similarity between two populations with corresponding unordered disjoint categories is described. The test statistic, resampling probability value, and measure of effect size are described.

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36

G, Dhanya, and J. Jayakumari. "Speech Scrambling Based on Chaotic Mapping and Random Permutation for Modern Mobile Communication Systems." APTIKOM Journal on Computer Science and Information Technologies 2, no. 1 (March 1, 2017): 20–25. http://dx.doi.org/10.11591/aptikom.j.csit.95.

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The expanding significance of securing data over the network has promoted growth of strong encryption algorithms. To enhance the information protection in network communications, this paper presents a Random permutation, chaotic mapping and pseudo random binary scrambling. It involves transforming the intelligible speech signal into an unintelligible form to protect it from interrupters. In this report, suggest a simple and secure procedure to secure the speech signal. The speech scrambling process makes use of two Permutations. In the first step, Random permutation algorithm is used to swap the rows of the original speech followed by swapping of rows using chaotic Bernoulli mapping. This produces an intermediary scrambled speech. In the second measure, pseudo random binary generator is used to make the final scrambled signal. Various analysis tests are then executed to determine the quality of the encrypted image. The test results determine the efficiency of the proposed speech scrambling process.

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37

Venkatraman, E. S. "A Permutation Test to Compare Receiver Operating Characteristic Curves." Biometrics 56, no. 4 (December 2000): 1134–38. http://dx.doi.org/10.1111/j.0006-341x.2000.01134.x.

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38

Cánovas, J. S., A. Guillamón, and S. Vera. "Testing for independence: Permutation based tests vs. BDS test." European Physical Journal Special Topics 222, no. 2 (June 2013): 275–84. http://dx.doi.org/10.1140/epjst/e2013-01841-0.

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39

Samonenko, Inga, and John Robinson. "A new permutation test statistic for complete block designs." Annals of Statistics 43, no. 1 (February 2015): 90–101. http://dx.doi.org/10.1214/14-aos1266.

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40

Finch, W. Holmes, and Heather Jeffers. "A Q3-Based Permutation Test for Assessing Local Independence." Applied Psychological Measurement 40, no. 2 (December 29, 2015): 157–60. http://dx.doi.org/10.1177/0146621615622635.

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41

Park, Hyo-Il, and Seung-Man Hong. "A permutation test for multivariate data with grouped components." Journal of Applied Statistics 37, no. 5 (March 24, 2010): 767–78. http://dx.doi.org/10.1080/02664760902889973.

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42

Kovács, Balázs. "A Monte Carlo permutation test for co-occurrence data." Quality & Quantity 48, no. 2 (December 19, 2012): 955–60. http://dx.doi.org/10.1007/s11135-012-9817-x.

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43

Hutson, Alan D., and Han Yu. "A robust permutation test for the concordance correlation coefficient." Pharmaceutical Statistics 20, no. 4 (February 17, 2021): 696–709. http://dx.doi.org/10.1002/pst.2101.

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44

Neuhäuser, Markus, and Bryan F. J. Manly. "The Fisher-Pitman Permutation Test When Testing for Differences in Mean and Variance." Psychological Reports 94, no. 1 (February 2004): 189–94. http://dx.doi.org/10.2466/pr0.94.1.189-194.

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The Fisher-Pitman permutation test can detect any type of difference between two samples; hence, a significant Fisher-Pitman permutation test does not necessarily provide evidence for a difference in means. It is possible, however, to test separately for differences in means and variances. Here, we present a recently proposed two-stage procedure to decide whether there are differences in means or variances that can be applied when samples may come from nonnormal distributions with possibly unequal variances.

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45

Kończak, Grzegorz. "A Multivariate Extension of McNemar’s Test Based on Permutations." Acta Universitatis Lodziensis. Folia Oeconomica 4, no. 349 (November 4, 2020): 93–105. http://dx.doi.org/10.18778/0208-6018.349.06.

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The purpose of this publication is to propose a permutation test to detect the departure from symmetry in multidimensional contingency tables. The proposal is a multivariate extension of McNemar’s test. McNemar’s test could be applied to 2 × 2 contingency tables. The proposal may be also treated as a modification of Cochran’s Q test which is used for testing dependency for multivariate binary data. The form of the test statistics that allows us to detect the departure from counts symmetry in multidimensional contingency tables is presented in the article. The permutation method of observations was used to estimate the empirical distribution of the test statistics. The considerations were supplemented with examples of the use of a multivariate test for simulated and real data. The application of the proposed test allows us to detect the asymmetrical distribution of counts in multivariate contingency tables.

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46

Jackson, Donald A., and Keith M. Somers. "Are probability estimates from the permutation model of Mantel's test stable?" Canadian Journal of Zoology 67, no. 3 (March 1, 1989): 766–69. http://dx.doi.org/10.1139/z89-108.

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Matrix comparison tests (i.e., Mantel's test or quadratic assignment) are employed with increasing frequency to measure the concordance between genetic, behavioural, morphological, ecological, and geographic distances. Such tests compare an observed measure of matrix association with a null distribution derived from a randomly generated subset of all possible permutations of one of the original matrices. Typically, 500–2000 randomly permutated matrices are used to generate the statistical distribution and thereby estimate the probability of obtaining an observed association between two matrices. We demonstrate that a considerable error (i.e., 5–6%) may be associated with probability estimates based on such low numbers of permutations. To ensure the stability of the probability estimates (i.e., increase the reliability of the test), we recommend the use of a minimum of 10 000 permutations, and 100 000 permutations if the observed probability approaches a critical significance value (e.g., 0.05).

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47

Abdulsadah, Ammar Khaleel, Abdullah Aziz Lafta, and Mohammad Dosh. "A multi-levels RNG permutation." Indonesian Journal of Electrical Engineering and Computer Science 18, no. 1 (April 1, 2020): 412. http://dx.doi.org/10.11591/ijeecs.v18.i1.pp412-419.

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<p><span>The paper proposes a new general method for producing a multilevel permutation functioning as an m-tree traversal. It is composed of two basic steps: a random number generator of period length equal m to determine which child to traverse, and recursive permutation in which permutated the subtree if found. The test results proved that the suggested method of permutation is successful depending on the correlation measure.</span></p>

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48

Che, Xiaohong, and Shizhong Xu. "Significance Test and Genome Selection in Bayesian Shrinkage Analysis." International Journal of Plant Genomics 2010 (June 10, 2010): 1–11. http://dx.doi.org/10.1155/2010/893206.

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Bayesian shrinkage analysis is the state-of-the-art method for whole genome analysis of quantitative traits. It can estimate the genetic effects for the entire genome using a dense marker map. The technique is now called genome selection. A nice property of the shrinkage analysis is that it can estimate effects of QTL as small as explaining 2% of the phenotypic variance in a typical sample size of 300–500 individuals. In most cases, QTL can be detected with simple visual inspection of the entire genome for the effect because the false positive rate is low. As a Bayesian method, no significance test is needed. However, it is still desirable to put some confidences on the estimated QTL effects. We proposed to use the permutation test to draw empirical thresholds to declare significance of QTL under a predetermined genome wide type I error. With the permutation test, Bayesian shrinkage analysis can be routinely used for QTL detection.

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Hayasaka, Satoru, and Thomas E. Nichols. "Combining voxel intensity and cluster extent with permutation test framework." NeuroImage 23, no. 1 (September 2004): 54–63. http://dx.doi.org/10.1016/j.neuroimage.2004.04.035.

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Cooperman, Gene, and Larry Finkelstein. "A strong generating test and short presentations for permutation groups." Journal of Symbolic Computation 12, no. 4-5 (October 1991): 475–97. http://dx.doi.org/10.1016/s0747-7171(08)80099-5.

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