Monte Carlo ensemble correlation coefficient for association detection

2020 ◽  
pp. 1-15
Author(s):  
Wejdan Deebani ◽  
Nezamoddin N. Kachouie
Keyword(s):  
Monte Carlo ◽  
Correlation Coefficient ◽  
Ensemble Correlation

A Monte Carlo Evaluation of the Tetrachoric Correlation Coefficient

2003 ◽  
Vol 63 (6) ◽  
pp. 931-950 ◽  
Author(s):  
Tammy Greer ◽  
William P. Dunlap ◽  
Gregory O. Beatty
Keyword(s):  
Monte Carlo ◽  
Correlation Coefficient ◽  
Tetrachoric Correlation ◽  
Monte Carlo Evaluation

A Monte Carlo Investigation of the Fisher Z Transformation for Normal and Nonnormal Distributions

2000 ◽  
Vol 87 (3_suppl) ◽  
pp. 1101-1114 ◽  
Author(s):  
Kenneth J. Berry ◽  
Paul W. Mielke
Keyword(s):  
Monte Carlo ◽  
Correlation Coefficient ◽  
Bivariate Normal Distribution ◽  
Small Samples ◽  
Bivariate Distributions ◽  
Nonnormal Distributions ◽  
Monte Carlo Investigation ◽  
Sample Correlation ◽  
Heavy Tailed ◽  
Z Transformation

The Fisher transformation of the sample correlation coefficient r (1915, 1921) and two related techniques by Gayen (1951) and Jeyaratnam (1992) are examined for robustness to nonnormality. Monte Carlo analyses compare combinations of sample sizes and population parameters for seven bivariate distributions. The Fisher, Gayen, and Jeyaratnam approaches are shown to provide useful results for a bivariate normal distribution with any population correlation coefficient ρ and for nonnormal bivariate distributions when ρ = 0. In contrast, the techniques are virtually useless for nonnormal bivariate distributions when ρ#0.0. Surprisingly, small samples are found to provide better estimates than large samples for skewed and symmetric heavy-tailed bivariate distributions.

Robustness of the Pearson Correlation against Violations of Assumptions

1976 ◽  
Vol 43 (3_suppl) ◽  
pp. 1319-1334 ◽  
Author(s):  
Larry L. Havlicek ◽  
Nancy L. Peterson
Keyword(s):  
Monte Carlo ◽  
Correlation Coefficient ◽  
Pearson Correlation ◽  
Measurement Scale ◽  
Measurement Scales ◽  
Pearson Product Moment Correlation ◽  
Basic Assumptions ◽  
Violation Of Assumptions ◽  
Scale Failure

The purpose of this study was to determine empirically effects of the violation of assumptions of normality and of measurement scales on the Pearson product-moment correlation coefficient. The effects of such violations were studied separately and in combination for samples of varying size from 5 to 60. Monte Carlo procedures were used to generate populations of scores for four basic distributions: normal, positively skewed, negatively skewed, and leptokurtic. Samples of varying sizes were then randomly selected from specific populations. Results of the study were based on distributions of rs which were calculated on 5,000 sets of samples of n = 5 or n = 15 and 3,000 sets of samples of n = 30 and n = 60. Results indicated that the Pearson r is insensitive to rather extreme violations of the basic assumptions of normality and type of measurement scale. Failure to meet the basic assumptions separately or in combinations had little effect upon the obtained distributions of rs.

Influence Research of Correlation of Random Variables on Structural Reliability

2011 ◽  
Vol 243-249 ◽  
pp. 245-250
Author(s):  
Yan Feng Fang ◽  
Li Yan Chen ◽  
Hua Xi Gao
Keyword(s):  
Monte Carlo ◽  
Correlation Coefficient ◽  
Structural Reliability ◽  
Limit State ◽  
Random Variables ◽  
State Equation ◽  
Maximum Intensity ◽  
State Function ◽  
Sampling Techniques ◽  
Limit State Function

In this paper, the influence of correlation of variables on structural reliability is discussed. Using importance, condition and duality sampling techniques of Monte Carlo method, accepted accuracy can be obtained. For the limit state function, the correlation of random variables will influence structural reliability, and the influence can be described. For the case of positive correlation, reliability will increase as the the correlation coefficient raise. For the case of negative correlation, reliability will drop as the correlation coefficient raise. The level of influence depends on the slope of limit state equation in standardized coordinate. When k=1, the influence attains maximum intensity for both cases.

scholarly journals Efficient use of Monte Carlo: the fast correlation coefficient

2018 ◽  
Vol 4 ◽  
pp. 15 ◽  
Author(s):  
Henrik Sjöstrand ◽  
Nicola Asquith ◽  
Petter Helgesson ◽  
Dimitri Rochman ◽  
Steven van der Marck
Keyword(s):  
Monte Carlo ◽  
Correlation Coefficient ◽  
Pearson Correlation ◽  
Uncertainty Propagation ◽  
Synthetic Data ◽  
Nuclear Data ◽  
Reactor Spectrum ◽  
Flux Reactor ◽  
Parameter Dependent ◽  
The Impact

Random sampling methods are used for nuclear data (ND) uncertainty propagation, often in combination with the use of Monte Carlo codes (e.g., MCNP). One example is the Total Monte Carlo (TMC) method. The standard way to visualize and interpret ND covariances is by the use of the Pearson correlation coefficient, [see formula in PDF] where x or y can be any parameter dependent on ND. The spread in the output, σ, has both an ND component, σND, and a statistical component, σstat. The contribution from σstat decreases the value of ρ, and hence it underestimates the impact of the correlation. One way to address this is to minimize σstat by using longer simulation run-times. Alternatively, as proposed here, a so-called fast correlation coefficient is used, [see formula in PDF] In many cases, cov(xstat; ystat) can be assumed to be zero. The paper explores three examples, a synthetic data study, correlations in the NRG High Flux Reactor spectrum, and the correlations between integral criticality experiments. It is concluded that the use of ρ underestimates the correlation. The impact of the use of ρfast is quantified, and the implication of the results is discussed.

Determining the Significance of Correlations Corrected for Unreliability and Range Restriction

2003 ◽  
Vol 27 (1) ◽  
pp. 52-71 ◽  
Author(s):  
Nambury S. Raju ◽  
Paul A. Brand
Keyword(s):  
Monte Carlo ◽  
Correlation Coefficient ◽  
Statistical Power ◽  
Type I ◽  
Sampling Variance ◽  
Type I Errors ◽  
Range Restriction ◽  
Population Correlation ◽  
Variance Formula ◽  
New Formula

A new asymptotic formula for estimating the sampling variance of a correlation coefficient corrected for unreliability and range restriction was proposed. A Monte Carlo assessment of the new sampling variance formula has resulted in the following conclusions. First, the formula-based (analytical) sampling variances were very close to the empirically derived sampling variances based on 5,000 replications. Second, the sampling variance formula was quite robust against committing Type I errors. Third, the statistical power was low to moderate in distinguishing between two unattenuated and unrestricted population correlations. Fourth, the new formula produced smaller sampling variances; was closer to nominal alpha levels; and was more powerful when sample size increased, when the population correlation coefficient increased, when range restriction was less severe, and when both the criterion and predictor reliabilities increased.

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