Data analysis

This part gives an overview of the content of the statistical toolbox that may be used to build uncertainty models according to the available data.

Comparison of two samples

• QQ-plot
• Two-sample Kolmogorov-Smirnov test

Estimation of a nonparametric model

• Empirical cumulative distribution function
• Kernel smoothing

Estimation of a parametric model

• Maximum Likelihood Principle
• Parametric Estimation

Calibration

• Bayesian calibration
• Code calibration
• Gaussian calibration
• The Metropolis-Hastings Algorithm

Analysis of the goodness of fit of a parametric model

• Graphical goodness-of-fit tests
• Chi-squared test
• The Kolmogorov-Smirnov goodness of fit test for continuous data
• Cramer-Von Mises test
• Anderson-Darling test
• Akaike Information Criterion (AIC)
• Bayesian Information Criterion (BIC)

Detection and quantification of dependencies

• Pearson correlation coefficient
• Pearson’s correlation test
• Spearman correlation coefficient
• Spearman correlation test
• Chi-squared test for independence
• Tail dependence coefficients

Regression

• Linear regression
• Regression analysis

Estimating a quantile

• Estimation of a quantile upper bound by Wilks’ method