= Overview =

OpenTURNS is able to perform a complete probabilistic study:
 * The first step consists in identifying the numerical model through which one wants to propagate uncertainties, and to define the decision criteria
 * The second step consists in quantifying uncertainty sources : OpenTURNS provides tools that can analyze data samples in order to chose the best uncertainty source modeling ;
 * The third step of a study allows to propagate the uncertainty in the numerical model ;
 * The fourth step of a study gives the possibility to analyze the importance of each parameter (ranking uncertainty sources, sensitivity analysis).

All the OpenTURNS' features (of version 0.12.0) for each step are listed below:

= First step: Quantifying uncertainty sources  =

 * Definition of the numerical model :
   - Link with external numerical simulation process (wrapper)
   - Analytical formulas
   - Python functions
   - Meta-model by Taylor Extension
   - Meta-model by Least Square method
 * Scalar failure criteria

= Second step: Quantifying uncertainty sources  =

 * Empirical cumulative distribution function
 * Density by Kernel Smoothing (General Kernel Product)
 * Composed distribution (1D marginals and copula)
 * Composed copula (copulas linked by the Independent Copula)
 * Standard parametric models:
  - Normal
  - Gumbel
  - Logistic
  - Student
  - Exponential
  - Weibull 
  - Gamma
  - Lognormal
  - Truncated Normal
  - Triangular distribution
  - Uniform
  - Beta
  - Geometric
  - Poisson
  - Multi-normal
  - Non-central Student
  - Epanechnikov
 * Independent Copula
 * Normal Copula
 * Clayton copula
 * Franck copula
 * Gumbel Copula
 * Using QQ-plot to compare two samples
 * Smirnov's test
 * Maximum Likehood Method
 * Graphical goodness-of-fit analysis
 * Chi-squared goodness-of-fit test
 * Kolmogorov Smirnov goodness-of-fit test
 * Cramer-Von Mises goodness-of-fit analysis
 * Anderson-Darling goodness-of-fit analysis
 * Bayesian Information Criterion
 * Pearson Correlation Coefficient
 * Pearson's correlation test
 * Spearman Correlation Coefficient
 * Spearman's correlation test
 * Chi-squared test for independence
 * Linear regression


= Third step: Uncertainty propagation =

 * Min-Max Approach using Design of Experiments
 * Deterministic Min-Max using TNC (Truncated Newton Constrained) algorithm
 * Quadratic Combination / Perturbation Method
 * Estimating the mean and variance using the MC Method
 * Iso-Probabilistic transformation preliminary to FORM-SORM methods
 * FORM
 * SORM
 * Optimization algorithms :
  - Cobyla
  - AbdoRackwitz
  - SQP
 * Calculation of Reliability index :
  - Hasofer reliability index
  - Generalized reliability index
  - Generalized Breitung reliability index
  - Generalized HohenBichler reliability index
  - Generalized Tvedt reliability index
 * Design point validation : Strong Maximum Test
 * Estimating the probability of an event :
  - Monte Carlo Sampling
  - Importance Sampling
  - Directional Simulation
  - Latin Hypercube Sampling
  - Controlled Importance Sampling in standard space
 * Estimating a quantile by Sampling / Wilk's Method

= Fourth step: Ranking uncertainty sources / sensitivity analysis =

 * Importance Factors derived from Quadratic Combination Method
 * Uncertainty ranking using Pearson's correlation
 * Uncertainty ranking using Spearman's correlation
 * Uncertainty ranking using Standard Regression Coefficients
 * Uncertainty ranking using Pearson's partial correlation coefficients
 * Uncertainty ranking using Partial Rank correlation coefficients
 * Importance Factors derived from FORM / SORM methods
 * Sensitivity Factors from FORM method